[qmeso-seminar] семинар сектора 6 сентября

[Mikhail A. Skvortsov]

                     СЕМИНАР СЕКТОРА КВАНТОВОЙ МЕЗОСКОПИКИ

                         пятница 6 сентября, 15:00, ИТФ


                  I. V. Gornyi (Karlsruhe and Ioffe PhysTech)

     Quantum Hall criticality and localization in graphene with short-range
                         impurities at the Dirac point


Strong impurities crucially affect the spectral and transport properties
of graphene near the Dirac point creating the "mid-gap" states.
We first consider the ultimate case of very strong on-site potential impurities
that are equivalent to vacancies in the lattice. Vacancies in the honeycomb
lattice possess two important properties: (i) they preserve the chiral
symmetry of the model and (ii) they scatter resonantly at zero energy (Dirac
point). We study the density of states in graphene with sublattice imbalance
[1]: we assume that the concentration of vacancies is different in the two
sublattices. The imbalance leads to a finite concentration of zero modes of the
tight-binding Hamiltonian. We derive the non-linear sigma model for the chiral
system with imbalance. Semiclassical density of states acquires a finite gap
around the Dirac point with the delta-function peak exactly in the center of
the gap. Finite density of zero modes results in the additional term in the
sigma-model action. The perturbative renormalization group analysis of this
theory yields corrections to the density of states above the gap. In order to
obtain a finite density of states below the semiclassical gap, we include non-
perturbative contributions to the partition function due to instanton
configurations of the field.

Further, we explore the longitudinal conductivity of graphene at the Dirac
point in strong magnetic field with two types of short-range scatterers of a
finite strength: adatoms that mix the valleys and "scalar" impurities that do
not mix them [2]. A scattering theory for the Dirac equation is employed to
express the conductance of a graphene sample at charge neutrality as a
function of impurity coordinates; an averaging over positions of impurities is
then performed numerically. The conductivity is equal to the ballistic value
for each disorder realization, provided the number of flux quanta considerably
exceeds the number of impurities. For weaker fields, the conductivity in the
presence of scalar impurities scales to the quantum-Hall critical point at
half filling or to zero away from half filling due to the onset of Anderson
localization. For adatoms, the localization behavior is obtained also at half
filling due to splitting of the critical energy by intervalley scattering. Our
results reveal a complex scaling flow governed by fixed points of different
symmetry classes.

[1] E.J. Koenig, I.V. Protopopov, P.M. Ostrovsky, I.V. Gornyi, A.D. Mirlin,
and M.A. Skvortsov, in preparation.

[2] S. Gattenloehner, W.-R. Hannes, P. M. Ostrovsky, I. V. Gornyi, A. D.
Mirlin, and M. Titov, "Quantum Hall criticality and localization in graphene
with short-range impurities at the Dirac point", arXiv:1306.5686.