Pseudo-gauge Fields in Dirac and Weyl Materials

Abstract

Electrons in low-temperature solids are governed by the non-relativistic Schrödinger equation, since the electron velocities are much slower than the speed of light. Remarkably, the low-energy quasi-particles given by electrons in various materials can behave as relativistic Dirac/Weyl fermions that obey the relativistic Dirac/Weyl equation. We refer to these materials as "Dirac/Weyl materials", which provide a tunable platform to test relativistic quantum phenomena in table-top experiments. More interestingly, different types of physical fields in these Weyl/Dirac materials, such as magnetic fluctuations, lattice vibration, strain, and material inhomogeneity, can couple to the "relativistic" quasi-particles in a similar way as the U (1) gauge coupling. As these fields do not have gauge-invariant dynamics in general, we refer to them as "pseudo-gauge fields". In this chapter, we overview the concept and physical consequences of pseudo-gauge fields in Weyl/Dirac materials. In particular, we will demonstrate that pseudo-gauge fields can provide a unified understanding of a variety of physical phenomena, including chiral zero modes inside a magnetic vortex core of magnetic Weyl semimetals, a giant current response at magnetic resonance in magnetic topological insulators, and piezo-electromagnetic response in time-reversal invariant systems. It turns out that these phenomena are deeply related to various concepts in high-energy physics, such as chiral anomaly and axion electrodynamics.

Effective field theories of topological crystalline insulators and topological crystals

“…One physical correspondence of the spatially dependent mass terms in TCIs is non-homogeneous lattice distortions or strain [79,80]. In the case when the couplings between electrons and the lattice distortions take the same form as the mass terms in this work, the topological terms will have a interpretations in the elasticity theory.…”

Ultrafast control of moiré pseudo-electromagnetic field in homobilayer semiconductors

“…We would also like to compare with dynamical magnetic structures [23,24] and materials subject to timemodulated deformations [33][34][35], where emergent electromagnetic fields can appear. Originated from the dynamical change of magnetization or the lattice structures, the controllability of pseudo-fields in these contexts is limited, and the modulation timescale is typically slow, where the Faraday's Law of induction suggests a small pseudo-electric field.…”

Thermal transport, geometry, and anomalies

“…Nevertheless anomalies related to these gauge fields have been described and the anomalous coefficients are contained in equations (80). In certain materials, typically those with pseudo-relativistic dispersion relations, the variation of microscopic material parameters, like the hopping, in space or time leads to the emergence of effective, axial pseudo-gauge fields [29,33,[155][156][157][158]. One of the most studied examples are the elastic axial gauge fields created by straining graphene, a 2D material with low-energy Dirac quasi-particles.…”

“…In this section we briefly review the emergence of axial pseudo-gauge fields in condensed matter and the new anomaly-induced transport phenomena that these fields can induce in Dirac and Weyl semimetals. We refer the interested reader to the focused reviews on axial gauge fields in 2D-materials [155] and 3D Weyl semimetals [33,158].…”

“…Refs [172][173][174][175][176][177][178][179][180][181][182][183]. For an in-depth discussion of these issues we refer the reader to the focused reviews [33,158]. It is important to keep in mind that these fields must average to zero over a finite sample, which at times complicates their interpretation in lattice models [142].…”