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

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-T c cuprates, and (b) the s-wave superfluid in the BCS-Bose-Einstein condensation (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. DOI: 10.1103/PhysRevLett.98.027004 PACS numbers: 74.25.Jb, 74.20.Fg, 74.72.ÿh, 74.90.+n The Fermi surface (FS), the locus of gapless electronic excitations in k-space, is one of the central concepts in theory of Fermi systems. In a Landau Fermi liquid at T 0, Luttinger [1] defined the FS in terms of the singleparticle Green's function G ÿ1 k; 0 0 and showed that it encloses the same volume as in the noninteracting system, equal to the fermion density n. In many Fermi systems of interest the ground state has a broken symmetry. Here we study states with superconducting (SC) long-range order, where there is no surface of gapless excitations, and ask the following question: Is there any way to define at T 0 the ''underlying Fermi surface'' that got gapped out by superconductivity?From a theoretical point of view, this question is of relevance to all superconductors irrespective of pairing symmetry or mechanism. The answers turn out to be of particular interest for strongly correlated superconductors, where the surprising effects that we find are large enough to be measured experimentally. Angle-resolved photoemission spectroscopy (ARPES) [2] has emerged as one of the most powerful probes of complex materials and has been extensively used to determine the FS in strongly correlated systems, often from data in the SC state [3,4]. One of our goals is to understand exactly what a T 0 measurement can tell us about the FS. This is especially important in the cuprates where the normal state must necessarily be studied at high temperatures and does not show sharp electronic excitations, expected in Fermi liquids, in contrast to the SC state which does show sharp Bogoliubov quasiparticles. Our results are also of interest for a completely different class of systems: strongly interacting Fermi atoms [5] in the BCS-Bose-Einstein condensation (BEC) crossover [6,7]. Here too the question of an underlying Fermi surface is of direct experimental relevance [8].In this Letter, we first show that Luttinger's original argument [1] cannot be generalized to the SC state, and this violation is related to broken gauge invariance [9]. We then explore various criteria for defining the ''underlying Fermi surface'' in the T 0 SC state, using...

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“…In this definition, p FS = p means that Luttinger's sum rule is fulfilled. 30 In LSCO, Luttinger's sum rule is approximately satisfied as shown in Fig. 1͑h͒ ͑Ref.…”

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

“…We would like to stress that the concept of an underlying Fermi surface is of central importance for the angular resolved photoemission spectroscopy ͑ARPES͒ studies of strongly correlated systems, like the high-temperature superconductors. [5][6][7][8] Note, that E q = ͱ ⑀ q 2 + ⌬ q 2 corresponds within renormalized meanfield theory 24 to the excitation spectrum of projected Bogoliubov quasiparticles and ⑀ q hence to the dispersion of the renormalized quasiparticles. Moreover, recent calculations on the t − J and the periodic Anderson models highlighted the possibility to assess the Fermi surface from the parametrization of a variational wave function.…”

“…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.…”

Fate of disorder-induced inhomogeneities in strongly correlated d-wave superconductors

“…The renormalization is easily rationalized; e.g., the electronic hopping is difficult due to the prohibition of double occupancy, whereas the effects of exchange interactions are enhanced due to a large number of singly occupied sites. The resulting model is solved within the framework of a renormalized mean-field theory [31,[47][48][49], which describes clean strongly correlated cuprates reasonably well [50,51].…”