Speaker
Prof.
Eduardo Marino
(Universidade Federal do Rio de Janeiro, Brazil)
Description
Abstract: We use Pseudo Quantum Electrodynamics
(PQED), a strictly 2D theory, in order to describe the full
electromagnetic interaction of the p-electrons of graphene
in a consistent formulation. By including the effects of the
interaction on the vacuum polarization tensor and on the
electron self-energy, we achieve the following physical
results: 1) QVHE - We predict the onset of a spontaneous
(interaction-driven) Quantum Valley Hall effect (QVHE)
below a critical temperature of the order of $0.05$ K. The
transverse (Hall) valley conductivity is evaluated exactly and
shown to coincide with the one in the usual Quantum Hall
effect. 2) DC-conductivity - By considering the corrections
induced by PQED in the vacuum polarization tensor or,
equivalently, in the current correlator, up to two-loops, we
are able to obtain a smooth zero-frequency limit in Kubo's
formula. Thereby, we obtain in zeroth order, the usual
expression for the minimal DC-conductivity plus higher-
order corrections due to the interaction. These make our
result, to the best of our knowledge, the closest to the
experimental value. 3) Gap and Midgap States - We study
the effects of the interaction on the electron self-energy
and show that this produces a shift in the electron
propagator poles. The energy spectrum is such that a set of
P- and T- symmetric gapped electron energy eigenstates are
dynamically generated, with an infinite number of midgap
states. This discrete set of states are related to the QVHE in
similar way the Landau levels are related to the ordinary
Quantum Hall Effect.
