The electronic structure of the pair-density-wave (PDW) superconductor in the cuprates

Pair density waves (PDWs) are a inhomogeneous superconducting states whose Cooper pairs possess a finite center-of-mass-momentum, ±Qi, resulting in a oscillatory gap in space in the ith directiond. In other words, the PDW order parameter is a Fourier expansion of the superconducting order with non trivial harmonics at ±Qi. As a result, multiple global U (1)-symmetries can be broken by this state resulting in a richer set of topological defects than that seen in conventional superconductors. Here I study the electronic structure of the topological defects of the PDW state, paying special attention to the half-vortex and its electronic structure that can be detected in scanning-tunneling-microscopy (STM) experiments. There is a growing body of evidence for the existence of PDW superconducting order in many strongly correlated materials in the absence of any external magnetic field, particularly in the cuprate superconductors. A crucial feature of the PDW state that reconciles certain aspects of the cuprates phenomenology is that inherently it has a charge-density-wave (CDW) as a composite order parameter associated with it. The view point of this thesis will be theses two orders are intertwined, the PDW giving birth to the daughter CDW. Many aspects of the cuprate phase diagram suggest a unidirectional PDW order parameter maybe be at play in the 2D CuO2 planes, motivating me to adopted the following ansatz : Qx̸ = 0 and Qy = 0. An effective microscopic theory will be forged by embedding the PDW order parameter into a Bogoliubov-de Gennes (BdG) Hamiltonian with whom I will compute various spectroscopic properties pertaining to the electronic structure of the PDW’s topological defects. Using the excitation spectrum of the BdG Hamiltonian I will discuss tell-tale signatures of the half-vortex in violations of inversion symmetry. The topography of the “Fermi surface” of the Bogoliubov quasiparticles will be covered for various PDW phases and a brief discussion of quasiparticle interference (QPI) and its role in modulating the dynamic charge-density. The cuprate phenomenology suggests that the PDW order coexists with a uniform d-wave superconductor, which is ordinarily dominate. Building on the analysis of the isolated PDW phase the case of coexisting uniform and PDW superconducting orders will be considered for a defect free state and in the presence of a half-vortex. An isolated half-vortex is no longer stable in the presence costing orders costing a linear divergent string energy, opposed to the more tame logarithmic divergence, resulting in a confined half-vortex anti-half-vortex pair. This confining potential acts along the branch cut put in the phase field of the half-vortex and arises from a quartic interaction in the Landau-Ginzburg expansion locking the coexisting superconducting phase fields together. A far field approximation will be adopted to illustrate the qualitative effects of the uniform order, paying special attention to this locking of phases. One immediate consequence of this is the uniform order inherits the half-flux quanta of the half-vortex. The spectroscopic properties will focus on the region of the half-vortex where the reconfigured electronic structure can be studied. Furthermore, the case of weak uniform order will be considered for coexistence with a half-vortex, but this restriction won’t be placed on the case of the pristine PDW. Coexistence gives birth to two daughter CDWs setting up additional interference patterns, due to both QPI and the mixing of Fourier harmonics from the presence of the defect. Many robust features remain in tact relative to the isolated phase, such as inversion symmetry breaking, but many new signatures arise. In particular, the possibility of time-reversal-symmetry (TRS) breaking is discussed for the half-vortex using signatures in the daughter CDWs to illustrate this. Various experimental signatures of the PDW will be proposed in relation to STM and angel-resolved-photo-emission (ARPES) as an attempt to aid in uncovering the mystery of high-temperature superconductivity in the cuprates.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Rosales, Marcus Ray

Contributors dc:contributor

• Fradkin, Eduardo H
• Stone, Michael
• Cooper, Lance
• Shelton, Jessie S

• N.A.

Statement dc:rights

• Copyright 2025 Marcus Rosales

Language dc:language

en

Handle dc:identifier

https://hdl.handle.net/2142/132566

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/132566