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Detection of pairing from the extended Aharonov-Bohm period in strongly correlated electron systems

K. Kusakabe, H. Aoki

Published Jan 1, 1995• 6 citations
OpenAlex

Abstract

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,

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

Koichi Kusakabe, Hideo Aoki

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.

arXiv:cond-mat/9512177•Journal of the Physical Society of Japan•Sep 15, 1996•14 citations

Extended Aharonov-Bohm Period Analysis of Strongly Correlated Electron Systems

Ryotaro Arita, Koichi Kusakabe, Kazuhiko Kuroki +1 more

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.

arXiv:cond-mat/9610199•Journal of the Physical Society of Japan•Jul 15, 1997•5 citations

Strong correlations versus U -center pairing and fractional Aharonov-Bohm effect

Fedor Vasilievich Kusmartsev, J. F. Weisz, Rishabh Kishore +1 more

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 ${\mathit{f}}_{\mathit{T}}$=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.

arXiv:cond-mat/9401064•Physical review. B, Condensed matter•Jun 15, 1994•42 citations

Bethe-Ansatz Analysis of the Extended AB Period in the One-Dimensional Hubbard Model

Koichi Kusakabe

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.

Journal of the Physical Society of Japan•Jul 15, 1997•4 citations

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The normal state of strongly coupled superconductors is characterized by the presence of ``preformed'' Cooper pairs well above the superconducting critical temperature. In this regime, the electrons are paired, but they lack the phase coherence necessary for superconductivity. The existence of preformed pairs implies the existence of a characteristic energy scale associated with a pseudogap. Preformed pairs are often invoked to interpret systems where some signatures of pairing are present without actual superconductivity, but an unambiguous theoretical characterization of a preformed-pair system is still lacking. To fill this gap, we consider the response to an external pairing field of an attractive Hubbard model, which hosts one of the cleanest realizations of a preformed pair phase, and a repulsive model where $s$-wave superconductivity cannot be realized. Using dynamical mean-field theory to study this response, we identify the characteristic features which distinguish the reaction of a preformed pair state from a normal metal without any precursor of pairing. The theoretical detection of preformed pairs is associated with the behavior of the second derivative of the order parameter with respect to the external field, as confirmed by analytic calculations in limiting cases. Our findings provide a solid test bed for the interpretation of state-of-the-art calculations for the normal state of the doped Hubbard model in terms of $d$-wave preformed pairs and, in perspective, of nonequilibrium experiments in high-temperature superconductors.

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Spin-Charge Separation in Aharonov-Bohm Rings of Interacting Electrons

K. Hallberg, Armando A. Aligia, A. P. Kampf +1 more

We investigate the properties of strongly correlated electronic models on a flux-threaded ring connected to semi-infinite free-electron leads. The interference pattern of such an Aharonov-Bohm ring shows sharp dips at certain flux values, determined by the filling, which are a consequence of spin-charge separation in a nanoscopic system.

arXiv:cond-mat/0406319•Physical Review Letters•Aug 4, 2004•29 citations
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,
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.
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.
The normal state of strongly coupled superconductors is characterized by the presence of ``preformed'' Cooper pairs well above the superconducting critical temperature. In this regime, the electrons are paired, but they lack the phase coherence necessary for superconductivity. The existence of preformed pairs implies the existence of a characteristic energy scale associated with a pseudogap. Preformed pairs are often invoked to interpret systems where some signatures of pairing are present without actual superconductivity, but an unambiguous theoretical characterization of a preformed-pair system is still lacking. To fill this gap, we consider the response to an external pairing field of an attractive Hubbard model, which hosts one of the cleanest realizations of a preformed pair phase, and a repulsive model where sss-wave superconductivity cannot be realized. Using dynamical mean-field theory to study this response, we identify the characteristic features which distinguish the reaction of a preformed pair state from a normal metal without any precursor of pairing. The theoretical detection of preformed pairs is associated with the behavior of the second derivative of the order parameter with respect to the external field, as confirmed by analytic calculations in limiting cases. Our findings provide a solid test bed for the interpretation of state-of-the-art calculations for the normal state of the doped Hubbard model in terms of ddd-wave preformed pairs and, in perspective, of nonequilibrium experiments in high-temperature superconductors.