Determining the underlying Fermi surface of strongly correlated superconductors

Abstract

The notion of a Fermi surface (FS) is one of the most ingenious concepts developed by solid-state physicists during the past century. It plays a central role in our understanding of interacting electron systems. Extraordinary efforts have been undertaken, by both experiment and theory, to reveal the FS of the high-temperature superconductors, the most prominent class of strongly correlated superconductors. Here, we discuss some of the prevalent methods used to determine the FS and show that they generally lead to erroneous results close to half-filling and at low temperatures, because of the large superconducting gap (pseudogap) below (above) the superconducting transition temperature. Our findings provide a perspective on the interplay between strong correlations and superconductivity and highlight the importance of strong coupling theories for the characterization and determination of the underlying FS in angle-resolved photoemission spectroscopy experiments.strong correlation ͉ renormalized mean-field theory ͉ high-temperature superconductors D uring the last decade, angle-resolved photoemission spectroscopy (ARPES) has emerged as a powerful tool (1, 2) for studying the electronic structure of the high-temperature superconductor (HTSC) (3). ARPES is a direct method for probing the Fermi surface (FS), the locus in momentum space where the one-electron excitations are gapless (4). However, because the low-temperature phase of the HTSC has a superconducting or pseudogap with d-wave symmetry, a FS can be defined only along the nodal directions or along the so-called Fermi arcs (1, 2, 5-7). The full ''underlying FS'' emerges only when the pairing interactions are turned off, either by a Gedanken experiment or by raising the temperature. Its experimental determination presents a great challenge because ARPES is more accurate at lower temperatures. Because the FS plays a key role in our understanding of condensed matter, it is important to know what is exactly measured by ARPES in a superconducting or a pseudogap state. The problem becomes even more acute in HTSC because of the presence of strong correlation effects (8 -11). Hence, it is desirable to examine a reference d-wave superconducting state with aspects of strong correlation built explicitly in its construction. Motivated by these considerations, we study the FS of a strongly correlated d-wave superconductor (8, 11) and discuss our results in the context of ARPES in HTSC. Fermi vs. Luttinger SurfaceWe begin by highlighting the differences between a FS and a Luttinger surface. The FS is determined by the poles of the one-electron Green's function (4). The Luttinger surface is defined as the locus of points in reciprocal space, where the one-particle Green's function changes sign (12). In the Fermi liquid state of normal metals, the Luttinger surface coincides with the FS. In a Mott-Hubbard insulator the Green's function changes sign because of a characteristic 1͞ divergence of the single-particle self-energy (13, 14) at momenta k of the noninteracting FS. In ...

Interaction-induced Fermi-surface renormalization in thet1−t2Hubbard model close to the Mott-Hubbard transition

“…In the insulating state, the underlying Fermi surface is given by the boundary of the occupied states of the renormalized dispersion relation, when the residual interactions giving rise to the charge gap are turned off in a Gedanken experiment. [5][6][7][8][9] Mathematically, the underlying Fermi surface is defined in a non Fermi-liquid state as the locus in k space where the real part of the oneparticle Green's function changes its sign. 5,10 By investigating magnetic and charge properties, we find that the Fermi surface reconstructs in a first-order manner right at the Mott transition.…”

“…[5][6][7][8][9] Mathematically, the underlying Fermi surface is defined in a non Fermi-liquid state as the locus in k space where the real part of the oneparticle Green's function changes its sign. 5,10 By investigating magnetic and charge properties, we find that the Fermi surface reconstructs in a first-order manner right at the Mott transition. In particular, the Fermi surface is generic, namely, non-nesting, in the metallic side, whereas it has perfect nesting properties in the insulating state, at the transition point.…”

Can One Determine the Underlying Fermi Surface in the Superconducting State of Strongly Correlated Systems?

“…We thank P. W. Anderson for sending us a copy of Ref. [31] while we were preparing this Letter. The results of Ref.…”

Charge order driven by Fermi-arc instability and its connection with pseudogap in cuprate superconductors

“…This electron momentum distribution is a quantity of great interest and its determination is very important, since EFS is also given by the set of k values for which n kσ shows a jump in discontinuity. When this discontinuity is smeared out, the gradient of n kσ , ∇n kσ , is assumed to be maximal at the locus of the underlying EFS 49 . In Fig.…”