Vortices in Hubbard Superconductors: A Bogoliubov-de Gennes Approach

Pérez, Luis A.; Galván, César G.; Wang, Chumín

doi:10.1007/s10948-015-3259-3

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…Apart from the above systems, one should mention ultracold fermionic gases or the condensed matter systems [65]. Here, the impurities [66][67][68] or vortices [69][70][71] play the role of inhomogeneity. It is worth mentioning the superconducting systems with spin-density (SDW) or charge-density (CDW) waves coexistence [72][73][74][75].…”

Section: Non-homogeneous Systemsmentioning

confidence: 99%

Superfluidity of fermionic pairs in a harmonic trap. Comparative studies: Local Density Approximation and Bogoliubov-de Gennes solutions

Cichy¹,

Ptok²

2020

J. Phys. Commun.

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Experiments with ultracold gases on the lattice give the opportunity to realize superfluid fermionic mixtures in a trapping potential. The external trap modifies the chemical potential locally. Moreover, this trap also introduces non-homogeneity in the superconducting order parameter. There are, among other approaches, two methods which can be used to describe the system of two-component mixtures loaded into an optical lattice: the Local Density Approximation (LDA) and the self-consistent Bogoliubov-de Gennes equations. Here, we compare results obtained within these two methods. We conclude that the results can be distinguishable only in the case of a small value of the pairing interaction.Recent progress in experimental techniques in ultracold quantum gases gives ground to believe that they are good candidates for realization of quantum simulators [1][2][3][4][5]. This progress gives the opportunity to study different types of quantum models, well established already in many-body physics [5][6][7].Parameters such as the depth of the periodic trapping potential or the lattice geometry can be tuned with a high level of control in experiments. Moreover, the interaction strengths can also be fully controlled via so-called Feshbach resonances [8], giving the possibility of realization of repulsively and attractively interacting systems [9]. The latter allows for an experimental study of superfluid states [10][11][12].Typically, a system of ultracold atoms is located in an external potential, for instance in a harmonic trap. This potential introduces some effective site-dependent chemical potential and non-homogeneous distribution of the particles in the system. As a consequence, non-uniform superconducting order parameter is expected. The system can be studied theoretically via several methods. In this paper, we compare the results obtained within the Local Density Approximation (LDA) and the self-consistent Bogoliubov-de Gennes (BdG) equations, for a system of an ultracold attractive fermionic gas loaded into a one-dimensional (1D) optical lattice, put in a harmonic trap.The paper is organized as follows: first, we shortly introduce the model as well as the above mentioned methods (section 2). In section 3, we present and discuss numerical results. Finally, we summarize in section 4. Model and techniquesWe investigate a fermionic gas loaded onto a one-dimensional lattice, in a harmonic trap, which is schematically illustrated in figure 1. The system under consideration can be described by the Hamiltonian

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Section: Non-homogeneous Systemsmentioning

confidence: 99%

Superfluidity of fermionic pairs in a harmonic trap. Comparative studies: Local Density Approximation and Bogoliubov-de Gennes solutions

Cichy¹,

Ptok²

2020

J. Phys. Commun.

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“…Let us consider a square lattice supercell of ( N + s ) × ( N + s ) atoms consisting of a superconducting grain represented by N × N A‐type atoms bordered by (2 N + s ) s B‐type ones, described by a single‐band attractive Hubbard Hamiltonian given by

\hat{H} = \sum_{l, σ} ϵ_{l} {\hat{n}}_{l, σ} + \sum_{true〈 l, m true〉, σ} t_{l, m} {\hat{c}}_{l, σ}^{†} {\hat{c}}_{m, σ} + \sum_{l} U_{l} {\hat{n}}_{l, ↑} {\hat{n}}_{l, ↓},

where

{true \overset{c}{true}}_{l, σ}^{normal†}

(

{true \hat{c}}_{l, σ}

) is the creation (annihilation) operator with spin

σ = ↑ or ↓

at site l ,

{true \overset{n}{true}}_{l, σ} = {true \overset{c}{true}}_{l, σ}^{normal†} {true \overset{c}{true}}_{l, σ}^{}

, and

true〈 l, m true〉

denotes nearest neighbor sites. In the supercell, A‐ and B‐type atoms, respectively, have on‐site energies

ϵ_{normalA}

and

ϵ_{normalB}

, and the hopping integrals between these atoms could be

t_{A A}

…”

Section: The Modelmentioning

confidence: 99%

Bogoliubov-de Gennes study of nanoscale Hubbard superconductors

Galván

Cabrera-Trujillo

Pérez

et al. 2016

Phys. Status Solidi B

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The effects of quantum confinement on the superconducting ground state are studied within the Bogoliubov-de Gennes (BdG) formalism and an attractive Hubbard model. We consider a periodic arrangement of two-dimensional superconducting grains composed by N Â N atoms surrounded by insulating, metallic or superconducting stripes with a thickness of s atoms, leading to 2(N þ s) 2 coupled self-consistent BdG equations for a supercell of (N þ s) Â (N þ s) atoms. These equations determine the spatial variation of superconducting gap as functions of temperature, electron-electron interaction, and hopping integrals analyzing three types of boundary stripes. The results show a clear enhancement of the superconducting gap and critical temperature induced by the electron confinement in the grain, being larger for the insulating boundary case. Finally, the numerical solutions of BdG equations are compared with those obtained by applying the BCS theory to each grain site.

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