Unified treatment of Fermi pockets and arcs scenarios for the cuprates: Sum-rule-consistent response functions of the pseudogap

Abstract

Essential to understanding the cuprate pseudogap phase is a study of the charge (and spin) response functions, which we address here via a consistent approach to the Fermi arcs and the Fermi pockets scenario of Yang, Rice and Zhang (YRZ). The two schemes are demonstrated to be formally similar, and to share a common physics platform; we use this consolidation to address the inclusion of vertex corrections which have been omitted in YRZ applications. We show vertex corrections can be easily implemented in a fashion analytically consistent with sum rules and that they yield important contributions to most observables. A study of the charge ordering susceptibility of the YRZ scenario makes their simple physics evident: they represent the inclusion of charged bosonic, spin singlet degrees of freedom, and are found to lead to a double peak structure.The discovery of the high temperature superconductors has led to the development of extensions (as well as replacements) for BCS theory in which strong correlations or self energy effects are present simultaneously with the underlying pairing interactions which drive superconductivity. These self energy contributions are associated with the anomalous pseudogap behavior which sets in above T c and which may persist as well below the transition. A proper treatment of highly correlated normal and superconducting states introduces consistency constraints (vertex corrections, Ward identities and sum rules). This was central in the long history of BCS theory, where these constraints led to an understanding of new types of "particles" or excitations such as the Higgs boson and its related mechanism.In the high-T c cuprates, characterizing the spin and charge response has been essential for clarifying whether the pseudogap is associated with pairing or with an alternative ordering, although there is as yet no unanimity. 1,2A growing enthusiasm is emerging for one particular pairing-based approach to the pseudogap developed by Yang, Rice and Zhang (YRZ), 3 which suggests the possibility of charge ordering in the presence of pairing. 4Accompanying this interest has been a fairly universal neglect of vertex corrections 4,5 in the calculated response functions. This omission is not a formal technicality. At a minimum such corrections are essential in order to ensure that the normal phase is not associated with an unphysical Meissner effect.This leads to the goal of the present paper, which is to present a calculation of self consistent response functions for the YRZ theory of Fermi pockets 3 along with an alternative approach involving Fermi arcs. 2,6,7 We show here that these two approaches to the pseudogap are in fact closely related, sharing common physical features and allowing nearly identical calculations of vertex corrections. We also show that these vertex corrections are consistent with sum rule constraints. Finally, we demonstrate that introducing self consistency leads to (hitherto ignored 4,5 ) contributions to the spin and charge response, which are of sizable magnitude ...

Exact correlation functions in the cuprate pseudogap phase: Combined effects of charge order and pairing

“…Figure (1) shows that there is little difference in the spin dynamics between the approach of YRZ [7] and that of a d-wave pseudogap, emphasized earlier in a different context [33] and helps to explain the literature claims of successful reconciliation with the data that surround both scenarios [26,27,31].…”

Unified approach to electrical and thermal transport in high-$T_c$ superconductors

“…We note that in describing the pseudogap state many other fermionic models have been proposed [52]. Notable is the so-called Yang, Rice, Zhang (YRZ) [55] model, which contains a rather similar form for the fermionic Green's function [56] in Eq. ( 5.3) but with some important differences.…”

Gauge-invariant theories of linear response for strongly correlated superconductors

“…When Σ corr = 0, then Λ µ = 0, and the full vertex reduces to the known strict BCS case [18]. If we set ∆ sc = 0, then the full vertex also reduces to the known full vertex in the exotic normal state [23,24].…”

“…Theories which belong to this general class include the work of Refs. [23,24] along with additional theories such as that proposed in Ref. [3], Ref.…”

“…Above the transition temperature, in Refs. [23,24] the WTI was implemented for a number of different exotic normal phases, which led to a consistent framework for computing all vertex corrections. The challenge in the present paper is then to extend this body of work and formulate a gauge invariant theory below the transition temperature.…”