Holographic Charge Density Waves

We discuss a gravity dual of a charge density wave consisting of a U(1) gauge field and two scalar fields in the background of an AdS$_4$ Schwarzschild black hole together with an antisymmetric field (probe limit). Interactions drive the system to a phase transition below a critical temperature. We numerically compute the ground states characterized by modulated solutions for the gauge potential corresponding to a dynamically generated unidirectional charge density wave in the conformal field theory. Signatures of the holographic density waves are retrieved by studying the dynamical response to an external electric field. We find that this novel holographic state shares many common features with the standard condensed matter version of charge density wave systems.Comment: 5 pages, 2 figures; improved discussion, published versio

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, 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.Comment: 9 pages, 2 figures, preprint versio