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arXiv:cond-mat/0603601 · Physical Review B

Two-band superfluidity from the BCS to the BEC limit

M. Iskin, C. A. R. Sá de Melo

Published Oct 25, 2006• 37 citations
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Abstract

We analyze the evolution of two-band superfluidity from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) limit. When the interband interaction is tuned from negative to positive values, a quantum phase transition occurs from a 0-phase to a $\ensuremath{\pi}$-phase state, depending on the relative phase of the two order parameters. Furthermore, population imbalances between the two bands can be created by tuning the intraband or interband interactions. We also find two undamped low-energy collective excitations corresponding to in-phase and out-of-phase modes. Lastly, we derive the coupled Ginzburg-Landau equations, and show that they reduce to coupled Gross-Pitaevskii equations for two types of bosons in the BEC limit.

DOI
10.1103/physrevb.74.144517

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We analyze the evolution of two-band superfluidity from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) limit. When the interband interaction is tuned from negative to positive values, a quantum phase transition occurs from a 0-phase to a \ensuremathπ\ensuremath{\pi}\ensuremathπ-phase state, depending on the relative phase of the two order parameters. Furthermore, population imbalances between the two bands can be created by tuning the intraband or interband interactions. We also find two undamped low-energy collective excitations corresponding to in-phase and out-of-phase modes. Lastly, we derive the coupled Ginzburg-Landau equations, and show that they reduce to coupled Gross-Pitaevskii equations for two types of bosons in the BEC limit.
Abstract We show that in two-band s -wave superfluids it is possible to induce quantum phase transitions (QPTs) by tuning intraband and interband s -wave interactions, in sharp contrast to single-band s -wave superfluids, where only a crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensation (BEC) superfluidity occurs. For non-zero interband and attractive intraband interactions, we demonstrate that the ground state has always two interpenetrating superfluids possessing three spectroscopically distinct regions where pairing is qualitatively different: I) BCS pairing in both bands (BCS-BCS), II) BCS pairing in one band and BEC pairing in the other (BCS-BEC), and III) Bose pairing in both bands (BEC-BEC). Furthermore, we show that by fine tuning the interband interactions to zero one can induce QPTs in the ground state between three distinct superfluid phases. There are two phases where only one band is superfluid ( S 1 or S 2 ), and one phase where both bands are superfluid , a situation which is absent in one-band s -wave systems. Lastly, we suggest that these crossovers and QPTs may be observed in multi-component systems such as 6 Li, 40 K, 87 Sr, and 173 Yb.
We show that in two-band sss-wave superfluids it is possible to induce quantum phase transitions (QPTs) by tuning intraband and interband sss-wave interactions, in sharp contrast to single-band sss-wave superfluids, where only a crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensation (BEC) superfluidity occurs. For non-zero interband and attractive intraband interactions, we demonstrate that the ground state has always two interpenetrating superfluids possessing three spectroscopically distinct regions where pairing is qualitatively different: (I) BCS pairing in both bands (BCS-BCS), (II) BCS pairing in one band and BEC pairing in the other (BCS-BEC), and (III) Bose pairing in both bands (BEC-BEC). Furthermore, we show that by fine tuning the interband interactions to zero one can induce QPTs in the ground state between three distinct superfluid phases. There are two phases where only one band is superfluid (S1S_1S1​ or S2S_2S2​), and one phase where both bands are superfluid (S1+S2)(S_1 + S_2)(S1​+S2​), a situation which is absent in one-band sss-wave systems. Lastly, we suggest that these crossovers and QPTs may be observed in 173^{173}173Yb and 87^{87}87Sr.
We analyze the phase diagram of superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) limit as a function of scattering parameter, population imbalance, and mass anisotropy. We identify regions corresponding to normal, or uniform or nonuniform superfluid phases, and discuss topological quantum phase transitions in the BCS, unitarity, and BEC limits. We derive the Ginzburg-Landau equation near the critical temperature, and show that it describes a dilute mixture of paired and unpaired fermions in the BEC limit. We also obtain the zero temperature low frequency and long wavelength collective excitation spectrum, and recover the Bogoliubov relation for weakly interacting dilute bosons in the BEC limit. Lastly, we discuss the effects of harmonic traps and the resulting density profiles in the BEC regime.
This thesis focuses on the analysis of Bardeen-Cooper-Schrieffer (BCS) \nto Bose-Einstein condensation (BEC) evolution in ultracold superfluid \nFermi gases when the interaction between atoms is varied. The tuning of \nattractive interactions permits the ground state of the system to evolve from a weak \nfermion attraction BCS limit of loosely bound and largely overlapping Cooper pairs \nto a strong fermion attraction limit of tightly bound small bosonic molecules \nwhich undergo BEC. \nThis evolution is accompanied by anomalous behavior of many superfluid \nproperties, and reveals several quantum phase transitions. \nThis thesis has two parts: \nIn the first part, I analyze zero and nonzero orbital angular momentum \npairing effects, and show that a quantum phase transition occurs for \nnonzero angular momentum pairing, unlike the sss-wave case where the BCS \nto BEC evolution is just a crossover. \nIn the second part, I analyze two-species fermion mixtures with mass and \npopulation imbalance in continuum, trap and lattice models. In contrast with \nthe crossover physics found in the mass and population balanced mixtures, \nI demonstrate the existence of phase transitions between normal and \nsuperfluid phases, as well as phase separation between superfluid (paired) \nand normal (excess) fermions in imbalanced mixtures as a function of scattering \nparameter and mass and population imbalance.
We consider the evolution of superfluid properties of a three-dimensional p-wave Fermi gas from a weak coupling Bardeen-Cooper-Schrieffer (BCS) to strong coupling Bose-Einstein condensation (BEC) limit as a function of scattering volume. At zero temperature, we show that a quantum phase transition occurs for p-wave systems, unlike the s-wave case where the BCS to BEC evolution is just a crossover. Near the critical temperature, we derive a time-dependent Ginzburg-Landau (GL) theory and show that the GL coherence length is generally anisotropic due to the p-wave nature of the order parameter, and becomes isotropic only in the BEC limit.
We review aspects of the evolution from Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) in two dimensions, which have now become relevant in systems with low densities, such as gated superconductors Li xZrNCl, magic-angle twisted trilayer graphene, FeSe, FeSe1− xS x, and ultracold Fermi superfluids. We emphasize the important role played by chemical potentials in determining crossovers or topological quantum phase transitions during the BCS–BEC evolution in one-band and two-band superfluids and superconductors. We highlight that crossovers from BCS to BEC occur for pairing in nonnodal s-wave channels, whereas topological quantum phase transitions, in which the order parameter symmetry does not change, arise for pairing in any nodal higher angular momentum channels, such as d-wave. We conclude by discussing a few open questions regarding the BCS-to-BEC evolution in 2D, including modulus fluctuations of the order parameter, tighter upper bounds on critical temperatures, and the exploration of lattice effects in two-band superconductors and superfluids.