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Physical review. B./Physical review. B

BCS-BEC crossover induced by a shallow band: Pushing standard superconductivity types apart

Sebastian Wolf, Alexei Vagov, Arkady A Shanenko, V. M. Axt, Andrea Perali, Jose Albino Aguiar

Published Mar 30, 2017• 21 citations
Publisher

Abstract

The appearance of a shallow band(s) drives a superconductor towards the BCS-BEC crossover, conventionally associated with notable changes in single-particle properties and an elevated critical temperature. Here we demonstrate that the proximity to the crossover induced by a shallow band has also a dramatic effect on the phase diagram of the superconducting magnetic properties. When the system passes from the BCS to BEC regime, the intertype domain between superconductivity types I and II enlarges systematically, being inversely proportional to the square of the Cooper-pair radius, the main parameter that controls the BCS-BEC superconductivity. We also show that despite the presence of a shallow band, the condensate fluctuations are suppressed when it coexists in one material with standard deep bands, as in recent iron chalcogenides ${\mathrm{Fe}\mathrm{Se}}_{x}{\mathrm{Te}}_{1\ensuremath{-}x}$ and $\mathrm{FeSe}$.

DOI
10.1103/physrevb.95.094521

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•Sep 9, 2020•0 citations
The appearance of a shallow band(s) drives a superconductor towards the BCS-BEC crossover, conventionally associated with notable changes in single-particle properties and an elevated critical temperature. Here we demonstrate that the proximity to the crossover induced by a shallow band has also a dramatic effect on the phase diagram of the superconducting magnetic properties. When the system passes from the BCS to BEC regime, the intertype domain between superconductivity types I and II enlarges systematically, being inversely proportional to the square of the Cooper-pair radius, the main parameter that controls the BCS-BEC superconductivity. We also show that despite the presence of a shallow band, the condensate fluctuations are suppressed when it coexists in one material with standard deep bands, as in recent iron chalcogenides FeSexTe1\ensuremath−x{\mathrm{Fe}\mathrm{Se}}_{x}{\mathrm{Te}}_{1\ensuremath{-}x}FeSex​Te1\ensuremath−x​ and FeSe\mathrm{FeSe}FeSe.
Superconductivity in iron-based, magnesium diborides, and other novel superconducting materials has a strong multi-band and multi-gap character. Recent experiments support the possibillity for a BCS-BEC crossover induced by strong-coupling and proximity of the chemical potential to the band edge of one of the bands. Here we study the simplest theoretical model which accounts for the BCS-BEC crossover in a two-band superconductor, considering tunable interactions and tunable energy separations between the bands. Mean-field results for condensate fraction, correlation length, and superconducting gap are reported in typical crossover diagrams to locate the boundaries of the BCS, crossover, and BEC regimes. When the superconducting gap is of the order of the local chemical potential, superconductivity is in the crossover regime of the BCS-BEC crossover and the Fermi surface of the small band is smeared by the gap opening. In this situation, small and large Cooper pairs coexist in the total condensate, which is the optimal condition for high-Tc superconductivity. The ratio between the gap and the Fermi energy in a given band results to be the best detection parameter for experiments to locate the system in the BCS-BEC crossover. Using available experimental data, our analysis shows that iron-based superconductors have the partial condensate of the small Fermi surface in the crossover regime of the BCS-BEC crossover, supporting the recent ARPES findings.
A combination of strong Cooper pairing and weak superconducting fluctuations is crucial to achieve and stabilize high-Tc{T}_{c}Tc​ superconductivity. We demonstrate that a coexistence of a shallow carrier band with strong pairing and a deep band with weak pairing, together with the Josephson-like pair transfer between the bands to couple the two condensates, realizes an optimal multicomponent superconductivity regime: it preserves strong pairing to generate large gaps and a very high critical temperature but screens the detrimental superconducting fluctuations, thereby suppressing the pseudogap state. Surprisingly, we find that the screening is very efficient even when the interband coupling is very small. Thus, a multiband superconductor with a coherent mixture of condensates in the BCS regime (deep band) and in the BCS-BEC crossover regime (shallow band) offers a promising route to higher critical temperatures.
We investigate pairing fluctuation effects in a two band fermionic system, where a shallow band in the Bardeen–Cooper–Schrieffer–Bose–Einstein condensation (BCS-BEC) crossover regime is coupled with a weakly interacting deep band. Within a diagrammatic T matrix approach, we report how thermodynamic quantities such as the critical temperature, chemical potential, and momentum distributions undergo the crossover from the BCS to BEC regime by tuning the intraband coupling in the shallow band. We also generalize the definition of Tan’s contact to a two band system and report the two contacts for different pair-exchange couplings. The present results are compared with those obtained by the simpler Nozières–Schmitt–Rink approximation. We confirm a pronounced enhancement of the critical temperature due to the multiband configuration, as well as to the pair-exchange coupling.
We have analyzed the doping and temperature dependencies of the physical properties of a square-lattice narrow-band superconductor with a relevant for systems with local Hubbard repulsion nematic pairing due to effective nearest-neighbor attraction. Our focus was a possible crossover of the system from the Bardeen–Cooper–Schrieffer (BCS) superconductivity to the Bose–Einstein condensation (BEC) regimes with increasing temperature. We have found that in the d-channel the crossover does not take place at realistic values of doping and temperature, and even at a large attraction, i.e., the system is always in the BCS regime, unlike the “usual” d-wave superconductor. Contrary to non-nematic d-wave superconductors, the chemical potential μ always grows with temperature increase that might indicate an unexpectedly large size of Cooper pairs. At the same time, in the s-channel, we have found a BCS–BEC crossover with temperature for a wide range of temperatures even at rather high dopings, nf ≈ 0.2. This result is different from the “usual” s-case, where a narrow-band (i.e., at strong coupling) system is always in the BEC state. We have found for a given large value of attraction that there is a value of doping when for a wide range of temperature the system is in a “pre-crossover” regime with μ ≈ 0, i.e., in a regime of coexistence of local and extended pairs. Thus, in narrow-band systems a “usual” s-superconductor is in a BEC state, but in the nematic case one can expect a BCS–to–BEC crossover with temperature growth at realistic system parameters, i.e., the crossover might be measured experimentally.
Ultranarrow superconductors are in the strong quantum confinement regime with formation of multiple coherent condensates associated with the many subbands of the electronic structure. Here we analyze the multiband BCS-BEC crossover induced by the chemical potential tuned close to a subband bottom, in correspondence of a superconducting shape resonance. The evolution of the condensate fraction and of the pair correlation length in the ground state as functions of the chemical potential demonstrates the tunability of the BCS-BEC crossover for the condensate component of the selected subband. The extension of the crossover regime increases when the pairing strength and/or the characteristic energy of the interaction get larger. Our results indicate the coexistence of large and small Cooper pairs in the crossover regime, leading to the optimal parameter configuration for high transition temperature superconductivity.
We demonstrate the rise-and-fall of multiple pseudogaps in the Bardeen-Cooper-Schrieffer-Bose-Einstein-condensation (BCS-BEC) crossover in two-band fermionic systems having different pairing strengths in the deep band and in the shallow band. The striking features of this phenomenon are an unusual many-body screening of pseudogap state and the importance of pair-exchange couplings, which induces multiple pseudogap formation in the two bands. The multi-band configuration suppresses pairing fluctuations and the pseudogap opening in the strongly-interacting shallow band at small pair-exchange couplings by screening effects, with possible connection to the pseudogap phenomenology in iron based superconductors. On the other hand, the multiple pseudogap mechanism accompanies with the emergence of binary preformed Cooper pairs originating from interplay between intra-band and pair-exchange couplings.