Critical Density-Wave Vestigial Phases of Commensurate Pair Density Wave

TL;DR

This paper investigates the vestigial phases of 2D commensurate pair-density-wave states, revealing complex phase transitions including charge-density-wave and critical phases, through theoretical modeling and simulations.

Contribution

It systematically studies the vestigial phases of commensurate PDW, including phase diagrams and critical phenomena, using Ginzburg-Landau theory, RG, and Monte Carlo methods.

Findings

Existence of charge-4e/2e superconductivity for n≤4

Discovery of a two-step transition process for n≥5

Identification of critical vestigial phases with power-law correlations

Abstract

The pair-density-wave (PDW) is an exotic pairing state hosting a spatially modulated pairing order parameter, which has attracted great interest. Due to its simultaneously breaking U(1)-gauge and translational symmetries, intriguing vestigial phases which restore only one broken symmetry can emerge at an intermediate temperature regime. Previously, investigations on the vestigial phases of PDW were mainly focused on incommensurate PDW. However, the experimentally observed PDW is usually commensurate, whose vestigial phases have not been systematically investigated. Here we study the vestigial phases of 2D commensurate PDW with $n$-times expanded unit vectors, hosting different numbers of wave vectors. Based on the Ginzburg-Landau theory, we get the low energy effective model Hamiltonian. Subsequent renormalization group (RG) and Monte-Carlo (MC) studies are conducted to obtain the phase diagram and spatial dependent correlation functions. Our RG and MC calculations consistently yield the following result. For $n\le 4$, besides the charge-4e/2e superconductivity, there exists the translational symmetry broken charge-density-wave (CDW) vetigial phase. Intriguingly, for $n\ge 5$, the restore of the translational symmetry with increasing temperature is realized through two successive Berezinskii-Kosterlitz-Thouless transitions. Such a two-step process leads into two critical vestigial phases, i.e. the critical-PDW and the critical-CDW phases, in which the discrete translational symmetry is quasily broken, leading into a power-law decaying density-density correlation even at 2D. Our work appeals for experimental verifications.