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arXiv:cond-mat/9512177 · Journal of the Physical Society of Japan

Detection of Pairing from the Extended Aharonov-Bohm Period in Strongly Correlated Electron Systems

Koichi Kusakabe, Hideo Aoki

Published Sep 15, 1996• 14 citations
arXivHTMLPDF

Abstract

Inspired from Sutherland's work [Phys. Rev. Lett. {\bf 74}, 816 (1995)] on detecting bound spin waves, we propose that bound electron states can be detected from the dependence of interacting electron systems to the Aharonov-Bohm flux in the `extended zone' scheme, where the electron pairing halves the original period $N_a$ flux quanta in a system of linear size $N_a$. Along with the Bethe-ansatz analysis, a numerical implementation for keeping track of the adiabatic flow of energy levels is applied to the attractive/repulsive Hubbard models and the $t-J$ ladder.

DOI
10.1143/jpsj.65.2772

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Inspired from Sutherland's work [Phys. Rev. Lett. {\bf 74}, 816 (1995)] on detecting bound spin waves, we propose that bound electron states can be detected from the dependence of interacting electron systems to the Aharonov-Bohm flux in the `extended zone' scheme, where the electron pairing halves the original period NaN_aNa​ flux quanta in a system of linear size NaN_aNa​. Along with the Bethe-ansatz analysis, a numerical implementation for keeping track of the adiabatic flow of energy levels is applied to the attractive/repulsive Hubbard models and the t−Jt-Jt−J ladder.
Inspired from Sutherland’s work [Phys. Rev. Lett. 74, 816 (1995)] on detecting bound spin waves, we propose that bound electron states can be detected from the dependence of interacting electron systems to the Aharonov-Bohm flux in the ‘extended zone ’ scheme, where the electron pairing halves the original period Na flux quanta in a system of linear size Na. Along with the Bethe-ansatz analysis, a numerical implementation for keeping track of the adiabatic flow of energy levels is applied to the attractive/repulsive Hubbard models and the t − J ladder. PACS numbers: 74.25.-q, 03.65.Ge, 71.27.+a Typeset using REVTEX 1 The response to an adiabatic change against external parameters is an interesting way to probe the nature of interacting electron systems. Some thirty years ago, Byers and Yang [1] proposed a notable example of detecting the Cooper pairing: while a normal state responds to an Aharonov-Bohm (AB) flux periodically with the period of flux quantum, Φ0 ≡ hc/e,
The `extended Aharonov-Bohm (AB) period' recently proposed by Kusakabe and Aoki [J. Phys. Soc. Jpn (65), 2772 (1996)] is extensively studied numerically for finite size systems of strongly correlated electrons. While the extended AB period is the system length times the flux quantum for noninteracting systems, we have found the existence of the boundary across which the period is halved or another boundary into an even shorter period on the phase diagram for these models. If we compare this result with the phase diagram predicted from the Tomonaga-Luttinger theory, devised for low-energy physics, the halved period (or shorter periods) has a one-to-one correspondence to the existence of the pairing (phase separation or metal-insulator transition) in these models. We have also found for the t-J model that the extended AB period does not change across the integrable-nonintegrable boundary despite the totally different level statistics.
The influence of the interaction between electrons on the Aharonov-Bohm effect is investigated in the framework of the Hubbard model. The repulsion between electrons associated with strong correlation is compared with the case of attraction such as U-center pairing. We apply the Bethe-ansatz method and exact numerical diagonalization to the Hubbard Hamiltonian. It is shown that the quasi-half-quantum-flux periodicity occurs for any nonzero values of U for two electrons. For a large number of sites, or strong U, the quasiperiodicity becomes an exact half-quantum flux periodicity. The character of the state created on the ring is different in both cases. In U-center pairing the electrons are bound in pairs located on the same site. For strong correlations (large positive U) the electrons tend to be as far from each other as possible. We show by numerical solution of the Bethe-ansatz equations that for three electrons the flux peiodicity of the ground-state energy is equal to 1/3. The one-third periodicity may occur even for small values of the ratio U/t, for the very dilute system. It is shown analytically using the Bethe-ansatz equations for N electrons that for dilute systems with arbitrary value of the Hubbard repulsion U, the fractional Aharonov-Bohm effect occurs with period fT{\mathit{f}}_{\mathit{T}}fT​=1/N in units of the elementary flux quantum. Such a period occurs when the value Nt/LU is small, where L is the number of sites. Parity effects disappear in this fractional regime. We discuss possible experiments to detect fractional Aharonov-Bohm effects.
The extended spectral flow at the normal-superconducting transition is investigated for the one-dimensional Hubbard model. Recombination of spectral flow lines at U =±0, which causes halving of the extended Aharonov-Bohm period for U <0 found in a recent paper [K. Kusakabe and H. Aoki: J. Phys. Soc. Jpn. 65 (1996) 2772], is exactly analyzed using the Bethe ansatz solution. Adiabatic motion of charge rapidities which are real for U >0 (normal Luttinger liquid) or complex for U <0 (superconducting Luther-Emery liquid) dominates sudden response of the spectral flow at the transition point. The extended period is obtained not only against the charge flux but also against the spin flux for both U >0 and U <0.
A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting Tc by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-Tc mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.