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arXiv:cond-mat/9803126 · Physical Review Letters

Fermi Surface Evolution, Pseudogap, and Staggered Gauge Field Fluctuations in Underdoped Cuprates

Xi Dai, Zhao-Bin Su

Published Sep 7, 1998• 7 citations
arXivHTMLPDF

Abstract

In the context of the $t\ensuremath{-}J$ model, we show that besides the long wave length gauge field fluctuation, an additional low energy fluctuation, i.e., the staggered gauge field fluctuation, plays a crucial role in the underdoped regime. Including the staggered gauge field fluctuation, we calculate the spectral function. The line shape near $(\ensuremath{\pi},0)$ is very broad in the underdoped case and is quite sharp in the overdoped case. The quasiparticle peaks near $(0.5\ensuremath{\pi},0.5\ensuremath{\pi})$ are always very sharp in both cases. We also calculate the Fermi surface (FS) crossover from a small four-segment-like FS to a large continuous FS. The pseudogap extracted from the photoemission data can be also interpreted by our calculation.

DOI
10.1103/physrevlett.81.2136

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In the context of the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model, we show that besides the long wave length gauge field fluctuation, an additional low energy fluctuation, i.e., the staggered gauge field fluctuation, plays a crucial role in the underdoped regime. Including the staggered gauge field fluctuation, we calculate the spectral function. The line shape near (\ensuremathπ,0)(\ensuremath{\pi},0)(\ensuremathπ,0) is very broad in the underdoped case and is quite sharp in the overdoped case. The quasiparticle peaks near (0.5\ensuremathπ,0.5\ensuremathπ)(0.5\ensuremath{\pi},0.5\ensuremath{\pi})(0.5\ensuremathπ,0.5\ensuremathπ) are always very sharp in both cases. We also calculate the Fermi surface (FS) crossover from a small four-segment-like FS to a large continuous FS. The pseudogap extracted from the photoemission data can be also interpreted by our calculation.
The flux phase predicted by the $t\text{\ensuremath{-}}J$ model in the large-NNN limit exhibits features that make it a candidate for describing the pseudogap regime of cuprates. However, certain properties, such as, for instance, the prediction of well-defined quasiparticle peaks, speak against this scenario. We have addressed these issues by computing self-energy renormalizations in the vicinity of flux phase. The calculated spectral functions show features similar to those observed in experiments. At low doping, near the flux phase, the spectral functions are anisotropic on the Fermi surface and very incoherent near the hot spots. The temperature and doping evolution of self-energy and spectral functions are discussed and compared with the experiment.
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Pseudogap phenomena and the formation of Fermi arcs in underdoped cuprates are numerically studied in the presence of phase fluctuations that are simulated by an XYXYXY model. Most importantly the spectral function for each Monte Carlo sample is calculated directly and efficiently by the Chebyshev polynomials without having to diagonalize the fermion Hamiltonian, which enables us to handle a system large enough to achieve sufficient momentum/energy resolution. We find that the momentum dependence of the energy gap is identical to that of a pure ddd-wave superconductor well below the Kosterlitz-Thouless (KT) transition temperature (TKT)({T}_{\text{KT}})(TKT​) while displays an upturn deviation from $\text{cos}\text{ }{k}_{x}\ensuremath{-}\text{cos}\text{ }{k}_{y}$ with increasing temperature. An abrupt onset of the Fermi arcs is observed above TKT{T}_{\text{KT}}TKT​ and the arc length exhibits a similar temperature dependence to the thermally activated vortex excitations.
Recently a pseudogap with d-wave symmetry was observed near the Fermi level in photoemission spectra of normal-state Bi2{\mathrm{Bi}}_{2}Bi2​Sr2{\mathrm{Sr}}_{2}Sr2​CaCu2{\mathrm{CaCu}}_{2}CaCu2​O8{\mathrm{O}}_{8}O8​ crystals. We demonstrate that an analogous pseudogap exists in the energy spectrum of the two-dimensional t-J model of cuprate perovskites. In agreement with experiment the magnitude of the pseudogap is 10--20 meV in underdoped crystals with hole concentration x\ensuremath{\lesssim}0.17 and the pseudogap disappears in optimally and overdoped crystals when x\ensuremath{\gtrsim}0.17. We demonstrate also that in the t-J model the overall energy spectrum near the Fermi level and the Fermi surface agree well with experimental observations.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping which respects an SU(2)\mathrm{SU}(2)SU(2) symmetry---a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The electron spectral function shows small Fermi pockets at low doping which continuously evolve into the large Fermi surface at high doping concentrations.
A model with d-wave pairing symmetry is studied by employing a nonperturbative sum-rule approach. At low temperature the magnitude of a normal-state pseudogap shows strong $\stackrel{\ensuremath{\rightarrow}}{k}$ or angle dependence well fitted by $\mathrm{cos}2\ensuremath{\varphi}$ form. With increasing temperature, the pseudogap closes at some critical angle ${\ensuremath{\varphi}}_{c},$ and beyond this angle a single quasiparticlelike peak appears. The resulting Fermi surface is strongly temperature dependent. Both in the spectral function and the density of states, the pseudogap disappears in a manner that the spectral weight fills in the pseudogap instead of closing it with increasing temperature. All these features are qualitatively consistent with angle resolved photoemission spectroscopy for underdoped cuprates.