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arXiv:0910.0981 · Physical Review B

Modeling a striped pseudogap state

Mats Granath, Brian M. Andersen

Published Jan 4, 2010• 13 citations
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Abstract

We study the electronic structure within a system of phase-decoupled one-dimensional superconductors coexisting with stripe spin and charge-density-wave order. This system has a nodal Fermi surface (Fermi arc) in the form of a hole pocket and an antinodal pseudogap. The spectral function in the antinodes is approximately particle-hole symmetric contrary to the gapped regions just outside the pocket. We find that states at the Fermi energy are extended whereas states near the pseudogap energy have localization lengths as short as the interstripe spacing. We consider pairing which has either local $d$-wave or $s$-wave symmetry and find similar results in both cases, consistent with the pseudogap being an effect of local pair correlations. We suggest that this state is a stripe-ordered caricature of the pseudogap phase in underdoped cuprates with coexisting spin-, charge-, and pair-density-wave correlations. Lastly, we also model a superconducting state which (1) evolves smoothly from the pseudogap state, (2) has a signature subgap peak in the density of states, and (3) has the coherent pair density concentrated to the nodal region.

DOI
10.1103/physrevb.81.024501

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We study the electronic structure within a system of phase-decoupled one-dimensional superconductors coexisting with stripe spin and charge-density-wave order. This system has a nodal Fermi surface (Fermi arc) in the form of a hole pocket and an antinodal pseudogap. The spectral function in the antinodes is approximately particle-hole symmetric contrary to the gapped regions just outside the pocket. We find that states at the Fermi energy are extended whereas states near the pseudogap energy have localization lengths as short as the interstripe spacing. We consider pairing which has either local ddd-wave or sss-wave symmetry and find similar results in both cases, consistent with the pseudogap being an effect of local pair correlations. We suggest that this state is a stripe-ordered caricature of the pseudogap phase in underdoped cuprates with coexisting spin-, charge-, and pair-density-wave correlations. Lastly, we also model a superconducting state which (1) evolves smoothly from the pseudogap state, (2) has a signature subgap peak in the density of states, and (3) has the coherent pair density concentrated to the nodal region.
Electronic Green's function across the pseudogap to stripe transition in the ttt-t′t't′-JJJ model
Superconducting domes in strongly correlated electronic systems are often accompanied by charge density waves and peculiar features in the electronic structure. The appearance of a pseudogap, in particular, and its relation to charge density waves remains insufficiently understood. Here, we investigate the electronic Green's function of the underdoped ttt-t′t't′-JJJ model of the cuprate superconductors using tensor network algorithms for finite temperature dynamics on cylinders of width 444. We find the prominent momentum differentiation, the hallmark of the pseudogap, to be strongly dependent on t′t't′, which develops into a momentum-dependent opening of a gap upon decreasing temperature, consistent with the formation of a Fermi arc at intermediate temperatures. The nodal gap around k=(π/2,π/2){\bf k}=(π/2,π/2)k=(π/2,π/2) closes and fills with increasing temperature as coherent stripe order melts into a regime of fluctuating charge clusters.
Using an exact diagonalization method within the dynamical mean-field theory we analyze the stable stripe structures found in the two-dimensional Hubbard model doped by $0.03<\ensuremath{\delta}<0.2$ holes, and discuss a scenario for stripe melting. Our results demonstrate the importance of dynamical correlations which lead to the metallic stripes, in contrast to the Hartree-Fock picture. The spectral functions show a coexistence of the coherent quasiparticles (polaron band) close to the Fermi energy \ensuremath{\mu}, and incoherent states at lower energies. The quasiparticles in the polaron band depend on hole doping, and hybridize strongly with the partly filled mid-gap band within the Mott-Hubbard gap, induced by stripe order. This explains the origin of nondispersive quasiparticles close to the Fermi energy \ensuremath{\mu}, observed near the $X=(\ensuremath{\pi},0)$ and $Y=(0,\ensuremath{\pi})$ points for the samples with coexisting (10) and (01) stripes. We reproduce the gap which opens for charge excitations at the $S=(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ point, observed in the angle-resolved photoemission experiments for ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4},$ and a pseudogap in the integrated spectral density pinned to \ensuremath{\mu}. Finally, we show that large spectral weight close to $\ensuremath{\mu}$ moves from the X to the S point when the second neighbor hopping element increases, and the (01) stripe phase is destabilized by kink fluctuations.
Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors leading to an unprecedented high transition temperature Tc{T}_{c}Tc​ is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gaplike behavior on parts of the Fermi surface, leaving a nongapped segment known as Fermi arc around the diagonal of the Brillouin zone. Two main interpretations of the origin of the pseudogap have been proposed: either the pseudogap is a precursor to superconductivity, or it arises from another order competing with superconductivity. Starting from the t-J model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase as well as the superconducting phase in the framework of a renormalization scheme called projector-based renormalization method. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at renormalized ``free'' Hamiltonians for correlated electrons for both phases. Our microscopic approach allows us to explain the experimental findings in the underdoped as well as in the optimal hole doping regime. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: For the pseudogap phase we find well-defined excitation peaks around $\ensuremath{\omega}=0$ near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small $\ensuremath{\omega}$ range around the Fermi energy. In the superconducting phase, the order parameter turns out to have ddd-wave symmetry with a coherence length of a few lattice constants. In good agreement with experiments, we find no superconducting solutions for very small hole doping.
We conclusively show that a pseudogap state can arise at T>TcT>{T}_{c}T>Tc​, for reasonable pairing interaction strength, from order parameter fluctuations in a two-dimensional minimal model of ddd-wave superconductivity. The occurrence of the pseudogap requires neither strong correlation nor the presence of competing order. We study a model with attractive nearest-neighbor interaction and establish our result using a combination of a cluster-based Monte Carlo method for the order parameter field and a twisted-boundary scheme to compute the momentum-resolved spectral function. Apart from a dip in the density of states that characterizes the pseudogap, the momentum and frequency resolution on our effective lattice size $\ensuremath{\sim}160\ifmmode\times\else\texttimes\fi{}160$ allows two major conclusions: (i) at T<TcT<{T}_{c}T<Tc​, despite the presence of thermal phase fluctuations, the superconductor has only nodal Fermi points while all non-nodal points on the normal state Fermi surface show a two-peak spectral function with a dip at $\ensuremath{\omega}=0$, and (ii) for T>TcT>{T}_{c}T>Tc​, the Fermi points develop into arcs, characterized by a single quasiparticle peak, and the arcs connect up to recover the normal state Fermi surface at a temperature T∗>Tc{T}^{*}>{T}_{c}T∗>Tc​. We show the variation of Tc{T}_{c}Tc​ and T∗{T}^{*}T∗ with coupling strength and provide detailed spectral results at a coupling where ${T}^{*}\ensuremath{\sim}1.5{T}_{c}$.
Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gap-like behavior on parts of the Fermi surface, leaving a non-gapped segment known as Fermi arc around the diagonal of the Brillouin zone. Starting from the ttt-JJJ model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase in the framework of a novel renormalization scheme called PRM. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at a renormalized 'free' Hamiltonian for correlated electrons. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: We find well-defined excitation peaks around ω=0ω=0ω=0 near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small ωωω-range around the Fermi energy. In a subsequent paper, also the supercunducting phase at moderate hole doping will be discussed within the PRM approach.
We compute high-resolution angle-resolved photoemission spectroscopy of the Hubbard model using the unbiased determinant quantum Monte Carlo algorithm, revealing an asymmetry between electron and hole doping. Electron doping exhibits more coherent quasiparticles and stronger antiferromagnetic correlations compared to hole doping. At low doping, a nodal-antinodal dichotomy on the Fermi surface is observed, similar to cuprate experiments. The dichotomy reflects the momentum dependence of the Mott gap, as manifested in both the spectral function and the self-energy. For hole doping, we observe a transition towards the pseudogap, without signature of pocket formation. The simulated nuclear magnetic resonance pseudogap temperatures do not necessarily agree with the temperature determined by spectroscopy. These findings collectively suggest the pseudogap is a smooth crossover driven by strong correlations.