Abstract
We study the electrodynamics of a PbTe-type bulk semiconductor with a domain wall. We show the existence of states bound to the wall. In the presence of static electric and magnetic fields a current with abnormal parity and a nonzero induced electric charge are shown to exist. These systems are a physical realization of the parity anomaly of 2 + 1 dimensional QED.
Highlights
In relativistic‘field theories of Fermi systems it is quite common to find situations in which classical symmetries are not respected at the quantum level
We show that certain lattice systems, such as PbTe, whose bulk states can be described in terms of massive relativistic fermions do exhibit the parity anomaly of 2+1 dimensional electrodynamics if a structural domain wall is included in the system: a shorter version of this paper is to be published elsewhere
To the best of our knowledge, apart from our proposal, the only other successful use of anomalies in condensed matter physics has only been achieved in the study of mass currents in superfluid He3 - A with chiral textures.[10-121 Our study points to a close analogy with the physics of fractional charge in onedimensional systems with solitons. 113’14I1n addition our analysis shows a possible way to study lattice systems with chiral fermions by considering a lattice gauge theory in higher dimensions in the background of a soliton
Summary
In relativistic‘field theories of Fermi systems it is quite common to find situations in which classical symmetries are not respected at the quantum level. The result is typically that a classically conserved current is found not to be conserved quantum mechanically Another milder form of anomaly is found, for example, in electrodynamics in two space dimensions. Semenoff17’ has proposed the study of “two-dimensional graphite” He found that the odd parity current is cancelled due to the pervasive doubling properties of lattice relativistic systems. We show that certain lattice systems, such as PbTe, whose bulk states can be described in terms of massive relativistic fermions (with a mass of the order of the gap) do exhibit the parity anomaly of 2+1 dimensional electrodynamics if a structural domain wall (or stacking fault) is included in the system: a shorter version of this paper is to be published elsewhere.
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