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arXiv:0909.0019 · Physical Review B

Aharonov-Bohm oscillations in the local density of states

A. Cano, Indranil Paul

Published Oct 1, 2009• 15 citations
arXivHTMLPDF

Abstract

The scattering of electrons with inhomogeneities produces modulations in the local density of states of a metal. We show that electron interference contributions to these modulations are affected by the magnetic field via the Aharonov-Bohm effect. This can be exploited in a simple scanning-tunneling-microscopy setup that serves as an Aharonov-Bohm interferometer at the nanometer scale.

DOI
10.1103/physrevb.80.153401

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The scattering of electrons with inhomogeneities produces modulations in the local density of states of a metal. We show that electron interference contributions to these modulations are affected by the magnetic field via the Aharonov-Bohm effect. This can be exploited in a simple scanning-tunneling-microscopy setup that serves as an Aharonov-Bohm interferometer at the nanometer scale.
Ever since Yakir Aharonov and David Bohm pointed out, in 1959, that electrons propagating around a magnetic field through a field-free vacuum should exhibit a quite surprising interference effect, its experimental and theoretical investigation has been contributing to our understanding of the fundamental character of the quantum theory. The recent appearance of this Aharonov–Bohm effect in a rather different context may eventually have a profound effect on our view of the solid state on a “mesoscopic” scale—between the microscopic and the truly macroscopic.
Introduction Aharonov and Bohm (1959) drew attention to the quantum mechanical prediction that an interference pattern due to a beam of charged particles could be produced or altered by the presence of a constant magnetic field in a region from which the particles were excluded. This effect was first experimentally detected by Chambers (1960), and since then has been repeatedly and more convincingly demonstrated in a series of experiments including the elegant experiments of Tonomura et al. (1986). At first sight, the Aharonov-Bohm effect seems to manifest nonlocality. It seems clear that the (electro)magnetic field acts on the particles since it affects the interference pattern they produce; and this must be action at a distance since the particles pass through a region from which that field is absent. Now it is commonly believed that this appearance of nonlocality can be removed by taking it to be the electromagnetic potential A μ rather than the field F μν that acts locally on the particles: indeed, Bohm and Aharonov themselves took the effect to demonstrate the independent reality of the (electro)magnetic potential. But the nonlocality is real, not apparent, and cannot be removed simply by invoking the electromagnetic potential. While there may indeed be more to electromagnetism than can be represented just by the values of F μν at all space-time points, acknowledging this fact still does not permit a completely local account of the Aharonov-Bohm effect.
When the electromagnetic potentials are expressed in the Coulomb gauge in terms of the electric and magnetic fields rather than the sources responsible for these fields they have a simple form that is nonlocal (i.e., the potentials depend on the fields at every point in space). It is this nonlocality of classical electrodynamics that is primarily responsible for the puzzle associated with the static Aharonov–Bohm effect: that its interference pattern is affected by fields in a region of space that the electron beam never enters.
This article describes the Aharonov-Bohm (AB) effect of electron waves travelling in free space and its application to the observation of gauge fields (vector potentials). The AB effect is inconceivable in classical physics since an observable effect is produced on electrons passing through field-free spaces. Electrons can be affected only by Lorentz forces due to electromagnetic fields. The situation is different in quantum mechanics, where electrons show wave properties: the concept of force is no longer relevant, so electric field E and magnetic field B, defined as forces acting on a unit charge, take on secondary meanings. “Phase shifts” come into play, and the primary physical entities become neither E nor B but electrostatic potential V and vector potential A. These potentials interact with electron waves and shift their phases.