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arXiv:cond-mat/0212101 · Physical Review Letters

Staggered Flux Fluctuations and the Quasiparticle Scattering Rate in the SU(2) Gauge Theory of the t−J Model

Carsten Honerkamp A, Patrick A. Lee

Published Jun 17, 2003• 7 citations
arXivHTMLPDF

Abstract

We study staggered flux fluctuations around the superconducting state of the SU(2) mean-field theory for the two-dimensional t-J model and their effect on the electron spectral function. The quasiparticle peaks near (pi,0),(0,pi) get strongly broadened and partially wiped out by these fluctuations while the quasiparticle peaks near the nodes of the d-wave gap are preserved over a wide parameter range. The strength of these effects is governed by an energy scale that decreases towards zero for doping x-->0 and that is related to the energy splitting between the SU(2)-related superconducting and staggered flux mean-field states.

DOI
10.1103/physrevlett.90.246402

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We study staggered flux fluctuations around the superconducting state of the SU(2) mean-field theory for the two-dimensional t-J model and their effect on the electron spectral function. The quasiparticle peaks near (pi,0),(0,pi) get strongly broadened and partially wiped out by these fluctuations while the quasiparticle peaks near the nodes of the d-wave gap are preserved over a wide parameter range. The strength of these effects is governed by an energy scale that decreases towards zero for doping x-->0 and that is related to the energy splitting between the SU(2)-related superconducting and staggered flux mean-field states.
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We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an 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 physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.
We study the stability of the staggered-flux phase in the t-J model away from half-filling using a systematic large-N slave-boson approach. Found below a critical doping concentration ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$=a(J/t)2{)}^{2})2, is a flux-density-wave instability with an incommensurability wave number \ensuremath{\sim}${\mathrm{\ensuremath{\delta}}}^{3/4}$. The instability towards a modulated-flux state is due to low-lying phase fluctuations of the valence bonds. When the doping parameter exceeds ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$, we find a fully gapped d-wave superconducting state due to residual quasiparticle interactions.
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.
A microscopical theory of electron spectrum and superconductivity within the two-dimensional $t\ensuremath{-}J$ model in paramagnetic state is proposed. By employing the projection technique for the Green functions in terms of the Hubbard operators self-consistent Eliashberg equations are derived. A strong coupling of electrons with spin and charge fluctuations due to exchange and kinematical interactions is obtained. In the normal state, one-electron spectral functions reveal narrow quasiparticle peaks close to the Fermi surface (FS) with an additional broad incoherent band. The FS changes from holelike at low doping to electronlike for hole concentrations $\ensuremath{\delta}>0.3.$ In the superconducting state we observe d-wave pairing with the maximal ${T}_{c}\ensuremath{\simeq}0.04t$ at optimal doping $\ensuremath{\delta}\ensuremath{\simeq}0.3.$
Cluster dynamical mean field methods are used to calculate the normal and anomalous components of the electron self-energy of the two-dimensional Hubbard model. Issues associated with the analytical continuation of the normal and anomalous parts of the gap function are discussed. Methods of minimizing the uncertainties associated with the pseudogap-related pole in the self-energy are discussed. From these the evolution of the superconducting gap and the momentum-dependent electron spectral function across the phase diagram are determined. In the pseudogap regime, decreasing the temperature into the superconducting state leads to a decrease in the energy gap and the formation of a ``peak-dip-hump'' structure in the electronic density of states. The peak feature disperses very weakly. The calculated spectral functions are in good qualitative agreement with published data. The mathematical origin of the behavior is found to be the effect of the superconductivity on the pole structure giving rise to the normal state pseudogap. In particular the ``hump'' feature is found to arise from a zero crossing of the real part of the electron self-energy rather than from an onset of scattering. The effect of superconductivity on the zone diagonal spectra is presented.