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arXiv:1605.05004 · Physical review. B./Physical review. B

Hidden-fermion representation of self-energy in pseudogap and superconducting states of the two-dimensional Hubbard model

志朗 酒井, Marcello Civelli, Masatoshi Imada

Published Sep 13, 2016• 28 citations
arXivHTMLPDF

Abstract

We study the frequency-dependent structure of electronic self-energy in the pseudogap and superconducting states of the two-dimensional Hubbard model. We present the self-energy calculated with the cellular dynamical mean-field theory systematically in the space of temperature, electron density, and interaction strength. We show that the low-frequency part of the self-energy is well represented by a simple equation, which describes the transitions of an electron to and from a hidden-fermionic state. By fitting the numerical data with this simple equation, we determine the parameters characterizing the hidden fermion and discuss its identity. The simple expression of the self-energy offers a way to organize numerical data of these uncomprehended superconducting and pseudogap states, as well as a useful tool to analyze spectroscopic experimental results. The successful description by the simple two-component fermion model supports the idea of ``dark'' and ``bright'' fermions emerging from a bare electron as bistable excitations in doped Mott insulators.

DOI
10.1103/physrevb.94.115130

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We study the frequency-dependent structure of electronic self-energy in the pseudogap and superconducting states of the two-dimensional Hubbard model. We present the self-energy calculated with the cellular dynamical mean-field theory systematically in the space of temperature, electron density, and interaction strength. We show that the low-frequency part of the self-energy is well represented by a simple equation, which describes the transitions of an electron to and from a hidden-fermionic state. By fitting the numerical data with this simple equation, we determine the parameters characterizing the hidden fermion and discuss its identity. The simple expression of the self-energy offers a way to organize numerical data of these uncomprehended superconducting and pseudogap states, as well as a useful tool to analyze spectroscopic experimental results. The successful description by the simple two-component fermion model supports the idea of dark'' and bright'' fermions emerging from a bare electron as bistable excitations in doped Mott insulators.
The dynamics of a microscopic cuprate model, namely, the two-dimensional Hubbard model, is studied with a cluster extension of the dynamical mean-field theory. We find a nontrivial structure of the frequency-dependent self-energies, which describes an unprecedented interplay between the pseudogap and superconductivity. We show that these properties are well described by quasiparticles hybridizing with (hidden) fermionic excitations, emergent from the strong electronic correlations. The hidden fermion enhances superconductivity via a mechanism distinct from a conventional boson-mediated pairing, and originates the normal-state pseudogap. Though the hidden fermion is elusive in experiments, it can solve many experimental puzzles.
We review nonperturbative numerical calculations on dynamical properties of the two-dimensional Hubbard model and their relevance to various spectroscopic experiments on high-temperature superconducting cuprates. The unbiased nonperturbative theories have revealed the existence of a self-energy singularity in slightly doped Mott insulators, which is responsible for both the pseudogap formation and high-temperature superconductivity. The self-energy pole traces back to the Mott gap at zero doping, underscoring that Mott physics lies at the heart of both the pseudogap and high-temperature superconductivity. This mechanism of the pseudogap relies neither on competing order nor preformed pair while that of the high superconducting transition temperature does not necessitate a bosonic glue to mediate Cooper pairing. Instead, both mechanisms are linked to the singular self-energy inherent to the Mott insulator. The presence of the self-energy pole accounts for various spectroscopic anomalies reported so far in experiments, deforming the spectral structure in a manner beyond a simple mass renormalization. The low-energy electron dynamics, as computed with the self-energy pole, suggest the existence of a hidden fermionic excitation coupling to quasiparticles.
We study the attractive Hubbard model within the dynamical mean-field theory, to elucidate how the pseudogap and superconductivity at strong attractive interaction are related to those found in the repulsive Hubbard model, and thereby to bridge cold fermions and cuprate high-temperature superconductors from a microscopic point of view. We propose that a unified understanding is obtained by investigating single-particle excitation dynamics, in which emergent and hidden fermions coupled to quasiparticles consistently account for the numerical results in both attractive and repulsive cases. In the attractive case, the quasiparticle dynamics is observable by virtually breaking a tightly bound pair, where we find two qualitatively different regions crossing over each other within the strong-coupling superconductivity phase. Among them, the region close to the critical temperature shares characteristic dynamics with the repulsive interaction case, where the normal and anomalous parts of the self-energy show strong low-energy peaks while they are hidden in the quasiparticle spectral weight. These prominent self-energy peaks are understood by the coupling of the quasiparticle to the hidden fermionic excitation, emergent from a strong-coupling effect. The pseudogap above the critical temperature is also accounted for by the same hidden fermion.
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.
The frequency dependence of the superconducting gap function represents the dynamics of the electrons forming the Cooper pairs. Bearing the high-temperature superconducting cuprates in mind, we calculate the superconducting gap function in the two-dimensional Hubbard model by means of a cluster extension of the dynamical mean-field theory. We scrutinize the frequency dependence and its change with temperature, doping concentration and interaction strength. The calculated superconducting gap function shows various different behaviors from the anomalous self-energy, owing to a strong frequency dependence of the normal self-energy. The calculated results also suggest that the superconductivity is stronger when the interaction strength is as large as or slightly smaller than the bare band width and is suppressed for larger interactions.
The effect of doping in the two-dimensional Hubbard model is studied within finite-temperature exact diagonalization combined with cluster dynamical mean-field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green's function onto $2\ifmmode\times\else\texttimes\fi{}2$ clusters, a considerably more accurate description of the low-frequency properties of the self-energy is achieved than in a pure site picture. To evaluate the phase diagram, the transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest-neighbor hopping, and temperature. The self-energy component ${\ensuremath{\Sigma}}_{X}$ associated with $X=(\ensuremath{\pi},0)$ is shown to develop a collective mode above EF{E}_{F}EF​, whose energy and strength exhibits a distinct dispersion with doping. This low-energy excitation gives rise to non-Fermi-liquid behavior as the hole doping decreases below a critical value ${\ensuremath{\delta}}_{c}$, and to an increasing particle-hole asymmetry, in agreement with recent photoemission data. This behavior is consistent with the removal of spectral weight from electron states above EF{E}_{F}EF​ and the opening of a pseudogap, which increases with decreasing doping. The phase diagram reveals that ${\ensuremath{\delta}}_{c}\ensuremath{\approx}0.15\dots{}0.20$ for various system parameters. For electron doping, the collective mode of ${\ensuremath{\Sigma}}_{X}(\ensuremath{\omega})$ and the concomitant pseudogap are located below the Fermi energy, which is consistent with the removal of spectral weight from the hole states just below EF{E}_{F}EF​. The critical doping, which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.