Violation of the integral quantum Hall effect: Influence of backscattering and the role of voltage contacts

Abstract

Heterostructure (GaAs-Al"Ga~-"As) Hall-bar devices with short cross gates are studied in the quantum Hall regime. A potential barrier introduced by the gate causes back scattering of edge currents, making steplike structures in the curves of the Hall and the diagonal resistances versus the gate bias voltage. The Hall resistance on either side of the gate deviates largely from expected quantized values, indicating a nonequilibrium occupation of edge states and its stability over a macroscopic distance (50 pm). An essential role of imperfect voltage contacts in probing the nonequilibrium edge currents is noted.The most fundamental characteristic of the integral quantum Hall effect (QHE) is that, when current I is transmitted through a channel of two-dimensional electron gas (2D EG) where bulk Landau levels are occupied, a quantized voltage of (It/ve )I appears across the channel, where v is the number of the filled Landau levels, h is the Planck constant, and e the unit charge. ' Significant deviation of the quantized Hall voltage has not been reported even in the studies on small devices of micron and submicron scales or on samples with an electrondensity discontinuity.We report here a significant violation of the QHE, which occurs when a potential barrier is introduced in a 2D EG channel by a short cross gate to cause a back scattering of electrons. According to our interpretation, the deviation of the Hall voltage is a consequence of a nonequilibrium occupation of edge states and imperfect voltage contacts that selectively probe different edge states. The experimental results further indicate that edge currents travel ballistically over a surprisingly long distance (50 pm).

Quantum Transport in Semiconductor Nanostructures

“…Selective backscattering of edge channels with n > n 0 is induced by a potential barrier across the sample, 113 ' 339 ' 340 ' 427 if its height is between the guiding center energies of edge channel n 0 and n 0 -l (note that the edge channel with a larger index n has a smaller value of £ G ). The anomalous Shubnikov-De Haas effect, 428 to be discussed in Section 19, has demonstrated that selective backscattering can also occur naturally in the absence of an imposed potential barrier.…”

Adiabatic Transport in the Fractional Quantum Hall Effect Regime

“…(12) and (13). The longitudinal resistance RL of the barrier (measured by two adjacent voltage probes, one at each side of the barrier) is given by This result follows from eqs.…”

“…The edge channel with the highest indcx n = N is sclcctivcly backscattcred when the Fermi level approaches the cnergy (7V -|) 1ιω 0 of the 7V-th bulk Landau levcl. The guiding center cnergy of the N-th edge channel thcn approaches zcro, and backscattering eithcr by tunneling or by thcrmally activatcd processes becomes effcctive -but for that edge channel only, which remains almost complctcly dccoupled from the other 7V -l edge channels over distances äs largc äs [13,28,29] 250 /tm (although on lhat length scale the edge channcls with n < N -l have cquilibrated to a large cxtcnt [14]). …”

“…These states are extended along the cdges of the 2 DEG whencver the Fermi level lies between two Landau levels in the bulk. Many of the anomalies in the integer QIIE can be understood äs resulting from the absence of local equilibrium at the edge, which in turn is a consequence of the reduction of scattering between edge channels in a strong magnetic field [10,13,14]. On short length scales the electron transport becomes fully adiabaiic, i.e.…”

Frequency dependence of the Hall-potential distribution in quantum Hall systems: Roles of edge channels and current contacts

“…The DC response of the edge channel is known to be remarkably different from that of the bulk region. In the steady state the nonequilibrium edge-channel population has been observed [15,16,17,18,19,20,21] in which the induced potential (more precisely the electrochemical potential) of the edge channel is largely deviated from that of the neighboring bulk region. This occurs because the electron transition between the edge channel and the bulk region is less frequent, resulting in a high effective resistance between the two regions.…”