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Physical Review B

Microscopic approach to high-temperature superconductors within the t-J model

Steffen Sykora, K. W. Becker

Published Jul 14, 2009• 6 citations
Publisher

Abstract

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 ${T}_{c}$ 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 $d$-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.

DOI
10.1103/physrevb.80.014511

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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 \ensuremathω=0\ensuremath{\omega}=0\ensuremathω=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 \ensuremathω\ensuremath{\omega}\ensuremathω 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.
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.
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 TcT_cTc​, is still lacking. Starting from the ttt-JJJ model, we present a microscopic approach to the physical properties of the superconducting phase at moderate hole-doping in the framework of a novel renormalization scheme, called PRM. Our microscopic approach allows us to explain the experimental findings in the underdoped as well as in the optimal hole doping regime. In good agreement with experiments, we find no superconducting solutions for very small hole doping. In the superconducting phase, the order parameter turns out to have d-wave symmetry with a coherence length of a few lattice constants. The spectral function, obtained from angle-resolved photoemission spectroscopy (ARPES) along the Fermi surface, is also in good agreement with experiment: The spectra display peak-like structures which are caused alone by coherent excitations in a small range around the Fermi energy.
Abstract The spectral properties of the doped t – t ’ Hubbard model, using parameters typical for high-temperature cuprate superconductors, and the mechanism of d-wave pairing remain among the longstanding problems of many-body fermionic materials. We used a strong-coupling Green’s function expansion around a correlated reference system, namely a particle-hole-symmetric undoped Hubbard lattice with t′=0{t}^{{\prime} }=0t′=0 t ′ = 0 , which can be treated numerically exactly using sign-problem-free lattice Quantum Monte Carlo calculations. This reference system exhibits a large antiferromagnetic Mott-Hubbard-Slater gap in the electronic spectrum. We investigate how the Mott-like spectrum is reconstructed under finite doping and nonzero t′{t}^{{\prime} }t′ t ′ using a dual-fermion-inspired perturbation expansion. For a large next-nearest-neighbor hopping t′=−0.3t{t}^{{\prime} }=-0.3tt′=−0.3t t ′ = − 0.3 t , characteristic of cuprate families with T c around 100 K, the electronic spectral function reveals a strongly renormalized flat-band feature with a pseudogap near the antinodal point. The superconducting response of this system to a small dx2−y2{d}_{{x}^{2}-{y}^{2}}dx2−y2​ d x 2 − y 2 -like external field shows a pseudogap at the antinodal point in the normal part of the Nambu Green’s function, associated with “bad-fermion” behavior in the normal phase. At the same time, the anomalous Green’s function exhibits a d-wave-like structure with zero response at the nodal point of the Brillouin zone.
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.
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 ${T}^{*}\ensuremath{\sim}1.5{T}_{c}$.
Cuprate superconductors host ddd-wave superconductivity (SC), a pseudogap (PG) with Fermi arcs and a strange metal (SM) with incoherent excitations and temperature-linear resistivity. These regimes emerge from the same doped Mott system but are usually described separately. Here a relative-momentum-local (RML) theory is constructed, with the exact spin-singlet Cooper representation of antiferromagnetic superexchange in the ttt-JJJ model serving as a common thread. Pair correlations organize the low-energy behaviour of this Cooper channel into phase-coherent static SC, phase-incoherent quasi-static PG and phase-incoherent dynamic SM. A static RML prescription yields an exactly solvable PG Hamiltonian with nodal electron poles, antinodal gaps, resolution-broadened Fermi arcs and gapless charge-2e2e2e Cooper surfaces. A Cooper-surface Lifshitz transition generates logarithmic enhancements in the specific-heat coefficient and charge response without a spin singularity. The particle-particle continuum at finite centre-of-mass momentum produces Ohmic damping, while a dynamic RML prescription yields a one-loop self-energy with marginal-Fermi-liquid scaling. Spectral-weight transfer in the physical pair spectrum diagnoses the PG--SM crossover, whereas nonzero phase stiffness and global phase coherence identify SC. The RML theory relates single-particle, pair-sensitive and thermodynamic probes to three infrared organizations of one Cooper channel. A decisive experimental signature would be zero-energy Cooper-surface ridges in two-electron angle-resolved photoemission spectroscopy (2e-ARPES).