Classical percolation fingerprints in the high temperature regime of the quantum Hall effect

Abstract

We have performed magnetotransport experiments in the hightemperature regime (up to 50 K) of the integer quantum Hall effect for two-dimensional electron gases in semiconducting heterostructures. While the magnetic field dependence of the classical Hall law presents no anomaly at high temperatures, we find a breakdown of the Drude-Lorentz law for the longitudinal conductance beyond a crossover magnetic field B c 1 T, which turns out to be correlated with the onset of the integer quantum Hall effect at low temperatures. We show that the high magnetic field regime at B > B c can be understood in terms of classical percolative transport in a smooth disordered potential. From the temperature dependence of the peak longitudinal conductance, we extract 7

Quantum transport in chemically functionalized graphene at high magnetic field: defect-induced critical states and breakdown of electron-hole symmetry

“…The specific role of disorder played in this study is different from literature predicting the QHE to be robust under three kinds of disorder, namely (i) weak potentials V W (satisfying ω <  V W c ) [44,45], (ii) scattering centers defined by potential V SC (satisfying a distance d between centers larger than the magnetic length l B ) [46][47][48] and (iii) smooth potentials V S (satisfying [47,[49][50][51][52][53][54][55][56]. Epoxy is a scattering center, in the sense that it induces intervalley mixing responsible for quantum localization effects [21].…”

Unconventional features in the quantum Hall regime of disordered graphene: Percolating impurity states and Hall conductance quantization

“…In very clean samples, the presence of this transition is ensured by the system edges, which force the formation of extended states, while bulk states are localized by the magnetic field. The robustness of the QHE in the bulk limit is guaranteed by the contribution of either weak impurity potentials satisfying the so-called weakness condition 3,4 , strong scattering centers sufficiently far away from each other [5][6][7] , or smooth potentials with long-range spatial variation [7][8][9][10][11][12][13][14][15] . Whenever disorder becomes too strong, all QHE features eventually vanish away.…”

A solvable model of Landau quantization breakdown

“…In terms of vortex Green's functions, only diagonal elements g n1,n1 (R; t) contribute to the overall electron dynamics in expression (5) after projection. Then, at the level of the guiding center motion, the star product operator (9) generates a hierarchy of local energy scales ordered by powers of l 2 B and successive spatial derivatives of the effective potential (8), which allows one to devise semiclassical nonperturbative approximation schemes for the vortex Green's functions g n1,n1 (R; t) valid at small times t (and physically justified at finite temperatures).…”

“…Indeed, Landau levels start to be witnessed only from an intermediate magnetic field regime, in which mild oscillation of thermodynamic and transport coefficients are observed. Only in a second range [7,8] of even higher magnetic field does full quantization of the Hall conductance finally emerge, with the Landau level index becoming a good quantum number.…”