Influence of geometry on the Hall effect in ballistic wires

Abstract

We present a systematic investigation of the influence of cross geometry on the Hall effect in narrow ballistic wires. Various differently shaped cross regions have been fabricated, which demonstrate that near zero magnetic field the Hall resistance can be quenched, enhanced over its classical value, or even negative. A "last plateau" is seen in all devices, proving that its cause is not intimately linked to the quenching. A simple physical picture is presented showing how these effects come about from the scattering of electrons in such geometries. PACS numbers: 72.20.My, 73.50.Jt, 73.60.Br The quenching of the Hall effect is an intriguing result observed in narrow high-mobility devices by Roukes et al x and others. 2,3 As the magnetic field B is reduced, the Hall resistance RH (measured at voltage probes on either side of a narrow channel) forms a plateaulike feature (the "last plateau") and then drops sharply below its classical value so as to be close to zero ("quenched") in some finite region around B-0. This phenomenon has received considerable theoretical attention but it still lacks a definitive explanation. It has not been clear whether or not the last plateau and the quench are related, or indeed whether the effects are explicable solely in terms of single-particle transport theory. In this Letter, we describe measurements on several different cross geometries which yield alternatively quenched, enhanced, or negative RH-The last plateau, however, appears in all samples.It has been proposed that RH would be quenched if the channel width were less than the size of the edge states formed by the Lorentz force, 4 but the quantitative agreement with experiment was limited. 2 Very recently such narrow channels have been modeled quantum mechanically by a direct numerical solution of the Schrodinger equation together with the multiprobe resistance formula 5 to calculate RH from the scattering coefficients. 6 "" 9 A perfect cross with an infinite squarewell potential ("hard walls") quenches only for very specific values of the Fermi energy Ef, 1 contrary to experimental results, 2 which quench for a wide range of Ef. A similar model with a parabolic potential obtains ranges of E F where realistic-looking quenches occur. For more than two subbands, however, the quench has almost disappeared, whereas early devices 1,2 probably had between three and nine subbands populated when quenching was observed.New theoretical work 9 obtains generic quenching over wide ranges of E F and width by modifying the geometry and by energy averaging. The important change incorporated into the new model is collimation of the electrons as they enter the cross region. This is accomplished by adiabatic widening of the wire near the junction. Because the widening of the wire is gradual, the electrons at the Fermi surface do not populate the extra subbands available in the wider region, and because the subbands are depressed in the wider region, the ratio of the longitudinal momentum to the transverse momentum increases: The electrons ar...

Quantum Hall effect on the Lobachevsky plane

“…Other branch of the QHE physics both theoretical [8,9,10,11,12,13,14,15,16,17,18,19] and experimental [20,21] concern the study of the surface curvature effects on the transport properties. The recent progress in nanotechnology has made it possible to produce curved 2D layers [22] and nanometer-size objects of desired shapes [23].…”

Collapse of Landau Levels in Gated Graphene Structures

“…Since the 1980s, many groups have investigated electron transport in semiconducting two-dimensional electron systems (2DES), where gateinduced spatially varying electric fields can be used to alter cyclotron motion. A variety of interesting phenomena were explored in these systems, including quenching of the quantum Hall effect [3,4], Weiss oscillations due to commensurability between cyclotron orbits and a periodic grating [5], pinball-like dynamics in 2D arrays of scatterers [6], and coherent electron focusing [7].…”

“…Since the 1980s, many groups have investigated electron transport in semiconducting two-dimensional electron systems (2DES), where gateinduced spatially varying electric fields can be used to alter cyclotron motion. A variety of interesting phenomena were explored in these systems, including quenching of the quantum Hall effect [3,4], Weiss oscillations due to commensurability between cyclotron orbits and a periodic grating [5], pinball-like dynamics in 2D arrays of scatterers [6], and coherent electron focusing [7].The experimental realization of graphene [8], a new high-mobility electron system, affords new opportunities to explore effects that were previously inaccessible. In particular, attempts to induce sharp potential barriers in III-V semiconductor quantum well structures have been limited by the depth at which the 2DES is buriedtypically about 100nm below the surface [9].…”

Room-Temperature Ballistic Transport in III-Nitride Heterostructures

“…In addition, the conductance is quantized at low temperatures, fundamentally similar to the quantized Hall effect [3], where only a small number of transverse quantum channels are occupied. These effects have been explored and demonstrated in a number of different devices based on quantum interference [4,5], quantized conductance in a point contact [6,7], electron focusing [8], negative bend resistance [9,10], quenched and negative Hall effects [11], and lateral hot ballistic electron [12].…”

“…In addition, the conductance is quantized at low temperatures, fundamentally similar to the quantized Hall effect [3], where only a small number of transverse quantum channels are occupied. These effects have been explored and demonstrated in a number of different devices based on quantum interference [4,5], quantized conductance in a point contact [6,7], electron focusing [8], negative bend resistance [9,10], quenched and negative Hall effects [11], and lateral hot ballistic electron [12].While these devices were demonstrated under low temperature, ballistic transport at RT would open a pathway for many practical applications [13][14][15][16], offering a new design space for high frequency devices with quicker switching responses and lower dissipation losses than conventional devices. At RT however, L m is largely reduced, below 100 nm in some III-V semiconductors.…”