Scattering amplitude in the Aharonov-Bohm gauge field

Abstract

A general expression for the scattering amplitude of nonrelativistic spinless particles in the Aharonov-Bohm gauge potential is obtained within the time independent formalism. The result is valid also in the backward and forward directions as well as for any choice of the boundary conditions on the wave function at the flux tube position.

Magnetic scattering of Dirac fermions in topological insulators and graphene

“…44 When the vector potential corresponds to an infinitely thin solenoid, we encounter an ultra-relativistic Dirac fermion generalization of the celebrated Aharonov-Bohm (AB) calculation. 45,46 This generalization was discussed before, [47][48][49][50][51][52] and exact results for the transmission amplitude can be deduced. Recent studies have also addressed the current induced by an AB flux 53 and the behavior of the conductance when the chemical potential is precisely at the Dirac neutrality point.…”

“…(3.1) has an additional phase factor e −iπα sgn(sin φ) e −iαφ , i.e., one has a multi-valued incoming plane wave. The precise relation between these two approaches has been discussed in several works and is still under debate, [47][48][49][50][51][52] albeit the difference is of little relevance to experimentally observable quantities. In particular, the transport cross section σ tr in Eq.…”

Hidden superconformal symmetry of the spinless Aharonov–Bohm system

“…2 Hidden N=2 supersymmetry in spinless AB system In general, a formal Hamiltonian operator H α (1.2) admits a four-parametric U (2) family of self-adjoint extensions, which specify physically different configurations, distinct in their spectral and scattering properties [31,33]. The spectrum depends strongly on the actual choice of the domain of definition of H α ; besides a continuous part of non-negative energy scattering states, it may contain up to two bound states of negative energy.…”

Unitarity of the Aharonov–bohm Scattering Amplitudes

“…where the integration contour is along the circle |z| = 1. The iǫ−prescription dictates to pick up the pole at z = e −iθ and the resulting expression of RHS coincides with LHS in (8).…”