Can one determine the underlying Fermi surface in the superconducting state of strongly correlated superconductors?

TL;DR

This paper investigates how to define the Fermi surface in superconductors of strongly correlated materials, showing that different definitions largely agree but all violate the Luttinger count due to spectral effects.

Contribution

It compares multiple Fermi surface definitions in superconducting states of strongly correlated systems, highlighting their limitations and the role of spectral weight and chemical potential renormalization.

Findings

Different Fermi surface definitions largely agree in superconductors.

All definitions violate the Luttinger count and do not enclose total electron density.

Spectral weight and chemical potential renormalization are key factors in this violation.

Abstract

The question of determining the underlying Fermi surface (FS) that is gapped by superconductivity (SC) is of central importance in strongly correlated systems, particularly in view of angle-resolved photoemission experiments. Here we explore various definitions of the FS in the superconducting state using the zero-energy Green's function, the excitation spectrum and the momentum distribution. We examine (a) d-wave SC in high Tc cuprates, and (b) the s-wave superfluid in the BCS-BEC crossover. In each case we show that the various definitions agree, to a large extent, but all of them violate the Luttinger count and do not enclose the total electron density. We discuss the important role of chemical potential renormalization and incoherent spectral weight in this violation.