Isotropically conducting (hidden) quantum Hall stripe phases in a two-dimensional electron gas

Abstract

Quantum Hall stripe (QHS) phases, predicted by the Hartree-Fock theory, are manifested in GaAs-based two-dimensional electron gases as giant resistance anisotropies. Here, we predict a "hidden" QHS phase which exhibits isotropic resistivity whose value, determined by the density of states of QHS, is independent of the Landau index N and is inversely proportional to the Drude conductivity at zero magnetic field. At high enough N , this phase yields to an Ando-Unemura-Coleridge-Zawadski-Sachrajda phase in which the resistivity is proportional to 1/N and to the ratio of quantum and transport lifetimes. Experimental observation of this border should allow one to find the quantum relaxation time.Quantum Hall stripe (QHS) phases in spin-resolved Landau levels (LLs) near half-integer filling factors ν = 9/2, 11/2, 13/2, ..., were predicted by the Hartree-Fock (HF) theory [1][2][3]. These phases consist of alternating stripes with filling factors ν ± 1/2, which, at exactly half-filling, both have the width Λ/2 ≃ 1.42R c [1,2,4,5], where R c is the cyclotron radius. QHSs are formed due to a repulsive box-like interaction of electrons with ring-like wave functions. Such an unusual interaction leads to an energy gain when electrons occupy the nearest states within the same stripe and avoid interacting with electrons in neighboring stripes. The selfconsistent HF theory is valid at LL indices N ≫ 1, when R c = l B (2N + 1) 1/2 ≫ l B , where l B = (c /eB) 1/2 is the magnetic length, a measure of quantum fluctuations of an electron's cyclotron orbit center, and B is the magnetic field. These fluctuations play a minor role even at N = 2, and QHSs determine the ground state for all ν ≥ 9/2 [2, 4, 5].QHSs were confirmed by the discovery of dramatic resistance anisotropies in two-dimensional electron gases in GaAs/AlGaAs heterostructures [6,7]. These anisotropies emerge because the diffusion mechanisms along and perpendicular to the stripe orientation are different [8]. In the stripe direction (ŷ) electrons drift along the stripe edge in the internal electric field E until they are scattered to an adjacent stripe edge by impurities. If such scattering is weak, this mechanism leads to a large diffusion coefficient in theŷ direction (large conductivity σ yy , large resistivity ρ xx ) and a small diffusion coefficient in the orthogonal (x) direction (small σ xx , small ρ yy ). As a result [9], if N is not too large

Hidden Quantum Hall Stripes in Al$_{x}$Ga$_{1-x}$As/Al$_{0.24}$Ga$_{0.76}$As Quantum Wells

“…For the hQHS phase to exist and be detected, it should span a sizable range of the filling factors ∆ν = ν 2 − max{ν 1 , 9/2} ≫ 1. The range ∆ν depends sensitively on both transport τ −1 and quantum τ −1 q scattering rates, which control ν 1 and ν 2 , respectively [37]. As we will see, ultrahigh mobility GaAs quantum wells do not support the hQHS phase as ν 1 ≈ ν 2 in these samples.…”

“…In this Letter, we report observation of transport signatures of the recently predicted [37] hidden QHS (hQHS) phases in a series of Al x Ga 1−x As/Al 0.24 Ga 0.76 As quantum wells with x < 10 −3 . In contrast to the ordinary QHS phases, the hQHS phases are characterized by isotropic resistivity (ρ xx = ρ yy = ρ) that is independent of ν, unlike the isotropic liquid phases in which ρ ∝ ν −1 .…”

“…x ne (10 11 cm −2 ) µ (10 6 cm 2 /Vs) σ0 (10 cal boundaries of the hQHS phase [37]. The lower boundary ν = ν 1 , separating the QHS and the hQHS phases, is given by [37]…”

“…The wide variation of mobilities in our samples allows us to construct an experimental phase diagram in the conductivityfilling factor plane. Its comparison to theoretical predictions [37] yields the electron quantum lifetimes and the stripe density of states. The latter turns out to be lower than predicted by original the Hartree-Fock theory [3,4], calling for further theoretical input.…”

“…We confirm this finding by a complementary experiment on an ultrahigh mobility GaAs quantum well, where we also show that, in this sample, the hQHS phase yields to the QHS phase in agreement with the theory. Before presenting our experimental data, we briefly summarize the physics behind the hQHS phases [37]. The resistance anisotropies in the ordinary QHS phase emerge due to different diffusion mechanisms along and perpendicular to the stripes [38][39][40].…”