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Science

Inducing a crossover

Jelena Stajic

Published Apr 8, 2021• 0 citations
Publisher

Abstract

Superconductivity In conventional superconductors, the electron pairs responsible for superconductivity are large and overlapping. Starting from this so-called Bardeen-Cooper-Schrieffer (BCS) limit, increasing interactions can set the system on a path of crossover to the opposite limit of small, tightly bound electron pairs that undergo Bose-Einstein condensation (BEC). Nakagawa et al. intercalated lithium ions into the insulating material zirconium nitride chloride, varying the carrier density across a large range (see the Perspective by Randeria). This induced superconductivity and enabled the system to enter the crossover regime between the BCS and BEC limits. Science , this issue p. [190][1]; see also p. [132][2] [1]: /lookup/doi/10.1126/science.abb9860 [2]: /lookup/doi/10.1126/science.abg1752

DOI
10.1126/science.372.6538.141-s

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Superconductivity
In conventional superconductors, the electron pairs responsible for superconductivity are large and overlapping. Starting from this so-called Bardeen-Cooper-Schrieffer (BCS) limit, increasing interactions can set the system on a path of crossover to the opposite limit of small, tightly bound electron pairs that undergo Bose-Einstein condensation (BEC). Nakagawa et al. intercalated lithium ions into the insulating material zirconium nitride chloride, varying the carrier density across a large range (see the Perspective by Randeria). This induced superconductivity and enabled the system to enter the crossover regime between the BCS and BEC limits.
Science , this issue p. 190; see also p. 132
The theory of unconventional superconductors continues to provide profound puzzles. The crossover between the weakly coupled Bardeen-Cooper-Schrieffer (BCS) state and the strong-pairing Bose-Einstein condensate (BEC) provides a useful perspective on how to address these questions. This paper describes a self-consistent framework for thinking about the crossover regime in between these two limits. The review discusses to what extent this BCS-BEC theory applies to a range of classes of superconducting materials including the cuprates, iron pnictides, twisted bilayer graphene, and interfacial superconductivity among others.
Bardeen-Cooper-Schrieffer (BCS) superfluidity and Bose-Einstein condensation (BEC) are the two extreme limits of the ground state of the paired fermion systems. We report crossover behavior from the BCS limit to the BEC limit realized by varying carrier density in a two-dimensional superconductor, electron-doped zirconium nitride chloride. The phase diagram, established by simultaneous measurements of resistivity and tunneling spectra under ionic gating, demonstrates a pseudogap phase in the low-doping regime. The ratio of the superconducting transition temperature and Fermi temperature in the low-carrier density limit is consistent with the theoretical upper bound expected in the BCS-BEC crossover regime. These results indicate that the gate-doped semiconductor provides an ideal platform for the two-dimensional BCS-BEC crossover without added complexities present in other solid-state systems.
The ability to control the interaction strength between atoms within strongly interacting Fermi gases by sweeping a magnetic field across a Feshbach resonance provides a powerful experimental system in which to study many-body physics. One example is the crossover from a Bose-Einstein condensate (BEC) regime, in which the atoms are strongly coupled into pairs, to the weak-coupling regime that mimics Bardeen-Cooper-Schrieffer (BCS) coupling of electrons in superconducting metals. Although behavior on either side of the resonance is fairly well understood, of immediate interest is to find out what happens in the BEC-BCS crossover regime. However, determining the relative contributions of atom pairing mechanisms is an experimental and theoretical challenge.
The role of random onsite and hopping disorder in inducing a Bardeen–Cooper–Schrieffer superconductor to Bose–Einstein condensate (BCS–BEC) crossover is investigated using the Bogoliubov–de Gennes (BdG) method on a negative- U Hubbard model in two dimensions. In the strong disorder limit, the BdG state becomes highly inhomogeneous with the formation of superconducting ' droplets ' which are characterized by large pairing amplitudes. The different physical properties calculated for the inhomogeneous state differ significantly from the pure system at all values of electron densities, while we show that a crossover to a BEC state, if at all, is possible at low electron densities. The random onsite disorder supports such a crossover scenario, which is confirmed by observing the chemical potential to slip below the noninteracting band (Leggett criterion). The hopping disorder, however, renders a delocalized phase which allows for overlapping between the pairs, thus preventing the formation of a 'local pair' phase. Also the increase in bandwidth induced by hopping disorder always accommodates the chemical potential inside the band, and hence rules out a crossover phenomenon. However, another variant of the off-diagonal inhomogeneity, i.e. an anisotropic hopping, offers a pro-crossover scenario in the large anisotropy limit.
Physical properties of two-dimensional (2D) superconductors is an active area of long time researches in which many, even principle, questions are still open. One of them is a possibility of a smooth crossover of the system from the standard Bardeen–Cooper–Schrieffer (BCS) regime of strongly overlapping Cooper pairs to the regime of Bose–Einstein condensation (BEC) of almost non-overlapping local pairs. The adequate to the real process description of this transition which can happen either by changing the doping or temperature would lead to a better understanding of the superconducting properties of materials. Though the crossover is not observed in one of the most important layered systems—namely, cuprate superconductors—we demonstrate that in systems with stronger electron-electron attraction it is possible. In particular, in the d-wave channel at sufficiently high doping the crossover can take place with growth of temperature two times, i.e., as BEC→BCS, and followed by reverse BCS→BEC condensation. The physical mechanisms of such transitions and possibility to detect them experimentally in real systems are discussed.
In our recent experiments at MIT, superfluidity has been observed in a strongly interacting atomic Fermi gas. These systems constitute a novel form of matter with model character: One can vary the temperature, density and dimensionality, the number of “spin up” versus “spin down” fermions, and, most remarkably, the interactions can be precisely controlled over an enormous range. This allows to study the crossover of a Bose-Einstein condensate of tightly bound molecules to a Bardeen-Cooper-Schrieffer superfluid of long-range Cooper pairs. Superfluidity in this crossover regime is demonstrated by setting the gas under rotation and observing ordered lattices of quantized vortices [1]. Thanks to its strong interactions, the gas is a high-temperature superfluid: Scaled to the density of electrons in a metal, superfluidity would occur already far above room temperature. A new regime is entered when the number of spin up versus spin down atoms is imbalanced. In this case, not every spin up atom can find a spin down partner. The ground state of such a system has been under debate for over 40 years. We observe the breakdown of superfluidity at a critical imbalance, the Chandrasekhar-Clogston limit [2]. The superfluid gives way to an intriguing, strongly-interacting Fermi gas with unequal spin populations [3, 4].