Charge density waves beyond the Pauli paramagnetic limit in 2D systems

Two-dimensional materials are ideal candidates to host Charge Density Waves (CDWs) that exhibit paramagnetic limiting behavior, similar 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 ground state 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 for 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.