Phase shifts, band geometry and responses in triple-Q charge and spin density waves

TL;DR

This paper explores how phase shifts in triple-Q charge and spin density waves influence electronic band structures and responses, revealing nontrivial band geometry and potential for novel electronic phenomena.

Contribution

It systematically investigates the effects of phase shifts in triple-Q density waves on band geometry and electronic responses, highlighting their significance in material properties.

Findings

Phase shifts induce nontrivial band geometry at hot spots.

Interference effects alter electronic states near the Fermi energy.

Symmetry-breaking from phase shifts leads to unique linear and nonlinear responses.

Abstract

Triple-Q density waves are commonly found in various materials, such as charge density waves in transition metal dichalcogenides and spin density waves (skyrmion crystals) in B20 compounds. Compared to single-Q density waves, triple-Q density waves possess an additional internal degree of freedom-a phase shift arising from the phase of the order parameters, in addition to the translations of the density waves. In this study, we systematically investigate the significant effects stemming from both triple-Q CDW and SDW order parameters, with particular emphasis on potential phase shifts. We demonstrate that these phase shifts play a crucial role in influencing the interference effects of triple-Q density waves on electronic states. Due to such interference, the band geometry in the momentum space becomes nontrivial at the hot spots, where multiband Dirac-like fermions are induced near the Fermi energy. Furthermore, we explicitly establish that the nontrivial band geometry, combined with symmetry-breaking induced by phase shifts, leads to a variety of intriguing linear and nonlinear responses.