Axionic band topology in inversion-symmetric Weyl-charge-density waves

Abstract

In recent theoretical and experimental investigations, researchers have linked the low-energy field theory of a Weyl semimetal gapped with a charge-density wave (CDW) to high-energy theories with axion electrodynamics. However, it remains an open question whether a lattice regularization of the dynamical Weyl-CDW is in fact a single-particle axion insulator (AXI). In this Rapid Communication, we use analytic and numerical methods to study both lattice-commensurate and incommensurate minimal (magnetic) Weyl-CDW phases in the mean-field state. We observe that, as previously predicted from field theory, the two inversion (I)-symmetric Weyl-CDWs with φ = 0, π differ by a topological axion angle δθ φ = π. However, we crucially discover that neither of the minimal Weyl-CDW phases at φ = 0, π is individually an AXI; they are instead quantum anomalous Hall (QAH) and "obstructed" QAH insulators that differ by a fractional translation in the modulated cell, analogous to the two phases of the Su-Schrieffer-Heeger model of polyacetylene. Using symmetry indicators of band topology and non-Abelian Berry phase, we demonstrate that our results generalize to multiband systems with only two Weyl fermions, establishing that minimal Weyl-CDWs unavoidably carry nontrivial Chern numbers that prevent the observation of a static magnetoelectric response. We discuss the experimental implications of our findings and provide models and analysis generalizing our results to nonmagnetic Weyl-and Dirac-CDWs.

Dynamical Piezomagnetic Effect in Time-Reversal-Invariant Weyl Semimetals with Axionic Charge-Density Waves

“…This agrees with the picture presented in Ref. 71 , in which tuning φ 0 pumps 2D TI layers in the WTI phase until a layer reaches the system boundary, causing a surface gap closing. The same argument can also be applied to the (100) surface.…”

Cubic 3D Chern photonic insulators with orientable large Chern vectors

“…When we couple the Weyl nodes by a lattice commensurate modulation, we backfold the BZ into a region commensurate with the Weyl node separation vector, which is a reciprocal lattice vector in the folded BZ. The additivity of the Chern number then ensures that every plane in the reduced BZ carries a nonzero Chern number, resulting in a 3D CI when the gap is opened 30 . This expresses the fact that the Chern number density of our 3D system does not change as a function of the (TR-even) supercell modulation; it simply goes from being unquantized in the original system (necessitating the existence of Weyl points), to being a quantized multiple of a reciprocal lattice vector in the modulated system.…”

“…For example, considering that every planar cut parallel to the magnetization direction is capable of supporting anomalous surface states, it could be worth investigating what occurs at a 3D C y I/3D C z I planar interface. Similarly, owing to cubic symmetry of the 3D CI system, it would be possible to tune the relative angular phase in the supercell modulation in order to either break spatial inversion or not, which could lead to interesting surface states at the boundary of an obstructed atomic insulator (OAI) 3D CI and a 3D CI 30 . This may allow to develop of interesting photonic analogues of axionic responses 26 , 30 that we are investigating as part of a future work.…”

“…In this work, we propose a method to design cubic 3D topological photonic crystals where Chern vectors of any magnitude, sign or direction can be implemented at will. Our method is based on the merging and annihilation of Weyl points through multi-fold supercell modulations in three dimensions 30 . As a result, we obtain a 3D CI phase with the following characteristics: First, since the Chern number is additive with respect to band-folding over large supercells, the system can support arbitrarily large Chern numbers and thus the coexistence of multi-channel unidirectional surface states.…”

Band Engineering of Dirac Semimetals Using Charge Density Waves

“…Recently, CDWs have gained increased interest in the context of TSMs due to their distinct role in the formation of novel topological phases. [34][35][36][37][38] It is well established that CDWs can be induced by chemical substitution in LnSbTe systems. [32,39] Here, we show how these CDWs, in combination with non-symmorphic symmetry, can be utilized to design "clean" non-symmorphic DSMs: The CDW gaps out states within the BZ, while the non-symmorphic symmetry-enforced band crossings at the BZ boundary, which is at the Fermi level in LnSb x Te 2−x for certain values of x, is unaffected.…”