Charge Density Waves beyond the Pauli paramagnetic limit in 2D systems

TL;DR

This paper develops a generalized mean-field theory to explore how charge density waves in 2D materials can persist beyond the Pauli limit under strong magnetic fields, revealing complex high-field phases including modulated CDWs and coexistence with SDWs.

Contribution

It introduces a comprehensive theoretical framework for CDWs under Zeeman fields, accounting for incommensurability, imperfect nesting, and temperature effects, and predicts new high-field phases.

Findings

Discovery of a $q$-modulated CDW phase analogous to FFLO at high fields.

Identification of a stable CDW+SDW coexistence phase below the Pauli limit.

Prediction that CDWs can survive beyond the Pauli limit without fragile FFLO states.

Abstract

Two-dimensional materials are ideal candidates to host Charge density waves (CDWs) that exhibit paramagnetic limiting behavior, similarly to the well known case of superconductors. Here we study how CDWs in two-dimensional systems can survive beyond the Pauli limit when they are subjected to a strong magnetic field by developing a generalized mean-field theory of CDWs under Zeeman fields that includes incommensurability, imperfect nesting and temperature effects and the possibility of a competing or coexisting Spin density wave (SDW) order. Our numerical calculations yield rich phase diagrams with distinct high-field phases above the Pauli limiting field. For perfectly nested commensurate CDWs, a $q$-modulated CDW phase that is completely analogous to the superconducting Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase appears at high-fields. In the more common case of imperfect nesting, the commensurate CDW groundstate undergoes a series of magnetic-field-induced phase transitions first into a phase where commensurate CDW and SDW coexist and subsequently into another phase where CDW and SDW acquire a $q$-modulation that is however distinct from the pure FFLO CDW phase. The commensurate CDW+SDW phase occurs for fields comparable to but less than the Pauli limit and survives above it. Thus this phase provides a plausible mechanism for the CDW to survive at high fields without the need of forming the more fragile FFLO phase. We suggest that the recently discovered 2D materials like the transition metal dichalcogenides offer a promising platform for observing such exotic field induced CDW phenomena.