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International Journal of Modern Physics B

Is Aharonov–Casher Effect Topological?

Tae-Yeon Lee

Published May 10, 1998• 0 citations
Publisher

Abstract

It is shown that the Aharonov–Casher effect and neutron scalar Aharonov–Bohm effect are topological in two dimension and this fact is not incompatible with the argument of Peshkin and Lipkin.
DOI
10.1142/s021797929800065x

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In this Comment we point out (i) that the Hamiltonian, Eq. (17) in the Letter(Phys. Rev. Lett. 108, 070405 (2012)), is not a relativistic Hamiltonian, (ii) then that the conditions in the Letter are irrelevant for a topological AC and SAB effects, and (iii) conclusively that the non-relativistic Hamiltonian employed by Peshkin and Lipkin (Phys. Rev. Lett. 74, 2847 (1995)) has the same U(1)mmU(1)_{mm}U(1)mm​ gauge structure for a fixed spin and then is not wrong, but their incorrect interpretation of the spin autocorrelations led to the incorrect conclusion.
Recent neutron interferometry experiments have been interpreted as demonstrating a new topological phenomenon similar in principle to the usual Aharonov-Bohm (AB) effect, but with the neutron's magnetic moment replacing the electron's charge. We show that he new phenomenon, called scalar AB (SAB) effect, follows from an ordinary local interaction, contrary to the usual AB effect, and we argue that the SAB effect is not a topological effect by any useful definition. We find that SAB actually measures an apparently novel spin autocorrelation whose operator equations of motion contain the local torque in the magnetic field. We note that the same remarks apply to the Aharonov-Casher effect.
The special and unique techniques of neutron interferometry have been used to observe a number of topological effects. These include the quantum mechanical phase shift of a neutron due to the Earth's rotation (the quantum analog of the Michelson–Gale–Pearson experiment with light), the phase shift of a particle carrying a magnetic moment (a neutron) encircling a line charge (the Aharonov–Casher effect) and the scalar Aharonov–Bohm effect, observed with a pulsed magnetic field solenoid and time-of-flight neutron detection. On the occasion of the 50th anniversary of the Aharonov–Bohm paper, we provide an overview of the neutron interferometry technique and a description of these three historic experiments.
We briefly review the theoretical formulations and applications of the Aharonov--Bohm effect and the Aharonov--Casher effect with emphasis on mesoscopic physics. Topics relating to the Aharonov--Bohm effect include: locality, periodicity, non-integrable phase factors, Abelian gauge theory, interference, the spectrum and persistent current of electrons on a ring pierced by a magnetic field, Onsager reciprocity relations, and Aharonov--Bohm interferometer. Topics relating to the Aharonov--Casher effect include: a magnetic dipole in an electric field, locality, periodicity, non-Abelian gauge invariance, SU(2) non-integrable phase factors, spin-orbit coupling, Pauli equation, Rashba Hamiltonian, Aharonov--Casher interferometer, conductance and polarization in two-channel systems due to the Aharonov--Casher effect.