### Venue

Nordita, Stockholm, Sweden

### Dates

August 24th to September 11th, 2015.

### Scope

A major direction of research in contemporary condensed matter physics is the effort to design materials with specific functionality by utilizing the unique properties of interfaces between materials of different types. The prospect of using the interface between two-dimensional layers at the nanoscale provides many potential avenues for tailoring materials. In the last few years we have seen rapid expansion in the field of artificial two-dimensional structures that possess many interesting and useful properties. Combining layers of these atomically thin crystals with, for example, superconducting or ferromagnetic layers opens a huge new number of possible configurations not available in bulk crystals, with the potential for engineering precise device characteristics. In this program, we bring together experimentalists and theorists to review the current status of this burgeoning field, identify the crucial areas where progress can be made, and foster collaborations and partnerships to vigorously pursue these goals.

### Format

The program will be arranged so that there will be a talks focusing on both the general directions of the field and the specific interests of the program participants. There will also be plenty of time set aside for informal discussions and collaborations since we hope that the program will be a venue where new connections can be made and real scientific progress can be achieved.

### Application

Registration is now closed.

### Participant photo

### Tentative schedule

Please note that this is not the final version of the schedule, and changes may be made.

Talks will be one hour each, including questions, so speakers should plan roughly 50 minutes of material.

All talks will take place in the seminar room of the **Nordita South** building, Roslagstullsbacken 11.

##### Week 1:

Mon 24th | Tues 25th | Weds 26th | Thurs 27th | Fri 28th | |

10:00 | Welcome/Intro | Rossi | Korovushkin | Ardonne | |

11:00 | Balatsky | Volovik | |||

13:30 | Horsdal | Fukuyama | Asgari | ||

14:30 | Abergel | ||||

Evening | Hawking lecture | BBQ/Posters | BBQ |

##### Week 2:

Mon 31st | Tues 1st | Weds 2nd | Thurs 3rd | Fri 4th | |

10:00 | Welcome/Intro | Kagawa | Pikulin | Hofmann | Ojanen |

11:00 | Simon | Yoshimi | |||

13:30 | Eschrig | Ortiz | Bonderson | Slingerland | Mandal |

14:30 | Nikolić | Heikkilä | Bernevig | Manna | |

Evening | BBQ/Posters | Program dinner |

##### Week 3:

Mon 7th | Tues 8th | Weds 9th | Thurs 10th | Fri 11th | |

10:00 | Welcome/Intro | Wehling | Ishikawa | Saito | |

11:00 | Kreisel | Babaev | |||

13:30 | Silaev | Plumb | Liu | Sochnikov | |

14:30 | Saunders | Chandrasekhar | Chung | Yao | |

15:30 | STO discussion | ||||

16:00 | Saxena talk (AlbaNova) | ||||

Evening | BBQ/Posters |

### Talk titles and abstracts

**David Abergel:** *Two-dimensional heterostructures.*

A major new avenue in research in two-dimensional materials is to combine different types of atomically thin lattices, either in stacks (called vertical heterostructures) or in a single monolayer plane (lateral heterostructures). In this talk, we first discuss the topological aspects related to 1D interfaces in 2D materials, showing that inversion of the Dirac mass will lead to topologically protected interface modes which may carry persistent spin and valley current [1], and that graphene nanoribbons encased in boron nitride will function as nano-scale wires with transport properties which are incredibly robust against lattice disorder. Then, we shall show how infra-red optical spectroscopy may be used as a tool to diagnose the inter-layer van der Waals interaction between graphene and hexagonal boron nitride. We find that careful examination of the optical spectrum as a function of the electronic density may distinguish between various competing theoretical descriptions of the inter-layer interactions [2].

[1] D. S. L. Abergel, J. Edge, and A. V. Balatsky, New J. Phys. 16, 065012 (2014).

[2] M. Mucha-Kruczynski, D. S. L. Abergel, arXiv:1507.03813.

**Eddy Ardonne:** *Topological phase transitions applied to generalized cluster models.*

We consider phase transitions between two-dimensional topological phases, that can be understood in terms of the condensation of a bosonic excitation. It turns out that the same underlying principle can be used to study the relation between different one-dimensional critical systems. By utilizing this connection, we study the critical behaviour of generalized cluster models, that have been studied in the context of quantum information theory.

**Reza Asgari:** *Electronic cooling in multilayer epitaxial graphene.*

Optical excitations generate a non-equilibrium distribution of carriers and optical spectroscopy provides the best process of determining such distribution functions. The purpose of ultrafast spectroscopy is to explore the carrier relaxation dynamics and transport dynamics after ultra-short pulse excitation. The rise time of non-degenerate electron distribution creation is in the order of a few fs therefore, we may say that high temperature non-equilibrium electron distribution has the same rise time as the laser pulse duration. Then over a time scale of a few fs, the non-equilibrium electrons redistribute their energy among themselves. Generally, it takes place through electron-electron, electron-phonon and electron-impurity interactions.
Coupling between layers is often extremely important for the electronic and opto-electronic properties of multilayer van der Waals systems, including multilayer graphene structures. Because the coupling between phonon modes localized in different layers is exceptionally weak in these materials, unconventional effects can become important.

In this talk, I will present a theoretical study of a unique electronic cooling pathway observed in multilayer epitaxial graphene systems [1]. We demonstrate that under many circumstances direct action-at-a-distance Coulomb scattering can lead to important heat transport between remote layers, bypassing the lattice, and in particular that this can be the dominant electron-cooling mechanism in the important case of multilayer epitaxial graphene devices. Basically, we compute the cooling powers of both acoustic phonon cooling and disorder-assisted electron-phonon cooling of a multilayer graphene and it turns out that interlayer Columbic energy transfer can dominate for a wide range of electron temperature and sample characteristics. Our theory for calculating thermal equilibration times are free of any fitting parameters, compare closely with the experimental relaxation time.

[1] M.T. Mihnev, J.R. Tolsma, C.J. Divin, D. Sun, R. Asgari, M. Polini, C. Berger, W.A. de Heer, A.H. MacDonald, and T.B. Norris, To appear in Nature Communications (2015).

**Egor Babaev:** *Experimental evidence of Type‐1.5 superconductivity in Sr _{2}RuO_{4}.*

In general superconductors with several superconducting c possess several coherence lengths. This allows a regime where some coherence lengths are larger and some are smaller than the magnetic field penetration length. As a consequence of this hierarchy of the length scales the type of superconductivity is realized which breaks the type‐1/type‐2 dichotomy [1,2,3]. This is a state where type‐1 and type‐2 supercurrent patterns are not antagonistic but coexistent, in particular resulting in long‐range attractive, short‐range repulsive intervortex interaction. I will focus on the recent experimental evidence that this kind of superconductivity is realized in Sr

_{2}RuO

_{4}[4,5].

[1] Egor Babaev, J. Martin Speight Phys. Rev. B 72 (2005) 1805.

[2] E. Babaev, J. Carlstrom, J. Garaud, M. Silaev, J. M. Speight Physica C 479, 2‐14 (2012).

[3] M. Silaev, E. Babaev Phys. Rev. B 84 (9), 094515 (2011).

[4] J. Carlström, E Babaev, M Speight Physical Review B 83 (17), 174509 (2011).

[5] S. J. Ray, A. S. Gibbs, S. J. Bending, P. J. Curran, Egor Babaev, C Baines, A. P. Mackenzie, and S. L. Lee, Phys. Rev. B 89, 094504

**Alexander Balatsky:** *Superconductivity in STO and STO derived interfaces.*

**Andrei Bernevig:** TBA

**Parsa Bonderson:** *Symmetry, Defects, and Gauging of Topological Phases.*

We examine the interplay of symmetry and topological order in 2+1 dimensional topological phases of matter. We describe how the global symmetries of the microscopic system act on the emergent topological degrees of freedom. A general framework is provided to classify symmetry fractionalization in topological phases, including phases that are non-Abelian and symmetries that permute the quasiparticle types and/or are anti-unitary. We develop a theory of extrinsic defects (fluxes) associated with elements of the symmetry group. This provides a general classification of symmetry-enriched topological phases derived from a topological phase of matter with unitary on-site symmetry. The algebraic theory of the defects, known as a G-crossed braided tensor category, allows one to compute many properties, such as the number of topologically distinct types of defects associated with each group element, their fusion rules, quantum dimensions, zero modes, braiding exchange transformations, a generalized Verlinde formula for the defects, and modular transformations of the G-crossed extensions of topological phases. We also examine the promotion of the global symmetry to a local gauge invariance, wherein the extrinsic G-defects are turned into deconfined quasiparticle excitations, which results in a different topological phase.

**Venkat Chandraseskhar:** *Superconductivity and Magnetism at the (001) and (111) LAO/STO interfaces.*

The conducting gas that forms at the interface between the two insulating oxides LaAlO_{3} (LAO) and SrTiO_{3} (STO) shows a rich variety of behavior, including an electric-field dependent conductivity, superconductivity, gate-controlled superconductor-to-insulator transition, and ferromagnetism. In the first part of this talk, I will review our experiments on (001) LAO/STO, where we showed for the first time the coexistence of superconductivity and ferromagnetism, which manifests itself as a superconducting phase diagram that is hysteretic in the applied magnetic field. This coexistence of ferromagnetism and superconductivity enables a novel demonstration of the concept of charge-vortex duality in the superconductor-to-insulator transition, which shows up as a magnetic field sweep-rate dependence of the magnetoresistance in the superconducting and insulating regimes. In the second part of the talk, I will discuss experiments on gate-tunable Josephson junctions in these systems, as well as more recent work on the (111) LAO/STO interface, which also shows the coexistence of superconductivity and magnetism with an unusually strong gate-voltage dependence.

[1] Dikin, D. A., Mehta, M., Bark, C. W., Folkman, C. M., Eom, C. B. and Chandrasekhar, V. Phys. Rev. Lett 107, 056802 (2011).

[2] Mehta, M., Dikin, D. A., Bark, C. W., Ryu S., Folkman, C. M., Eom, C. B. and Chandrasekhar, V. Nature Comm. 3, 955 (2012).

[3] M. M. Mehta, D.A. Dikin, C.W. Bark, S. Ryu, C.M. Folkman, C.B. Eom and V. Chandrasekhar, Phys. Rev. B 90, 100506(R) (Rapid Communications) (2014).

**Suk Bum Chung:** *Symmetry and Collective Modes in the Sr _{2}RuO_{4} Superconductor.*

As collective modes in a condensed matter system is intimately related to its symmetry, its detection has been instrumental in identifying the intricate symmetry breaking in spin-triplet condensate, the classic example being the identification of the A and B phases of the

^{3}He superfluid. Therefore calculating the collective modes is a natural step in investigating the Sr

_{2}RuO

_{4}superconductor, widely believed to be an electronic analogue of

^{3}He -A as both have the chiral p-wave Cooper pairing. However, in comparing the collective modes of the two systems, one needs to take into account that while the latter has the continuous rotational symmetry, the former only has a fourfold rotational symmetry around the c-axis. Two strongest manifestation of this lower symmetry of the Sr

_{2}RuO

_{4}superconductor are the presence of the quasi-1D band at the Fermi level [1] and the strong anisotropy of the pairing gap [1,2]. Strikingly, low-energy collective modes emerge from both manifestations of the breakdown of continuous rotational symmetry.

[1] S B Chung, S Raghu, A Kapitulnik, and S A Kivelson, Phys Rev B 86 (2012) 064525.

[2] J A Sauls, H Wu, and S B Chung, Front Phys 3:36 (2015).

**Matthias Eschrig:** *Superconductivity in the vicinity of spin-active interfaces in strongly spin-polarized ferromagnets.*

The field of superconducting spintronics, or "superspintronics", which emerged during the past 15 years, combines the phenomena of quantum coherence and interference with the phenomena of spin-selectivity and spin magnetism. The building blocks are spin-triplet Cooper pairs, which are generated at the interface between a superconducting and a ferromagnetic material. Non-collinear magnetic inhomogeneity creates long-ranged equal-spin Cooper pairs in the ferromagnet, and non-coplanar inhomogeneity introduces geometric phases giving rise to unusual current phase relations and to spin currents.

We discuss various results in the light of Andreev scattering at spin-polarized interfaces and discuss challenges which hybrid structures with strongly spin-polarized parts pose for realistic theoretical models. Our goal is to provide an appropriate framework for studying hybrid structures that involve strongly spin-polarized ferromagnets like, e.g., iron, cobalt, nickel, CrO_{2}, Heusler alloys, EuO, EuS, or Y_{3}Fe_{5}O_{12}.

**Hiroshi Fukuyama:** *Quantum Phenomena in Monolayers of Helium on Graphite.*

Atomic monolayers of helium (He) adsorbed by the van der Waals force on a graphite surface provide a unique arena to investigate novel quantum phenomena of fermions (^{3}He: nuclear spin 1/2) and bosons (^{4}He: spinless) in two dimensions (2D). As a function of areal density of He in a vast range, this simple system shows a variety of quantum phases below 1 K ranging classical gas, quantum liquid, hypothetical quantum liquid crystal (QLC) and quantum solid. The QLC [1] is a quantum counterpart of classical liquid crystal of molecules. The electronic nematic phase discussed in other layered materials or heterostructures is considered to be one of QLCs.

In this talk, I will discuss the following four topics:

(1) We found a new quantum spin liquid state in the QLC phase of ^{3}He monolayer adsorbed on a graphite surface preplated with a bilayer of HD molecules (^{3}He/HD/HD/gr) below 10 mK. Measured specific heat (C) and magnetic susceptibility (chi) follow peculiar T-dependencies with fractional powers of 2/3 for C and -1/3 for chi down to 0.3 mK or even lower-T. They are indicative of an exotic elementary excitation such as spinon caused by fermion fractionalization (or spin-mass separation) in 2D.

(2) We have now several circumstantial evidences for the supersolid ground state in the QLC phase of ^{4}He bilayer (^{4}He/^{4}He/gr) below 1 K. They are superfluid responses in torsional oscillator experiments and an anomalous isotope effect on melting temperature [1].

(3) We found theoretically unexpected liquefaction of ^{3}He in 2D [2]. The apparent disagreement with existing ab initio calculations is a serious puzzle. We point out the possible importance of indirect attractive interactions among ^{3}He atoms which have not been taken into account in the previous calculations.

(4) Theories predict a p-wave superfluid phase at low densities and a d-wave one at high densities in monolayer liquid ^{3}He. Potentially this system will give us an unparalleled opportunity to study an interchange of different types of Cooper pairs within a single material.

[1] S. Nakamura et al., arXiv:1406.4388v1.

[2] D. Sato et al., PRL 109, 235306 (2012).

**Tero Heikkilä:** *Dirac lines, flat bands and possible high-temperature interface superconductivity in graphite.*

In this talk I will summarize our recent work on the topological properties of multilayer graphene and graphite [1-7], including the assessment of the possible superconducting state in these structures. I will show how the topologically protected Dirac node of graphene evolves into a nodal Dirac line in graphite, and how the properties of this nodal line depends on the graphite stacking. Due to the nodal lines graphite surfaces and internal interfaces contain flat bands, i.e., states with a vanishing energy over a range of momenta. Such flat bands promote strong interaction effects and can for example lead to surface or interface superconductivity with a very high critical temperature. I will also show how, for the flat bands in topological semimetals containing Dirac lines, mean field theory fails and fluctuation effects dominate down to the lowest temperatures [8]. This means that in the presence of interactions such surface states of semimetals are strongly correlated. However, this statement is generic only for flat bands generated as interface states of topological semimetals, and there are other flat band models where mean field theory works well. Our theory may explain the recent (albeit controversial) experimental indications of very high-temperature superconductivity in graphite containing internal interfaces [9].

[1] Tero T. Heikkilä and G.E. Volovik, Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface, JETP Lett. 93, 59 (2011).

[2] Nikolai B. Kopnin, Tero T. Heikkilä, and G.E. Volovik, High-temperature surface superconductivity in topological flat-band systems, Phys Rev B 83, 220503(R) (2011).

[3] Tero T. Heikkilä, Nikolai B. Kopnin, and G.E. Volovik, Flat bands in topological media, JETP Lett. 94, 233 (2011).

[4] N.B. Kopnin, Mari Ijäs, Ari Harju and Tero T. Heikkilä, High-temperature surface superconductivity in rhombohedral graphite, Phys. Rev. B 87, 140503(R) (2013).

[5] N.B. Kopnin and Tero T. Heikkilä, Surface superconductivity in rhombohedral graphite, Ch. 9 in "Carbon-based new superconductors - towards high temperature superconductivity" (Edited by Junji Haruyama, Pan Stanford 2014) [arXiv:1210.7075].

[6] T.T. Heikkilä and G.E. Volovik, Flat bands as a route to high-temperature superconductivity in graphite, arXiv:1504.05824.

[7] T.T. Heikkilä and G.E. Volovik, Nexus and Dirac lines in topological materials, arXiv:1505.03277.

[8] V. Kauppila, T. Hyart, and T.T. Heikkilä, Collective amplitude mode fluctuations in a flat band superconductor, arXiv:1505.02670.

[9] P. Esquinazi, Graphite and its hidden superconductivity, Papers in Physics 5, 050007 (2013) (and the references therein).

**Philip Hofmann:** *Electronic Structure and electron Dynamics in Two-Dimensional Materials.*

Changing the dimensionality of a material results in significant modifications of its electronic properties. This is even the case if the parent material already has a layered structure with little interaction between the layers, as in the case of graphene, and the layered transition metal chalcogenides. This talk discusses the possibility to epitaxially grow high-quality two-dimensional materials on single crystal surface, such that they can be used for electronic structure investigations by time- and angle-resolved photoemission spectroscopy. Results of such studies are presented for graphene, bilayer graphene and single-layer MoS_{2}.

**Mats Horsdal:** *Enhancing Triplet Superconductivity by the Proximity to a Singlet Superconductor in Oxide Heterostructures.*

We show how, in principle, a coherent coupling between two superconductors of opposite parity can be realised in a three-layer oxide heterostructure [1]. Due to strong intraionic spin-orbit coupling in the middle layer singlet Cooper pairs are converted into triplet ones, and vice versa. The result is a large enhancement of the triplet order parameter that persist well beyond the native triplet critical temperature.

[1] Horsdal et al., 2015 arXiv:1501.02077.

**Osamu Ishikawa:** *Novel Proximity Effect at Edge of Topological Superfluid 3He-B phase.*

Recently, topological superfluidity of liquid 3He attracts the attention of condensed matter physics since the richness of symmetry and well-known bulk properties. The theoretical model has been well established for understanding superfluid 3He as a spin triplet p-wave BCS type condensate. In topological materials a novel conservative quantity exists in bulk and there simultaneously appears a non-trivial edge state corresponding to the bulk conservative quantity. This is often called the bulk-edge correspondence. Such a topological conservative quantity is protected by symmetry of bulk material. The topological superfluid 3He-B phase has non-trivial edge state where the quasiparticles shows Majorana fermions with a linear dispersion relation protected by bulk symmetry. This edge state is also the Andreev bound state. The interesting issue is a proximity effect using aerogel in superfluid 3He because both the proximity effect and the Andreev bound state do not coexist for s-wave and d-wave superconducting states. Superfluidity of 3He is suppressed by local inhomogeneity of aerogel. So we can make the interface between superfluid 3He-B phase and normal liquid 3He inside aerogel or at the surface of it. The proximity effect by spin triplet Cooper pairs is expected to appear in normal liquid, which is very similar to a superconducting proximity effect appears in the normal metal contacting with the conventional s-wave BCS superconductors. However, theoretical argument shows that the Cooper pair amplitude with spin triplet, odd frequency and even parity appears as the proximity effect in aerogel, which shows the enhancement of magnetic susceptibility attributed to the Andreev bound state with Majorana fermions. Here we report experimental results of NMR on liquid 3 He and superfluid 3He-B phase in aerogel and discuss about the odd frequency Cooper pairs in normal liquid at the edge of superfluid 3He-B phase.

**Fumitaka Kagawa:** *Topological stability versus thermal agitation in a metastable magnetic skyrmion lattice.*

Topologically stable matters can have a long lifetime, even if thermodynamically costly, when the thermal agitation is sufficiently low. A magnetic skyrmion lattice (SkL) represents a unique form of long-range magnetic order that is topologically stable, and therefore, a long-lived, metastable SkL can form. Experimental observations of the SkL in bulk crystals, however, have mostly been limited to a finite and narrow temperature region in which the SkL is thermodynamically stable; thus, the benefits of the topological stability remain unclear. In this talk, I show a metastable SkL created by quenching a thermodynamically stable SkL. Hall-resistivity measurements of MnSi reveal that, although the metastable SkL is short-lived at high temperatures, the lifetime becomes prolonged (>>1 week) at low temperatures. The manipulation of a delicate balance between thermal agitation and the topological stability enables a deterministic creation/annihilation of the metastable SkL by exploiting electric heating and subsequent rapid cooling. Quenching effects on a quasi-two-dimensional charge-ordering material are also discussed.

**Maxim Korovushkin:** *The Kohn-Luttinger superconductivity in idealized monolayer and bilayer graphene.*

The effect of Coulomb interaction between Dirac fermions on the formation of the Kohn-Luttinger superconducting state in monolayer and bilayer doped graphene is studied disregarding of the effect of the Van der Waals potential of the substrate and impurities. The phase diagrams determining the boundaries of superconductive domains with different types of symmetry of the order parameter are constructed using the extended Hubbard model in the weak-coupling approximation with allowance for the intratomic, interatomic, and interlayer (in the case of bilayer graphene) Coulomb interactions between electrons. It is shown that the Kohn-Luttinger polarization contributions up to the second order of perturbation theory in the Coulomb interaction inclusively and an account for the long-range intraplane Coulomb interactions significantly affect the competition between the superconducting phases with the f-, p+ip-, and d+id-wave symmetries of the order parameter. It is demonstrated that the account for the interlayer Coulomb interaction enhances the critical temperature of the transition to the superconducting phase in idealized graphene bilayer.

**Andreas Kreisel:** TBA

**Ying Liu:** *Detection of chiral edge currents in spin-triplet superconductor Sr _{2}RuO_{4}.*

Experimental evidence suggesting that odd-parity, spin-triplet superconductor Sr

_{2}RuO

_{4}is a chiral p-wave superconductor featuring domain and domain walls as predicted by theory was obtained in µSR and Kerr rotation experiments. However, scanning SQUID and Hall probe detections for the presence of chiral edge currents revealed no evidence for the presence of these currents. In the past few years we have worked on the preparation and measurements on single-crystal ramp Josephson junctions between Sr

_{2}RuO

_{4}and a conventional s-wave superconductor for the detection of the chiral surface current using a combination of conventional and unconventional nanofabrication techniques. We detected a small, but non-zero edge chiral current by using a transport current to tune the magnetic flux threading the ramp junction. I will discuss the implications of this observation.

Work done in collaboration with Yiqun A. Ying, Xinxin Cai, Brian Zakrzewski, David Fobes, Tijiang Liu, and Zhiqiang Mao. Work done at Penn State is supported by DOE.

**Ipsita Mandal:** *UV/IR mixing in non-Fermi liquids.*

We devise a renormalization group analysis for quantum field theories with Fermi surface to study scaling behaviour of non-Fermi liquid states in a controlled approximation. The non-Fermi liquid fixed points are identified from a Fermi surface in (*m+1*) spatial dimensions, while the co-dimension of Fermi surface is also extended to a generic value. We also study superconducting instability in such systems as a function of dimension and co-dimension of the Fermi surface. The key point in this whole analysis is that unlike in relativistic QFT, the Fermi momentum *k _{F}* enters as a dimensionful parameter, thus modifying the naive scaling arguments. The effective coupling constants are found to be combinations of the original coupling constants and

*k*.

_{F}**Sujit Manna:** *Interfacial electronic and magnetic properties in Fe-chalcogenide thin films
studied by spin-polarized STM.*

The discovery of very high superconducting transition temperature above 100K in one unit cell FeSe/SrTiO_{3} has motivated an intense work on these materials worldwide, as described in several recent reports [1–2]. Like in many unconventional superconductors, in Fe-chalcogenides the superconductivity emerges from an antiferromagnetic parent compound. The strength of the antiferromagnetic exchange coupling in the magnetic state is, in some theoretical models, related to the Cooper pairing energy in the superconducting state [3]. Achieving a microscopic picture of the relation between these two properties is believed to be the key to a fundamental insight of the physics of unconventional superconductivity. In this talk, we report on the growth of two-dimensional Fe-chalcogenide based heterostructures, which showed unexpected electronic properties and magnetism as studied by spin polarized scanning tunneling microscopy/spectroscopy (SP-STM/STS).

[1] I. Bozovic et. al. Nature Phys. 10, 892 (2014).

[2] D. Huang et.al. Phys. Rev. Lett. 115, 017002(2015).

[3] J. Hu & H. Ding et.al. Sci. Rep. 2, 381(2012).

**Branislav Nikolić:** *What can Dirac-material/ferromagnet heterostructures do for spintronics?*

Topological insulators (TIs) are newly discovered class of Dirac materials which possess an energy gap in the bulk, akin to conventional band insulators, while hosting metallic surfaces where electrons behave as massless Dirac fermions analogous to the ones found in graphene. However, unlike graphene where spin-orbit coupling (SOC) is negligible due to the lightness of carbon atoms, in TIs it plays a crucial role by locking the direction of spin and momentum of surface electrons. This feature is considered to be a great resource for spintronic applications where combinations of TIs with ferromagnets (FM) could lead to ultralow-power memory and logic devices. On the other hand, graphene is envisaged as interconnect in lateral devices due to long spin diffusion lengths or perfect spin filtering barrier in vertical heterostructures where it is sandwiched by Co or Ni layers. In this talk, I will discuss possible routes of integration of graphene and TIs with FMs into vertical and lateral heterostructures exhibiting: (i) perfect spin filtering at finite bias voltage and spin-transfer torque driven by low injected current in Ni/few-layer-graphene/Ni and Co/few-layer-graphene/Co vertical heterostructures; (ii) current-driven SO torques by which TI surface induces magnetization dynamics of the FM layer; and (iii) spin-to-charge conversion after the magnetization of the FM overlayer on the surface of TI is brought into steady state precession by the microwave absorption.

[1] F. Mahfouzi, B. K. Nikolić, and N. Kioussis, “Large antidamping-like spin-orbit torque driven by spin-flip reflection mechanism on the surface of a topological insulator,” arXiv:1506.01303.

[2] P.-H. Chang, T. Markussen, S. Smidstrup, K. Stokbro, and Branislav K. Nikolić, “Nonequilibrium spin texture within a thin layer below the surface of current-carrying topological insulator Bi2Se3: A first-principles quantum transport study,” arXiv:1503.08046.

[3] F. Mahfouzi, N. Nagaosa, and B. K. Nikolić, “Spin-to-charge conversion in lateral and vertical topological-insulator/ferromagnet heterostructures with microwave-driven precessing magnetization,” Phys. Rev. B 90, 115432 (2014).

[4] K. K. Saha, A. Blom, K. S. Thygesen, and B. K. Nikolić, “Magnetoresistance and negative differential resistance in Ni/Graphene/Ni vertical heterostructures driven by finite bias voltage: A first-principles study,” Phys. Rev. B 85, 184426 (2012).

[5] F. Mahfouzi, N. Nagaosa, and B. K. Nikolić, “Spin-orbit coupling induced spin-transfer torque and current polarization in topological-insulator/ferromagnet vertical heterostructures,” Phys. Rev. Lett. 109, 166602 (2012).

[6] F. Mahfouzi, B. K. Nikolić, S.-H. Chen, and C.-R. Chang, “Microwave-driven ferromagnet–topological-insulator heterostructures: The prospect for giant spin battery effect and quantized charge pump devices,” Phys. Rev. B 82, 195440 (2010).

**Teemu Ojanen:** * Topological superconductivity and high Chern numbers in ferromagnetic Shiba lattices.*

Inspired by the recent experimental observation of topological superconductivity in ferromagnetic chains, we consider a dilute 1D and 2D lattices of magnetic atoms deposited on top of a superconducting surface with a Rashba spin-orbit coupling. We show that the studied systems supports a generalization of px +ipy superconductivity and that its topological phase diagram contains Chern numbers higher than ξ/a, where ξ is the superconducting coherence length and a is the distance between the magnetic atoms. The signatures of nontrivial topology can be observed by STM spectroscopy in finite-size islands.

**Gerardo Ortiz:** * What is a particle-conserving topological superconductor?*

What distinguishes trivial from topological superfluids in interacting many-body systems with a conserved number of particles? What is the meaning and fate of Majorana modes in fermionic superfluids? These are questions that require a concrete operational answer if one seriously considers using these physical systems for quantum information processing purposes.

Most of what we know about topological superfluids and Majorana excitations is based on a mean-field approximation, the Bogoliubov-de Gennes equation, that breaks particle number conservation and, by construction, displays a particle-hole symmetry and thus a zero mode structure. I will attempt to answer the questions above by introducing and analyzing the Richardson-Gaudin-Kitaev wire, an interacting number-conserving variation of the Kitaev model.

If time permits I will explain how a topological superconductor relates to a topological insulator in terms of duality transformations. These mathematical equivalences are relevant for the classification of interacting topological quantum matter.

**Dmitry Pikulin:** *Helical quantum Hall exciton condensate in quantum spin Hall bilayers.*

We study inverted electron-hole bilayers in perpendicular magnetic field. These systems, for example InAs/GaSb bilayers, host quantum spin Hall effect in zero field. We identify phases of these bilayers as a function of magnetic field or gating: uncorrelated bilayer with helical edge states, helical quantum Hall exciton condensate, and uncorrelated bilayer without edge states. We show that the helical quantum Hall exciton condensate hosts unusual confined fractionally charged excitations. We predict that this state generates ideal drag in a narrow system.

**Nicholas Plumb:** *Metallicity, Spin-Splitting, and Magnetism on an Oxide Surface.*

In recent years, transition metal oxide thin films and interfaces have been at the frontier of developing next-generation multifunctional devices. The hope – and challenge – is to wield the rich, complex, and often poorly understood behaviors emergent in oxide systems in order to achieve coupling and control over various phases such as superconductivity, colossal magnetoresistance, metal-insulator transitions, multiferroicity, and so on. SrTiO_{3} (STO) is a crucial player in this game, serving as the most common substrate for oxide film growth, and quite often being found to exhibit low-dimensional conductivity (and even sometimes magnetism or superconductivity) at various film interfaces. All of this is a bit surprising, since in bulk STO is a nonmagnetic insulator with a ~3 eV bandgap. Attempts to better understand such complex behaviors eventually led to the discovery that a metallic surface state can actually form atop bare STO. I will present some of the latest findings from this surface state using angle-resolved photoemission spectroscopy (ARPES). We have uncovered a number of remarkable properties of its electronic structure: a mixture of 2D and nonbulklike 3D carriers in the near-surface region inhabiting a unique form of spatio-orbital ordering; quite robust "universality" of the surface electron dispersion and carrier density; intriguing photosensitive behavior; and giant "Rashba-like" spin-splitting combined with an implicit magnetic order. In trying to reconcile these observations into a coherent picture, we are forced to conclude that subtle structural features of the surface region play an outsized role in dictating the electronic structure. The findings give insights into many related oxide surface and interface systems while illustrating the powerful phenomena that can arise when oxides play host to confined metallic states.

**Enrico Rossi:** *Two-dimensional heterostructures with spin-orbit coupling.*

In the past few years there has been an explosion in the number of novel two-dimensional (2D) materials that have been realized experimentally. Using these newly discovered 2D materials it is now possible to realize 2D systems with unique electronic properties. 2D systems in which one of the layers has strong spin-orbit coupling are of particular fundamental and technological interest. In the first part of the talk I will present our results [1] on the theoretical study of heterostructures formed by one sheet of graphene, or bilayer graphene, and a topological insulator. I will show how the twist angle between the graphene layer and the TI can be used to tune the electronic properties of such heterostructures and I will discuss their spin-dependent transport properties. In the second part of the talk I will present our recent results on the effects of spin-orbit coupling on the bound states induced by impurities on the surface of superconductors [2]. Due to the presence of spin-orbit coupling
impurity-induced bound states corresponding to different angular momentum channels hybridize and display a number of qualitatively different features from that of the well-known Yu-Shiba-Rusinov states in conventional s-wave superconductors. I will then discuss the implications of our results for the Majorana proposals based on chains of magnetic atoms placed on the surface of superconductors with strong spin-orbit coupling [3].

[1] J. Zhang, C. Triola, E. Rossi, "Proximity effect in graphene-topological insulator heterostructures", Phys. Rev. Lett. 112, 096802 (2014).

[2] Y. Kim, J. Zhang, E. Rossi, R.M. Lutchyn, “Impurity-induced bound states in superconductors with spin-orbit coupling”, Phys. Rev. Lett. 114, 236904 (2015).

[3] J. Zhang, Y. Kim, E. Rossi, R.M. Lutchyn, “Topological superconductivity in a multichannel Yu-Shiba-Rusinov chain”, Preprint arXiv:1505.05862 (2015).

**Yu Saito:** *Ion-gated interface superconductivity in two-dimensional layered materials.*

Superconductivity in confined geometries is attracting renewed interest as a platform of exotic and possibly high Tc superconductivity. Among a variety of techniques dealing with interfacial superconductivity, including those applied to LaAlO_{3}/SrTiO_{3} [1] and FeSe/SrTiO_{3} [2] interfaces, the electric-double-layer transistor (EDLT) possesses a unique position, because of its ease of use and material versatility. The EDLT has been used to generate extremely high carrier densities without sacrificing the material’s quality so far [3]. However, the other aspects of this technique such as control of dimensionality, tunable quantum confinement and breaking of inversion symmetry, have remained to be investigated.

In this talk, after a short review of two-dimensional (2D) superconductors, we report the 2D nature of electric-field-induced superconductivity in ZrNCl [4] and MoS_{2} [5], both of which shows that the effective superconducting thickness is less than 2 nm. The majority of the vortex phase diagram down to 2 K in ion-gated ZrNCl is occupied by a metallic state with a finite resistance. This is a manifestation of the motion of vortices and a realization of metallic ground state through the quantum tunneling and vortex flow caused by the extreme two-dimensionality and weak pinning potential originating from its atomically flat and clean surface [6], indicating the universal nature of clean 2D superconductors. Also, we describe a huge upper critical field of 52 Tesla, a four times larger value than the conventional Pauli limit, observed in ion-gated MoS_{2}, which has been attracting widespread attention as a 2D material beyond graphene, owing to its multiple functionalities especially in the field of valleytronics [7]. Using tight binding calculations based on density functional theory, we reveal that such an unusual behaviour is owing to totally new mechanism; an inter-valley Cooper pairing which is symmetrically protected against external magnetic fields by spin-valley locking.

Our findings suggest that unprecedented exotic nature of superconductivity has become accessible by the geometrical confinement and broken inversion symmetry due to a strong electric field, indicating that electric-field-induced superconductivity offers a new platform for quantum phases in clean 2D superconductors.

[1] N. Reyren et al. Science 317, 1196 (2007).

[2] Q. Y. Wang et al. Chin. Phys. Lett. 29, 037402 (2012).

[3] Y. Saito et al. ACS Nano 9, 3192 (2015).

[4] Y. Saito et al, submitted.

[5] Y. Saito et al. submitted. (arXiv: 1506.04146).

[6] J. T. Ye et al. Nature Mater. 9, 125 (2010).

[7] Q. H. Wang et al. Nature Nanotechnol. 7, 699 (2012), X. Xu et al. Nature Phys. 10, 343 (2014).

**James Sauls:** *From Spontaneous Symmetry Breaking to Topological Order
in Chiral Superconductors and Superfluid ^{3}He^{†.} *

The superfluid phases of

^{3}He provide a paradigm for the role of spontaneous symmetry breaking in quantum field theory and condensed matter physics. Recent developments in theoretical condensed matter physics emphasize an organizing principle based on topology. An exciting frontier in condensed matter physics is the search for exotic excitations - Majorana and Weyl fermions - that are signatures of topological order. In this context the ground states of the quantum liquid phases of

^{3}He provide remarkable examples of emergent topological order, i.e. non-trivial topology of the Hilbert space of quanta that characterize classes of broken symmetry ground states. In this talk I discuss the fermionic and bosonic excitations of 2D chiral

^{3}He-A and chiral superconductors, and their relation to broken space- and time-inversion symmetries and the emergent topology of the chiral ground state. I highlight key features of the B-phase of

^{3}He, which is the realization of a 3D time-reversal invariant topological superfluid characterized by a spectrum of helical Majorana fermions confined on the surface and a rich spectrum of bosonic (Nambu-Goldstone and Higgs) modes that reflect the broken gauge and relative spin-orbit symmetries of the B-phase ground state. The marriage of ultra-low temperature and nano-fabrication technologies, combined with low-noise/high-precision acoustic, optical and NMR spectroscopies opens new possibilities for the study of (i) new broken symmetry states under strong confinement, as well as (ii) novel excitations reflecting topological order. I conclude with an overview of strategies and progress in detecting and manipulating these novel excitations in superfluid

^{3}He and chiral superconductors.

† My research is supported by National Science Foundaation Grant # DMR-1106315.

**John Saunders:** *Helium films at ultralow temperatures: from strongly correlated atomically layered films to topological superfluidity.*

Helium films provide model systems for strongly correlated quantum matter and topological superfluidity. The bottom-up approach is to grow atomically layered helium films on the surface of graphite. Here we find: the Mott-Hubbard transition of a ^{3}He monolayer into a putative quantum spin liquid; 2D solid ^{3}He as a model for frustrated magnetism on a triangular lattice; heavy fermion physics and quantum criticality in ^{3}He bilayer films; model 2D Fermi liquids with tuneable interactions in ^{3}He atop a superfluid ^{4}He film; a novel condensate in a ^{4}He monolayer with intertwined superfluid and density wave order. The top-down approach involves the confinement of topological superfluid ^{3}He in engineered nanoscale geometries. This controlled confinement has a profound effect on the p-wave superfluid order parameter, which can be determined by NMR. New phases may be stabilized. It offers the prospect to study Majorana surface excitations (in time reversal invariant superfluid ^{3}He-B), edge excitations (in chiral superfluid ^{3}He-A) and a variety of interfaces and domain walls.

**Mihail Silaev:** *Mixed modes, thermoelectric effects and vortex dynamics in time-reversal symmetry breaking multiband superconductors.*

We show that mixed phase-density modes result in unconventional thermoelectric properties and a novel vortex viscosity mechanism in multiband superconductors with broken time reversal symmetry [1-3]. In contrast to the usual mechanisms both the unconventional thermoelectric coefficient and the vortex viscosity have a remarkable behavior near the time-reversal symmetry breaking phase transition. These effects can be used to confirm or rule out the s + is state, which is widely expected to be realized in pnictide compounds Ba_{1-x}K_{x}Fe_{2}As_{2}.

[1] M. Silaev, J. Garaud, E. Babaev, arXiv:1503.02024.

[2] J. Garaud, M. Silaev, E. Babaev arXiv:1507.04712.

[3] M. Silaev, E. Babaev, Phys. Rev. B 88, 220504(R) (2013).

**Stephen Simon:** TBA

**Joost Slingerland:** *Energy Projection and Modified Laughlin States.*

Trial wave functions for fractional quantum Hall systems often involve explicit projection onto the lowest Landau level. This can make their evaluation very costly and can limit investigation of the trial wave functions to sizes much smaller even than those which are accessible to exact numerical diagonalization. We propose a projection method which makes use of the low lying eigenstates of a suitably chosen Hamiltonian and which makes it possible for many such problematic trial states to be investigated better. This method should hopefully also be of use in strongly interacting systems beyond the fractional quantum Hall context. As an application, we consider a simple one-parameter modification of the Laughlin wave function (but which needs projection). We show that in a number of ways it improves upon the original.

**Ilya Sochnikov:** *Studies of unconventional Josephson junctions and magnetic materials with a scanning SQUID microscope.*

Scanning Superconducting QUantum Interference Device (SQUID) microscopy is an efficient technique for studies of emergent phenomena at interfaces and in bulk materials. Here, I will present two such examples:
First system, hybrid devices made of a superconductor and a 3-dimensional topological insulator where spin-momentum locking protects the charge carriers at the topological insulator surface against elastic backscattering. We use SQUID microscopy to characterize the current-phase relation of Josephson junctions composed of the 3-dimensional topological insulator HgTe. In these experiments, we find clear skewness in the current-phase relations of HgTe junctions of varying dimensions. The skewness indicates that the Josephson current is predominantly carried by Andreev bound states with high transmittance, and the fact that the skewness persists in junctions that are longer than the elastic mean free path suggests that the effect may be related to the helical nature of the Andreev bound states in the surface of HgTe.

Second system, a special class of frustrated magnets called spin-ices where topological magnetic excitations are predicted to emerge. Using scanning SQUID microscopy we obtain real time images of spontaneous magnetic fluctuations in the spin-ice Ho_{2}Ti_{2}O_{7}. We compare the fluctuations data to the previous susceptibility and magnetization data and theoretical models with the aim to identify the origin of the magnetic dynamics in these materials.

These two experiments demonstrate a powerful magnetic imaging approach for studies of magnetic properties that may reveal emergent phenomena.

**Grigory Volovik:** * 3He topological materials.*

The phases of liquid ^{3}He serve as the most pronounced examples of the topological quantum materials. At the moment the known phases of liquid ^{3}He belong to 4 different topological classes:

(i) The normal liquid ^{3}He belongs to the class of systems with topologically protected Fermi surfaces.

(ii) Superfluid ^{3}He-A and ^{3}He-A1 are chiral superfluids with topologically protected Majorana-Weyl fermions. The analog of the chiral anomaly experienced by the relativistic quantum fields with Weyl fermions has been experimentally demonstrated in ^{3}He-A. The singly quantized vortices in superfluids with Weyl points contain dispersionless band (flat band) of Andreev-Majorana fermions in their cores.

(iii) ^{3}He-B, which is the fully gapped superfluid with topologically protected gapless Dirac fermions on the surface, serves as analog of the relativistic quantum vacuum in the gapped phase. Some evidence of gapless fermions on the surface of ^{3}He-B has been reported.

(iv) The recently discovered polar phase of superfluid ^{3}He belongs to the class of fermionic materials with topologically protected lines of nodes. It contains two-dimensional flat band of Andreev-Majorana fermions on the surface of the sample. The half quantum vortex, which has been recently observed in the polar phase, can be represented as a vortex in a single spin component, and thus contains a single isolated branch of Anfreev-Majorana fermions.

Among the still missing topological phases of 3He, which can be reached with the proper engineered nano-structural confinement, there are:

(i) The planar phase, which is the non-chiral superfluid with Dirac nodes in the bulk
and with Fermi arc of Anfreev-Majorana fermions on the surface.

(ii) a-phase, which contains 4 left-handed and 4 right-handed Weyl points in the vertices of cube, represents the analog of the 3D graphene.

(iii) The two-dimensional topological states in the ultra-thin films of ^{3}He. The films with the order parameters of the ^{3}He-A and of the planar phase belong to the 2D fully gapped topological materials, which experience the intrinsic quantum Hall effect and spin current QHE (in the absence of magnetic field).

**Tim Wehling:** *From optics to superconductivity: Coulomb interactions in two-dimensional materials.*

Two-dimensional (2d) materials combine pronounced surface effects with distinct many body interactions and offer unique possibilities for controlling charge carrier densities. Here, we discuss how the electronic structure and optical properties of graphene and MoS_{2} are determined by the interplay of interactions, dielectric environments and doping. First, we discuss how local and non-local Coulomb interactions generally compete in 2d materials. We then show that substrates, vertical heterostructuring as well as doping and optical excitations present means to drastically manipulate Coulomb interactions and material properties in these systems. We explain that screening due to excited carriers has a strong impact on the optical properties of MoS_{2}, where we find electronic quasiparticle band gap shifts and renormalizations of exciton binding energies on the scale of several hundred meV. Upon charge doping group VI transition metal dichalcogenides undergo a series of transitions from semiconducting, to metallic and finally superconducting phases. We show how electronic screening affects these transitions.

**Hong Yao:** *Emergent Spacetime Supersymmetry in 3D Weyl Semimetals and 2D Dirac Semimetals.*

Supersymmetry (SUSY) interchanges bosons and fermions but no direct evidence of it has been revealed in nature yet. In this talk, we observe that fluctuating pair density waves (PDW) consist of two complex order parameters which can be superpartners of the unavoidably doubled Weyl fermions in three-dimensional lattice models. We construct explicit fermionic lattice models featuring 3D Weyl fermions and show that PDW is the leading instability via a continuous phase transition as short-range interactions exceed a critical value. Using a renormalization group, we theoretically show that N=2 space-time SUSY emerges at the continuous PDW transitions in 3D Weyl semimetals, which we believe is the first realization of emergent (3+1)D space-time SUSY in microscopic lattice models. We further discuss possible routes to realize such lattice models and experimental signatures of emergent SUSY at the PDW criticality [1].

[1] Shao-Kai Jian, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 114, 237001 (2015) (Editors' Suggestion)

**Ryutaro Yoshimi:** *Quantum Hall effects on surface Dirac states of 3D topological insulator (Bi _{1-x}Sb_{x})_{2}Te_{3}.*

The three-dimensional (3D) topological insulator (TI) is a novel state of matter as characterized by two-dimensional (2D) metallic Dirac states on its surface. Quantum transport in Dirac electron systems such as half integer quantum Hall effect (QHE) and quantum anomalous Hall effect (QAHE) has recently been attracting much attention by breaking time reversal symmetry. These quantized phenomena in the 3D TIs have been extensively studied in Bi-based chalcogenides such as Bi

_{2}Se

_{3}, Bi

_{2}Te

_{3}, Sb

_{2}Te

_{3}and their combined/mixed compounds in both bulk and thin films form. Here, we report the realization of the QHE and QAHE on the surface Dirac states in (Bi

_{1−x}Sb

_{x})

_{2}Te

_{3}films (x = 0.84 and 0.88) and its Cr-doped compound Cr

_{x}(Bi

_{1−y}Sb

_{y})

_{2-x}Te

_{3}(x = 0.2, y = 0.78), respectively. In the pristine (Bi

_{1−x}Sb

_{x})

_{2}Te

_{3}, with electrostatic gate-tuning of the Fermi level in the bulk band gap under magnetic field, the QH states with filling factor of 1 and -1 are resolved with quantized Hall resistance of R

_{yx}= h/e

^{2}, -h/e

^{2}and zero longitudinal resistance, owing to the formation of chiral edge modes at top/bottom surface Dirac states. In the magnetically doped compound, quantization and transition with magnetization reversal is observed. These observations of the quantization of Hall effects in 3D TI films may pave a way toward TI-based electronics.