Effect of a nonuniform magnetic field on a two-dimensional electron gas in the ballistic regime

Abstract

The single-particle electronic structure of a two-dimensional electron gas in a nonuniform magnetic field B consists of states that propagate perpendicularly to the field gradient \B and have a remarkable time-reversal asymmetry. In one of the allowed directions the propagation has free-electron character and is confined to a narrow one-dimensional channel localized about the region where \B\ is minimum. In the opposite direction, the Landau states propagate throughout the rest of the sample with a velocity proportional to |V#| I/2 . PACS numbers: 72.15.Gd, 72.20.My, 73.20.DxThe electrical behavior of a two-dimensional electron gas (2DEG) subjected to a uniform magnetic field has been studied recently in much detail [1,2]. In the ballistic regime, the system is characterized by stationary Landau states, which do not propagate and yield no contribution to its conductance. The charge flow observed in finite samples was shown to be due to edge states localized at the boundary of the 2DEG [3]. This Letter discusses the situation in which the magnetic field in the interior of the sample is not uniform. In this case the Landau states are no longer stationary but propagate perpendicularly to the field gradient and exhibit a remarkable time-reversal asymmetry. In one of the allowed directions the propagation has free-electron character, and it is confined to a narrow one-dimensional region localized near the line where the magnitude of the magnetic field is minimum. In the opposite direction the Landau states propagate throughout the rest of the sample with a velocity which depends on the field gradient.The asymmetric propagation of electrons in a nonuniform magnetic field can be understood by the following classical argument illustrated in Fig. 1. Consider a 2DEG constrained by rigid walls to -£/2 :<>>:< L/2, but infinite along the x axis, and subjected to a magnetic field with a component perpendicular to the x-y plane, given bysuch that it changes sign at the line >>=0 [4]. The trajectory of a classical electron moving in the plane has an instantaneous radius of curvature given by r =cp/eB, where p is the momentum of the electron, and B the local magnitude of the magnetic field [5]. This means that the part of the trajectory that scans larger (smaller) values of the magnetic field will have a smaller (larger) radius, giving rise to an open orbit that drifts perpendicularly to the field gradient, as illustrated by the drift (d) trajectories in Fig. 1. For the case of a sufficiently small field gradient, VZ?=#iy, a straightforward classical calculation shows that the magnitude of the drift velocity is given by [5] v=er 2 B\/2mc. (2) Near the boundaries of the sample, collisions against the rigid walls force the electrons into skipping orbits as illustrated by the edge (e) trajectories in Fig. 1, which propagate in the same direction as the d trajectories. On the other hand, in the region where B-0 the electrons scan magnetic fields with alternating positive and negative signs, giving rise to the s trajectory, that propa...

Composite fermions, edge currents, and the fractional quantum Hall effect

“…53 For the situation in Fig.6(a), Müller's argument can be summarized briefly as follows. Inserting equations (6) and (8) in (7) yields (19) where the effective potential is given by .…”

Hidden degree of freedom and critical phase in a two-dimensional electron gas in the presence of a random magnetic field

“…In addition, the quantum tunneling between a pair of drift (snake) states results in a new pair of symmetric/antisymmetric states, or equivalently, states of opposite parity pairwise. Detailed quantum mechanical treatments 30 further confirm that, in most cases, in each pair of energy bands there are two snake and two drift states at the Fermi energy. Most prominent are the snake states which peak right on the B = 0 line; so in the context of the network model, they have a considerable chance to percolate and thus carry extended wavefunctions.…”

Energetic and Dynamic Properties of a Quantum Particle in a Spatially Random Magnetic Field with Constant Correlations along one Direction

“…Another class of UMF's yielding only absolutely continuous spectrum of H(b) covers in particular the UMF's of indefinite sign studied in [46] and [56]. Example 2.6 (Semi-bounded vector potential).…”

“…To our knowledge, the first rigorous work explicitly dealing with a model involving a random UMF (with zero mean-value) is one of Ueki [67]. Models for a single particle on the plane Ê 2 subjected to a non-random unidirectionally constant magnetic field (UMF) have been the object of various studies in the mathematics [28,13,45,42] and physics [46,49,37,56,61,39] literature. These models illustrate unadulteratedly that inhomogeneous magnetic fields have a tendency to delocalise charged particles along the direction perpendicular to the magnetic-field gradient.…”