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arXiv:1309.6680

The influence of magnetic field on the superconducting properties and the BCS-BEC crossover in systems with local fermion pairing

Agnieszka Cichy

Published Sep 25, 2013• 2 citations
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Abstract

The aim of this Ph.D. thesis was to investigate superconducting properties in the presence of Zeeman magnetic field in systems with local fermion pairing on the lattice. The study also concerned the evolution from the weak coupling (BCS-like) limit to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, both in the ground state and at finite temperatures, within the spin-polarized extended Hubbard model. The analysis was also extended to the case of spin dependent hopping integrals (mass imbalance), with special attention paid to the BCS-BEC crossover physics in the ground state. The methods used included: the mean field approximation (BCS-Stoner type) and the estimation of the phase coherence temperature within the Kosterlitz-Thouless (KT) scenario in two dimensions. The BCS-BEC crossover was also analyzed in three dimensions, at finite temperatures, within the spin polarized Attractive Hubbard Model (AHM), going beyond the mean field approximation. In this case, the critical temperatures of the superconducting transition were determined within the self-consistent T-matrix method. The strong coupling expansion was applied to map the spin polarized AHM onto the model of hard-core bosons on the lattice.

DOI
10.48550/arxiv.1309.6680

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•Sep 12, 2005•2 citations
The aim of this Ph.D. thesis was to investigate superconducting properties in the presence of Zeeman magnetic field in systems with local fermion pairing on the lattice. The study also concerned the evolution from the weak coupling (BCS-like) limit to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, both in the ground state and at finite temperatures, within the spin-polarized extended Hubbard model. The analysis was also extended to the case of spin dependent hopping integrals (mass imbalance), with special attention paid to the BCS-BEC crossover physics in the ground state. The methods used included: the mean field approximation (BCS-Stoner type) and the estimation of the phase coherence temperature within the Kosterlitz-Thouless (KT) scenario in two dimensions. The BCS-BEC crossover was also analyzed in three dimensions, at finite temperatures, within the spin polarized Attractive Hubbard Model (AHM), going beyond the mean field approximation. In this case, the critical temperatures of the superconducting transition were determined within the self-consistent T-matrix method. The strong coupling expansion was applied to map the spin polarized AHM onto the model of hard-core bosons on the lattice.
The influence of the Zeeman magnetic field (h) on the ground state evolution of superfluid properties from the weak coupling (BCS-like) to the strong coupling limit of tightly bound local pairs with increasing attraction has been studied.The analysis was carried out within the spin-polarized attractive Hubbard model, for a fixed number of particles and a d = 3 simple cubic lattice.The broken symmetry Hartree approximation was used.For strong attraction and in the dilute limit, the homogeneous magnetized superconducting phase (SC M ) was found in the h-|U | and P -|U | diagrams.
We analyze the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs in the 2D asymmetric attractive Hubbard model, in the presence of the Zeeman magnetic eld (h).The broken symmetry Hartree approximation is used.We also apply the KosterlitzThouless scenario to determine the phase coherence temperatures.We obtain that for the spin dependent hopping integrals (t ↑ ̸ = t ↓ ) the homogeneous polarized superuid (SCM ) phase in the ground state for the strong attraction and lower lling can be stabilized.We nd a topological quantum phase transition (the Lifshitz type) from the unpolarized superuid phase (SC0) to SCM and tricritical point in the (h -µ) and spin polarization (P ) vs. attraction (U < 0) ground state phase diagrams.The nite temperatures phase diagrams for t ↑ ̸ = t ↓ are constructed.
We study the superconducting properties of population-imbalanced ultracold Fermi mixtures in one-dimensional optical lattices that can be effectively described by the spin-imbalanced attractive Hubbard model in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain the ground-state phase diagrams including some unconventional superconducting phases such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, and the $\ensuremath{\eta}$ phase (an extremal case of the FFLO phase), both for the case of a fixed chemical potential and for a fixed number of particles. It allows us to determine optimal regimes for the FFLO phase as well as $\ensuremath{\eta}$-pairing stability. We also investigate the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, at T=0T=0T=0. Finally, the obtained results show that in spite of the occurrence of the Lifshitz transition induced by an external magnetic field, the superconducting state can still exist in the system, at higher magnetic field values.
We study the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LPs) with increasing attraction, in the presence of the Zeeman magnetic field ( h ) for d =2, within the spin-polarized attractive Hubbard model. The broken symmetry Hartree approximation as well as the strong coupling expansion are used. We also apply the Kosterlitz-Thouless (KT) scenario to determine the phase coherence temperatures. For spin-independent hopping integrals ( t ↑ = t ↓ ), we find no stable homogeneous polarized superfluid (SC M ) state in the ground state for the strong attraction and obtain that for a two-component Fermi system on a 2D lattice with population imbalance, phase separation (PS) is favoured for a fixed particle concentration, even on the LP (BEC) side. We also examine the influence of spin-dependent hopping integrals (mass imbalance) on the stability of the SC M phase. We find a topological quantum phase transition (Lifshitz type) from the unpolarized superfluid phase (SC 0 ) to SC M and tricritical points in the h -| U | and t ↑ / t ↓ -| U | ground-state phase diagrams. We also construct the finite temperature phase diagrams for both t ↑ = t ↓ and t ↑ ≠ t ↓ and analyze the possibility of occurrence of a spin-polarized KT superfluid.
The superfluid characteristics of the attractive Hubbard model are analyzed for any coupling |U| and arbitrary electron concentration (0n2) by means of the slave-boson mean-field method and also by the perturbative treatment of the strong-coupling limit. The slave boson method takes into account correlations of electrons and yields a reliable description of the crossover from BCS-type superconductivity to local pair (composite bosons) superconductivity with increasing |U|. The results for the ground state (the free energy, the gap in the excitation spectrum) and the electromagnetic characteristics (the critical magnetic field, the London penetration depth, the coherence length) are compared with those obtained by the Hartree-Fock approximation and by the self-consistent second-order perturbation theory in the weak-coupling limit as well as with those obtained using perturbational approaches in the strong-coupling limit. We show that the slave-boson method, in contrast to the Hartree-Fock approximation, gives credible results for all investigated quantities in the whole interaction range, interpolating smoothly between the BCS and local pair regimes. A comparison of theoretical predictions for our simple model with experimental data for various families of short-coherence-length superconductors suggests that the best agreement can be obtained for intermediate values of the local attraction. \textcopyright{} 1996 The American Physical Society.
The problem of the evolution from BCS theory with cooperative Cooper pairing to the formation and condensation of composite bosons has attracted considerable attention for the past several decades. It has gained renewed impetus in the mid-eighties with the discovery of the high-Tc superconductors, which have a coherence length comparable to the interparticle spacing. More recently, this subject has spurred a great deal of research activity in connection with experiments involving dilute atomic gases of fermionic atoms. The initial objective of this work will be to use functional integral techniques to analyze the low-temperature BCS-to-BEC evolution of d-wave superconductors within the saddle point (mean field) approximation for a continuum model. Then, the same mathematical formalism will be applied to the problem of the BCS-to-BEC evolution of fully spin-polarized p-wave Fermi gases in two dimensions. We find that a quantum phase transition occurs for both systems as they are driven from the BCS-like regime of weakly interacting fermionic pairs to the opposite BEC-like regime of strongly interacting bosonic molecules. This is in contrast to the smooth crossover predicted and observed in systems that exhibit s-wave pairing symmetry. We calculate several spectroscopic and thermodynamic properties that signal the occurrence of this phase transition, and suggest some possible experimental realizations. Finally, fluctuations about the saddle point solution are included in the calculations, and the effects of such correction are analyzed in the low (T~0) and high (T~Tc) temperature limits. We conclude that, at high temperatures, the bosonic degrees of freedom that arise from two-particle bound states become essential to describe the strong coupling limit,\nas the saddle point approximation alone becomes unreliable.