M. R. Norman

Destruction of the Fermi surface in underdoped high-Tc superconductors

The Fermi surface—the set of points in momentum space describing gapless electronic excitations—is a central concept in the theory of metals. In this context, the normal ‘metallic’ state of the optimally doped high-temperature superconductors is not very unusual: above the superconducting transition temperature, Tc, there is evidence for a large Fermi surface, despite the absence of well-defined elementary excitations. In contrast, the normal state of underdoped high-temperature superconductors differs in that there is evidence for a ‘pseudogap’ above Tc (refs 4–6). Here we examine, using angle-resolved photoemission spectroscopy, the temperature dependence of the Fermi surface in underdoped Bi2Sr2CaCu2O8+δ. We find that, on cooling the sample, the pseudogap opens up at different temperatures for different points in momentum space. This leads to an initial breakup of the Fermi surface, at a temperature T *, into disconnected arcs, which then shrink with decreasing temperature before collapsing to the point nodes of the superconducting ground state below Tc. This unusual behaviour, where the Fermi surface does not form a continuous contour in momentum space as in conventional metals, is unprecedented in that it occurs in the absence of long-range order. Moreover, although the superconducting gap below Tc evolves smoothly into the pseudogap above Tc, the pseudogap differs in its unusual temperature-dependent anisotropy, implying an intimate but non-trivial relationship between the pseudogap and the superconducting gap.

Evolution of the pseudogap from Fermi arcs to the nodal liquid

The pseudogap phase in the cuprates is a most unusual state of matter: it is a metal, but its Fermi surface is broken up into disconnected segments known as Fermi arcs. Using angle resolved photoemission spectroscopy, we show that the anisotropy of the pseudogap in momentum space and the resulting arcs depend only on the ratio T/T*(x), where T*(x) is the temperature below which the pseudogap first develops at a given hole doping x. In particular, the arcs collapse linearly with T/T* and extrapolate to zero extent as T goes to 0. This suggests that the T = 0 pseudogap state is a nodal liquid, a strange metallic state whose gapless excitations are located only at points in momentum space, just as in a d-wave superconductor.

Electronic Spectra and Their Relation to the ( π,π) Collective Mode in High- Tc Superconductors

The photoemission line shape near (pi, 0) in Bi(2)Sr(2)CaCu(2)O(8+delta) below T(c) is characterized by a sharp peak, followed at higher energy by a dip and hump. We study the evolution of this line shape as a function of momentum, temperature, and doping. We find the hump scales with the peak and persists above T(c) in the pseudogap state. We present strong evidence that the peak-dip-hump structure arises from the interaction of electrons with a collective mode of wave vector (pi, pi). The inferred mode energy and its doping dependence agree well with a magnetic resonance observed by neutron scattering.

Superconducting Gap Anisotropy and Quasiparticle Interactions: A Doping Dependent Photoemission Study

Comparing photoemission measurements on Bi2212 with penetration depth data, we show that a description of the nodal excitations of the d-wave superconducting state in terms of noninteracting quasiparticles is inadequate, and we estimate the magnitude and doping dependence of the Landau interaction parameter which renormalizes the linear T contribution to the superfluid density. Furthermore, although consistent with d-wave symmetry, the gap with underdoping cannot be fit by the simple coskx 2 cosky form, which suggests an increasing importance of long range interactions as the insulator is approached.

Evolution of the Fermi Surface with Carrier Concentration in Bi2Sr2CaCu2O8+δ

We show, by use of angle-resolved photoemission spectroscopy, that underdoped Bi2Sr2CaCu2O8+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.

Renormalization of spectral line shape and dispersion below Tc in Bi2Sr2CaCu2O8+delta.

Angle-resolved photoemission data in the superconducting state of Bi2Sr2CaCu2O8+delta show a kink in the dispersion along the zone diagonal, which is related via a Kramers-Krönig analysis to a drop in the low energy scattering rate. As one moves towards (pi,0), this kink evolves into a spectral dip. The occurrence of these anomalies in the dispersion and line shape throughout the zone indicates the presence of a new energy scale in the superconducting state.

Phenomenology of the low-energy spectral function in high-T-c superconductors

We introduce a simple phenomenological form for the self-energy which allows us to extract important information from angle resolved photoemission data on the high Tc superconductor Bi2212. First, we find a rapid suppression of the single particle scattering rate below Tc for all doping levels. Second, we find that in the overdoped materials the gap Delta at all k-points on the Fermi surface has significant temperature dependence and vanishes near Tc. In contrast, in the underdoped samples such behavior is found only at k-points close to the diagonal. Near (pi,0), Delta is essentially T-independent in the underdoped samples. The filling-in of the pseudogap with increasing T is described by a broadening proportional to T-Tc, which is naturally explained by pairing correlations above Tc.

PHENOMENOLOGICAL MODELS FOR THE GAP ANISOTROPY OF BI2SR2CACU2O8 AS MEASURED BY ANGLE-RESOLVED PHOTOEMISSION SPECTROSCOPY

Recently, high resolution angle-resolved photoemission spectroscopy has been used to determine the detailed momentum dependence of the superconducting gap in the high temperature superconductor Bi-2212. In this paper, we first describe tight binding fits to the normal state dispersion and superlattice modulation effects. We then discuss various theoretical models in light of the gap measurements. We find that the simplest model which fits the data is the anisotropic s-wave gap

Unusual Dispersion and Line Shape of the Superconducting State Spectra of Bi2Sr2CaCu2O8+δ

\cos(k_x)\cos(k_y)

Evidence for pairing above the transition temperature of cuprate superconductors from the electronic dispersion in the pseudogap phase.

, which within a one-band BCS frame- work suggests the importance of next near neighbor Cu-Cu interactions. Various alternative interpretations of the observed gap are also discussed, along with the implications for microscopic theories of high temperature superconductors.