Determining the underlying Fermi surface of strongly correlated superconductors

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, both by experiment and by theory, to reveal the FS of the high temperature superconductors (HTSC), the most prominent strongly correlated superconductors. Here, we discuss some of the prevalent methods used to determine the FS and show that they lead generally to erroneous results close to half filling and at low temperatures, due to 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 as well as the determination of the underlying FS in ARPES experiments

Proposal for an Experiment to Test a Theory of High Temperature Superconductors

A theory for the phenomena observed in Copper-Oxide based high temperature superconducting materials derives an elusive time-reversal and rotational symmetry breaking order parameter for the observed pseudogap phase ending at a quantum-critical point near the composition for the highest $T_c$. An experiment is proposed to observe such a symmetry breaking. It is shown that Angle-resolved Photoemission yields a current density which is different for left and right circularly polarized photons. The magnitude of the effect and its momentum dependence is estimated. Barring the presence of domains of the predicted phase an asymmetry of about 0.1 is predicted at low temperatures in moderately underdoped samples.Comment: latex, 2 figure

Photoemission Evidence for a Remnant Fermi Surface and d-Wave-Like Dispersion in Insulating Ca2CuO2Cl2

An angle resolved photoemission study on Ca2CuO2Cl2, a parent compound of high Tc superconductors is reported. Analysis of the electron occupation probability, n(k) from the spectra shows a steep drop in spectral intensity across a contour that is close to the Fermi surface predicted by the band calculation. This analysis reveals a Fermi surface remnant even though Ca2CuO2Cl2 is a Mott insulator. The lowest energy peak exhibits a dispersion with approximately the |cos(kxa)-cos(kya)| form along this remnant Fermi surface. Together with the data from Dy doped Bi2Sr2CaCu2O(8 + delta) these results suggest that this d-wave like dispersion of the insulator is the underlying reason for the pseudo gap in the underdoped regime.Comment: 9 pages, including 7 figures. Published in Science, one figure correcte

The electronic specific heat in the pairing pseudogap regime

When pairing correlations in a quasi two dimensional electron system induce a pseudogap in the single particle density of states, the specific heat must also contain a sizeable pair contribution. The theoretically calculated specific heat for such a system is compared to the experimental results of Loram and his collaborators for underdoped YBa_2Cu_3O_{6+x} and La_{2-x}Sr_{x}CuO_4 samples. The size and doping dependence of the extracted pseudogap energy scale for both materials is comparable to the values obtained from a variety of other experiments.Comment: 4 pages, 5 eps figure

Normal-state magnetic susceptibility in a bilayer cuprate

The magnetic susceptibility of high-T_c superconductors is investigated in the normal state using a coupled bilayer model. While this model describes in a natural way the normal-state pseudogaps seen in c-axis optical conductivity on underdoped samples, it predicts a weakly increasing susceptibility with decreasing temperature and cannot explain the magnetic pseudogaps exhibited in NMR measurements. Our result, together with some experimental evidence suggest that the mechanism governing the c-axis optical pseudogap is different from that for the $a-b$ plane magnetic pseudogap.Comment: 5 pages, 2 figure

Impurity-induced moments in underdoped cuprates

We examine the effect of a nonmagnetic impurity in a two-dimensional spin liquid in the spin-gap phase, employing a drone-fermion representation of spin-1/2 operators. The properties of the local moment induced in the vicinity of the impurity are investigated and an expression for the nuclear-magnetic- resonance Knight shift is derived, which we compare with experimental results. Introducing a second impurity into the spin liquid an antiferromagnetic interaction between the moments is found when the two impurities are located on different sublattices. The presence of many impurities leads to a screening of this interaction as is shown by means of a coherent-potential approximation. Further, the Kondo screening of an impurity-induced local spin by charge carriers is discussed.Comment: 8 pages, 1 figure. To be published in Phys. Rev. B, Vol. 56, No. 1

Truncation of a 2-dimensional Fermi surface due to quasiparticle gap formation at the saddle points

We study a two-dimensional Fermi liquid with a Fermi surface containing the saddle points $(\pi,0)$ and $(0,\pi)$. Including Cooper and Peierls channel contributions leads to a one-loop renormalization group flow to strong coupling for short range repulsive interactions. In a certain parameter range the characteristics of the fixed point, opening of a spin and charge gap and dominant pairing correlations are similar to those of a 2-leg ladder at half-filling. An increase of the electron density we argue leads to a truncation of the Fermi surface with only 4 disconnected arcs remaining.Comment: Reference added. RevTeX 4 pages incl. 4 ps file

Evolution of the Fermi surface with carrier concentration in Bi_2Sr_2CaCu_2O_{8+\delta}

We show, by use of angle-resolved photoemission spectroscopy, that underdoped Bi_2Sr_2CaCu_2O_{8+\delta} appears to have a large Fermi surface centered at (\pi,\pi), even for samples with a T_c as low as 15 K. No clear evidence of a Fermi surface pocket around (\pi/2,\pi/2) has been found. These conclusions are based on a determination of the minimum gap locus in the pseudogap regime T_c < T < T^*, which is found to coincide with the locus of gapless excitations in momentum space (Fermi surface) determined above T^*. These results suggest that the pseudogap is more likely of precursor pairing rather than magnetic origin.Comment: 4 pages, revtex, 4 postscript color figure

Coherent quasiparticle weight and its connection to high-T_c superconductivity from angle-resolved photoemission

In conventional superconductors, the pairing energy gap (\Delta) and superconducting phase coherence go hand-in-hand. As the temperature is lowered, both the energy gap and phase coherence appear at the transition temperature T_c. In contrast, in underdoped high-T_c superconductors (HTSCs), a pseudogap appears at a much higher temperature T^*, smoothly evolving into the superconducting gap at T_c. Phase coherence on the other hand is only established at T_c, signaled by the appearance of a sharp quasiparticle (QP) peak in the excitation spectrum. Another important difference between the two types of superconductors is in the ratio of 2\Delta / T_c=R. In BCS theory, R~3.5, is constant. In the HTSCs this ratio varies widely, continuing to increase in the underdoped region, where the gap increases while T_c decreases. Here we report that in HTSCs it is the ratio z_A\Delta_m/T_c which is approximately constant, where \Delta_m is the maximum value of the d-wave gap, and z_A is the weight of the coherent excitations in the spectral function. This is highly unusual, since in nearly all phase transitions, T_c is determined by an energy scale alone. We further show that in the low-temperature limit, z_{\it A} increases monotonically with increasing doping x. The growth is linear, i.e. z_A(x)\propto x, in the underdoped to optimally doped regimes, and slows down in overdoped samples. The reduction of z_A with increasing temperature resembles that of the c-axis superfluid density.Comment: 11 pages, 5 figures, revised versio

Non-interacting Cooper pairs inside a pseudogap

I present a simple analytical model describing the normal state of a superconductor with a pseudogap in the density of states, such as in underdoped cuprates. In nearly two-dimensional systems, where the superconducting transition temperature is reduced from the mean-field BCS value, Cooper pairs may be present as slow fluctuations of the BCS pairing field. Using the self-consistent T-matrix (fluctuation exchange) approach I find that the fermion spectral weight exhibits two BCS-like peaks, broadened by fluctuations of the pairing field amplitude. The density of states becomes suppressed near the Fermi energy, which allows for long-lived low-energy Cooper pairs that propagate as a sound-like mode with a mass. A self-consistency requirement, linking the width of the pseudogap to the intensity of the pairing field, determines the pair condensation temperature. In nearly two-dimensional systems, it is proportional to the degeneracy temperature of the fermions, with a small prefactor that vanishes in two dimensions.Comment: LaTeX (prbbib.sty included), 24 pages, 4 PostScript figures To appear in Phys.Rev.