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Journal of Physics Conference Series

Frequency-dependent structure of superconducting gap function in two-dimensional Hubbard model

志朗 酒井

Published Jul 1, 2018• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1742-6596/1054/1/012012

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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.
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 structure of the superconducting correlations in cuprates gives insights on the pairing mechanism. Here we present an exhaustive study of this problem in the two-dimensional Hubbard model with cellular dynamical mean-field theory. To this end, we systematically quantify the dependence on doping δ and interaction strength U of the superconducting gap, of the frequency scales where d-wave pairing occurs, and of their relative contribution to pairing. For all values of U and δ, we find pair-forming processes confined to frequencies set by the superexchange interaction and followed by pair-breaking processes, ruling out both pair-forming and pair-breaking processes on the scale of U. This suggests that at high frequencies, the effect of U is eliminated by the d-wave paring, and that at small frequencies, U generates the superexchange interaction that leads to low-frequency pair-forming processes providing the net contribution to pairing.
Recent experiments (angle-resolved photoemission spectroscopy and Raman) suggest the presence of two distinct energy gaps in high-temperature superconductors (HTSC), exhibiting different doping dependences. The results of a variational cluster approach to the superconducting state of the two-dimensional Hubbard model are presented which show that this model qualitatively describes this gap dichotomy. The antinodal gap increases with less doping, a behavior long considered as reflecting the general gap behavior of the HTSC. On the other hand, the near-nodal gap does even slightly decrease with underdoping. An explanation of this unexpected behavior is given which emphasizes the crucial role of spin fluctuations in the pairing mechanism.
We analyze the interplay of antiferromagnetism and pairing in the two-dimensional Hubbard model with a moderate repulsive interaction. Coupled charge, magnetic, and pairing fluctuations above the energy scale of spontaneous symmetry breaking are treated by a functional renormalization group flow, while the formation of gaps and order below that scale is treated in mean-field theory. The full frequency dependences of the interaction vertices and gap functions are taken into account. We compute the magnetic and pairing gap functions as a function of doping ppp and compare with results from a static approximation. In spite of the strong frequency dependences of the effective interactions and of the pairing gap, important physical results from previous static functional renormalization group calculations are confirmed. In particular, there is a sizable doping regime with robust pairing coexisting with N\'eel or incommensurate antiferromagnetism. The critical temperature for magnetic order is interpreted as the pseudogap crossover temperature. Computing the Kosterlitz-Thouless temperature from the superfluid phase stiffness, we obtain a superconducting dome in the (p,T)(p,T)(p,T) phase diagram centered around 15% hole doping.
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 present an approach to investigate the interplay of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model within a numerically exact cluster dynamical mean-field approximation. Self-consistent solutions with two nonzero order parameters exist in a wide range of doping level and temperatures. A linearized equation for the energy spectrum near the Fermi level has been solved. The resulting d-wave gap has the correct magnitude and k dependence, but some distortion compared to the pure ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting order parameter due to the presence of underlying antiferromagnetic ordering.