arXiv:1511.00380 · Physical review. B./Physical review. B

Effect of site dilution in the two-dimensional attractive Hubbard model

Saurabh Pradhan, G. Venketeswara Pai

Published Oct 26, 2018• 4 citations

Abstract

We study the percolative superconducting transition as the density of randomly placed attractive centers grows in a host metal. Employing the Hubbard-Stratanovich transformation for the interaction and allowing for spatial, thermal fluctuations of the pairing field, we obtain real-space features of the transition from weak to strong coupling. Spectral and transport properties are studied in detail. BCS-BEC crossover is discussed in the context of site dilution of attractive centers.

DOI: 10.1103/physrevb.98.165142

Related papers

Pairing Fluctuations and Anomalous Transport Above the BCS-BEC Crossover in the Two Dimensional Attractive Hubbard Model

Sabyasachi Tarat, Pinaki Majumdar

arXiv:1105.1156May 5, 20110 citations

BCS–BEC Crossover in the Two-Dimensional Attractive Hubbard Model: Variational Cluster Approach

Tatsuya Kaneko, Yukinori Ohta

arXiv:1308.0664Journal of the Physical Society of JapanJan 21, 20149 citations

Dimensional crossover of the superfluid state in the attractive Hubbard model

Naoki Ogawa, Tatsuya Kaneko, Y. Ohta

Journal of Physics Conference SeriesMar 18, 20151 citation

Ginzburg–Landau expansion in BCS–BEC crossover region of disordered attractive Hubbard model

É. Z. Kuchinskiǐ, N. A. Kuleeva, Michael V. Sadovskii

arXiv:1606.05125Low Temperature PhysicsJan 1, 20174 citations

Disorder effects in the BCS-BEC crossover region of the attractive Hubbard model

E. Z. Kuchinskii, N. A. Kuleeva, M. V. Sadovskii

arXiv:1406.5603Journal of Experimental and Theoretical Physics LettersOct 1, 201410 citations

From BCS-like superconductivity to condensation of local pairs: A numerical study of the attractive Hubbard model

Johannes Maria Singer, M. H. Pedersen, T. Schneider +2 more

Physical review. B, Condensed matterJul 1, 199697 citations

arXiv:1511.00380 · Physical review. B./Physical review. B

Effect of site dilution in the two-dimensional attractive Hubbard model

Saurabh Pradhan, G. Venketeswara Pai

Published Oct 26, 2018• 4 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.98.165142

Related papers

Pairing Fluctuations and Anomalous Transport Above the BCS-BEC Crossover in the Two Dimensional Attractive Hubbard Model

Sabyasachi Tarat, Pinaki Majumdar

A Fermi liquid with weak attractive interaction undergoes a BCS transition to a superconductor with reducing temperature. With increasing interaction strength, the thermal transition is progressively modified as the high temperature `metallic' phase develops a pseudogap due to pairing fluctuations and the resistivity above T_c shows insulating behaviour. The crossover to insulating character occurs much before the system can be considered to be in the BEC regime of preformed fermion pairs. We use a new Monte Carlo tool to map out the BCS-BEC crossover in the attractive Hubbard model on large two dimensional lattices and explicitly compute the resistivity to demonstrate how the metal to superconductor (MS) thermal transition at weak coupling crosses over to an insulator to superconductor (IS) transition at intermediate coupling. Our high resolution access to the single particle and optical spectrum at finite temperature allows us to completely describe the transport crossover in this longstanding problem.A Fermi liquid with weak attractive interaction undergoes a BCS transition to a superconductor with reducing temperature. With increasing interaction strength, the thermal transition is progressively modified as the high temperature `metallic' phase develops a pseudogap due to pairing fluctuations and the resistivity above T_c shows insulating behaviour. The crossover to insulating character occurs much before the system can be considered to be in the BEC regime of preformed fermion pairs. We use a new Monte Carlo tool to map out the BCS-BEC crossover in the attractive Hubbard model on large two dimensional lattices and explicitly compute the resistivity to demonstrate how the metal to superconductor (MS) thermal transition at weak coupling crosses over to an insulator to superconductor (IS) transition at intermediate coupling. Our high resolution access to the single particle and optical spectrum at finite temperature allows us to completely describe the transport crossover in this longstanding problem.

arXiv:1105.1156May 5, 20110 citations

BCS–BEC Crossover in the Two-Dimensional Attractive Hubbard Model: Variational Cluster Approach

Tatsuya Kaneko, Yukinori Ohta

We use the variational cluster approximation to study the superconducting ground state in the two-dimensional attractive Hubbard model, putting particular emphasis on the significance of quantum fluctuations of the system. We first show that the order parameter is suppressed in comparison with that obtained using the mean-field theory owing to the effects of spatial fluctuations in two-dimensional systems. We then show that the calculated Bogoliubov quasiparticle spectra and condensation amplitude clearly exhibit the character of Cooper pairs in momentum space and that the pair coherence length $ξ$ evaluated from the condensation amplitude demonstrates a smooth crossover in real space from a weakly paired BCS state ( $ξ\gg a$ ) to a BEC state of tightly bound pairs ( $ξ\ll a$ ), where $a$ is the lattice constant. The calculated kinetic and potential energies in the superconducting and normal ground states indicate that the superconducting state in the weak-coupling region is driven by the gain in potential energy, while that in the strongcoupling region is driven by the gain in kinetic energy.We use the variational cluster approximation to study the superconducting ground state in the two-dimensional attractive Hubbard model, putting particular emphasis on the significance of quantum fluctuations of the system. We first show that the order parameter is suppressed in comparison with that obtained using the mean-field theory owing to the effects of spatial fluctuations in two-dimensional systems. We then show that the calculated Bogoliubov quasiparticle spectra and condensation amplitude clearly exhibit the character of Cooper pairs in momentum space and that the pair coherence length $ξ$ evaluated from the condensation amplitude demonstrates a smooth crossover in real space from a weakly paired BCS state ($ξ\gg a$) to a BEC state of tightly bound pairs ($ξ\ll a$), where $a$ is the lattice constant. The calculated kinetic and potential energies in the superconducting and normal ground states indicate that the superconducting state in the weak-coupling region is driven by the gain in potential energy, while that in the strongcoupling region is driven by the gain in kinetic energy.

arXiv:1308.0664Journal of the Physical Society of JapanJan 21, 20149 citations

Dimensional crossover of the superfluid state in the attractive Hubbard model

Naoki Ogawa, Tatsuya Kaneko, Y. Ohta

The superfluid state in the attractive Hubbard is studied for the stacked square lattices to simulate the two- to three-dimensional crossover effects. We use the variation cluster approximation to calculate the order parameter and pair coherence length from the weak-coupling BCS state to the strong-coupling BEC state at T = 0 K. We show that in the weak-coupling BCS region the density of states at Fermi level plays an important role in the dimensional crossover of the superfluid state but in the strong-coupling BEC region the quantum fluctuations depending on the dimensionality of the system play an essential role.The superfluid state in the attractive Hubbard is studied for the stacked square lattices to simulate the two- to three-dimensional crossover effects. We use the variation cluster approximation to calculate the order parameter and pair coherence length from the weak-coupling BCS state to the strong-coupling BEC state at T = 0 K. We show that in the weak-coupling BCS region the density of states at Fermi level plays an important role in the dimensional crossover of the superfluid state but in the strong-coupling BEC region the quantum fluctuations depending on the dimensionality of the system play an essential role.

Journal of Physics Conference SeriesMar 18, 20151 citation

Ginzburg–Landau expansion in BCS–BEC crossover region of disordered attractive Hubbard model

É. Z. Kuchinskiǐ, N. A. Kuleeva, Michael V. Sadovskii

We have studied disorder effects on the coefficients of Ginzburg-Landau expansion for attractive Hubbard model within the generalized DMFT+Σ approximation for the wide region of the values of attractive potential U—from the weak-coupling limit, where superconductivity is described by BCS model, towards the strong coupling, where superconducting transition is related to Bose-Einstein condensation (BEC) of compact Cooper pairs. For the case of semi-elliptic initial density of states disorder influence on the coefficients A and B before the square and the fourth power of the order parameter is universal for at all values of electronic correlations and is related only to the widening of the initial conduction band (density of states) by disorder. Similar universal behavior is valid for superconducting critical temperature Tc (the generalized Anderson theorem) and specific heat discontinuity at the transition. This universality is absent for the coefficient C before the gradient term, which in accordance with the standard theory of “dirty” superconductors is strongly suppressed by disorder in the weak-coupling region, but can slightly grow in BCS–BEC crossover region, becoming almost independent of disorder in the strong coupling region. This leads to rather weak disorder dependence of the penetration depth and coherence length, as well as the slope of the upper critical magnetic field at Tc, in BCS–BEC crossover and strong coupling regions.We have studied disorder effects on the coefficients of Ginzburg-Landau expansion for attractive Hubbard model within the generalized DMFT+Σ approximation for the wide region of the values of attractive potential U—from the weak-coupling limit, where superconductivity is described by BCS model, towards the strong coupling, where superconducting transition is related to Bose-Einstein condensation (BEC) of compact Cooper pairs. For the case of semi-elliptic initial density of states disorder influence on the coefficients A and B before the square and the fourth power of the order parameter is universal for at all values of electronic correlations and is related only to the widening of the initial conduction band (density of states) by disorder. Similar universal behavior is valid for superconducting critical temperature Tc (the generalized Anderson theorem) and specific heat discontinuity at the transition. This universality is absent for the coefficient C before the gradient term, which in accordance with the standard theory of “dirty” superconductors is strongly suppressed by disorder in the weak-coupling region, but can slightly grow in BCS–BEC crossover region, becoming almost independent of disorder in the strong coupling region. This leads to rather weak disorder dependence of the penetration depth and coherence length, as well as the slope of the upper critical magnetic field at Tc, in BCS–BEC crossover and strong coupling regions.

arXiv:1606.05125Low Temperature PhysicsJan 1, 20174 citations

Disorder effects in the BCS-BEC crossover region of the attractive Hubbard model

E. Z. Kuchinskii, N. A. Kuleeva, M. V. Sadovskii

We study the disorder effects upon superconducting transition temperature T c and the number of local pairs within the attractive Hubbard model in the combined Nozieres-Schmitt-Rink and DMFT + Σ approximations. We analyze the wide range of attractive interaction U, from the weak coupling region, where instability of the normal phase and superconductivity are well described by the BCS model, to the limit of strong coupling, where superconducting transition is determined by Bose-Einstein condensation of compact Cooper pairs, forming at temperatures much higher than superconducting transition temperature. It is shown that disorder can either suppress T c in the weak coupling limit, or significantly enhance T c in the case of strong coupling. However, in all cases we actually prove the validity of generalized Anderson theorem, so that all changes in T c are related to change in the effective bandwidth due to disorder. Similarly, disorder effects on the number of local pairs are only due to these band-broadening effects.We study the disorder effects upon superconducting transition temperature T c and the number of local pairs within the attractive Hubbard model in the combined Nozieres-Schmitt-Rink and DMFT + Σ approximations. We analyze the wide range of attractive interaction U, from the weak coupling region, where instability of the normal phase and superconductivity are well described by the BCS model, to the limit of strong coupling, where superconducting transition is determined by Bose-Einstein condensation of compact Cooper pairs, forming at temperatures much higher than superconducting transition temperature. It is shown that disorder can either suppress T c in the weak coupling limit, or significantly enhance T c in the case of strong coupling. However, in all cases we actually prove the validity of generalized Anderson theorem, so that all changes in T c are related to change in the effective bandwidth due to disorder. Similarly, disorder effects on the number of local pairs are only due to these band-broadening effects.

arXiv:1406.5603Journal of Experimental and Theoretical Physics LettersOct 1, 201410 citations

From BCS-like superconductivity to condensation of local pairs: A numerical study of the attractive Hubbard model

Johannes Maria Singer, M. H. Pedersen, T. Schneider +2 more

We investigate the two-dimensional attractive Hubbard model with quantum Monte Carlo techniques to reveal the crossover from a BCS-type superconductivity in the weak-coupling regime to a superconductivity properly described by a Bose-Einstein condensation (BEC) of local, preformed pairs. The crossover from BCS to BEC is particularly well exposed in the temperature dependence of both the spin susceptibility and the double occupancy, as well as by the appearance of a pseudogap in the density of states far above ${\mathit{T}}_{\mathit{c}}$ . These features are also mirrored in the shape of the specific-heat peak around ${\mathit{T}}_{\mathit{c}}$ , the separation of the temperature regimes where pair formation and their condensation occur, and in the transfer of spectral weight from the single-particle excitation branch to a pair band in the normal state. \textcopyright{} 1996 The American Physical Society.We investigate the two-dimensional attractive Hubbard model with quantum Monte Carlo techniques to reveal the crossover from a BCS-type superconductivity in the weak-coupling regime to a superconductivity properly described by a Bose-Einstein condensation (BEC) of local, preformed pairs. The crossover from BCS to BEC is particularly well exposed in the temperature dependence of both the spin susceptibility and the double occupancy, as well as by the appearance of a pseudogap in the density of states far above ${\mathit{T}}_{\mathit{c}}$. These features are also mirrored in the shape of the specific-heat peak around ${\mathit{T}}_{\mathit{c}}$, the separation of the temperature regimes where pair formation and their condensation occur, and in the transfer of spectral weight from the single-particle excitation branch to a pair band in the normal state. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterJul 1, 199697 citations

ξ

evaluated from the condensation amplitude demonstrates a smooth crossover in real space from a weakly paired BCS state (

ξ\gg a

) to a BEC state of tightly bound pairs (

ξ\ll a

), where

a

is the lattice constant. The calculated kinetic and potential energies in the superconducting and normal ground states indicate that the superconducting state in the weak-coupling region is driven by the gain in potential energy, while that in the strongcoupling region is driven by the gain in kinetic energy.

{\mathit{T}}_{\mathit{c}}

. These features are also mirrored in the shape of the specific-heat peak around

{\mathit{T}}_{\mathit{c}}

, the separation of the temperature regimes where pair formation and their condensation occur, and in the transfer of spectral weight from the single-particle excitation branch to a pair band in the normal state. \textcopyright{} 1996 The American Physical Society.