Pseudo-electromagnetic fields in 3D topological semimetals

Abstract

Dirac and Weyl semimetals, materials where electrons behave as relativistic fermions, react to position-and time-dependent perturbations, such as strain, as if emergent electromagnetic fields were applied. Since they differ from external electromagnetic fields in their symmetries and phenomenology they are called pseudo-electromagnetic fields, and enable a simple and unified description of a variety of inhomogeneous systems involving topological semimetals. We review the different physical ways to create effective pseudo-fields, their observable consequences as well as their similarities and differences compared to electromagnetic fields. Among these difference is their effect on quantum anomalies, the absence of a classical symmetry in the quantum theory, which we revisit from a quantum field theory and a semiclassical viewpoint. We conclude with predicted observable signatures of the pseudo-fields and the nascent experimental status. * All authors contributed equally to the preparation of this review arXiv:1903.11088v1 [cond-mat.mes-hall]

Chiral Hall effect in strained Weyl semimetals

“…We note that the group velocity is independent of the chirality, i.e. both modes are right-moving in a bulk in contrast to applying a real magnetic field where each mode disperses oppositely [14,15].…”

“…Strain, on the other hand, couples to the low-energy electronic sector through the elastic gauge fields [13][14][15]. The general form of the axial gauge potential induced by lattice distortion can be described by the displacement vector u:…”

“…If the axial four-vector b µ , in other words, varies smoothly in space and time, the axial-or psedogauge fields A µ 5 emerges in the low-energy Hamiltonian couples with electrons. Since b µ varies over the whole sample the average of its corresponding pseudomagnetic filed (B 5 ) vanishes [14,15,19]. Recently it has been predicted that electron-phonon coupling in systems with time-reversal symmetry breaking leads to the nonzero Hall viscosity [13,20,21].…”

“…The anomalous transport induced by axial fields or axial chemical potential has been studied to gain much attention [30] more recently. In addition to the chiral magnetic effect (CME) induced by chirality imbalance between two nodes [11,31], chiral pseudo magnetic effect [14], chiral torsional effect [15], and visco-Hall current [21] can be induced in strained Weyl semimetals owing to the presence of the pseudomagnetic and pseudoelectric fields. In this paper, we discuss a generation of a transverse chiral Hall current (CHE) [32,33] induced by the pseudomagnetic field.…”

Bulk-boundary quantum oscillations in inhomogeneous Weyl semimetals

“…Therefore, this position-dependent Weyl node separation and, as a result, bulk strain leads to intrinsic pseudo-magnetic fields. We note however, that unlike in the case of regular magnetic field, p 0 is not a gauge-dependent quantity as it is directly observable as a bandstructure parameter [37]. The pseudo-magnetic field breaks the linear Dirac spectrum around each node into Landau levels, with a dispersion relation…”