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.
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.
Abstract The Bardeen–Cooper–Schrieffer (BCS) condensation and Bose–Einstein condensation (BEC) are the two limiting ground states of paired Fermion systems, and the crossover between these two limits has been a source of excitement for both fields of high temperature superconductivity and cold atom superfluidity. For superconductors, ultra-low doping systems like graphene and Li x ZrNCl successfully approached the crossover starting from the BCS-side. These superconductors offer new opportunities to clarify the nature of charged-particles transport towards the BEC regime. Here we report the study of vortex dynamics within the crossover using their Hall effect as a probe in Li x ZrNCl. We observed a systematic enhancement of the Hall angle towards the BCS-BEC crossover, which was qualitatively reproduced by the phenomenological time-dependent Ginzburg-Landau (TDGL) theory. Li x ZrNCl exhibits a band structure free from various electronic instabilities, allowing us to achieve a comprehensive understanding of the vortex Hall effect and thereby propose a global picture of vortex dynamics within the crossover. These results demonstrate that gate-controlled superconductors are ideal platforms towards investigations of unexplored properties in BEC superconductors.
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.
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
In paired Fermi systems, strong many-body effects exhibit in the crossover regime between the Bardeen–Cooper–Schrieffer (BCS) and the Bose–Einstein condensation (BEC) limits. The concept of the BCS–BEC crossover, which is studied intensively in the research field of cold atoms, has been extended to condensed matters. Here by analyzing the typical superconductors within the BCS–BEC phase diagram, we find that FeSe-based superconductors are prone to shift their positions in the BCS–BEC crossover regime by charge doping or substrate substitution, since their Fermi energies and the superconducting gap sizes are comparable. Especially at the interface of single-layer FeSe on SrTiO 3 substrate, the superconductivity is relocated closer to the crossover unitary than other doped FeSe-based materials, indicating that the pairing interaction is effectively modulated. We further show that hole-doping can drive the interfacial system into the phase with possible pre-paired electrons, demonstrating its flexible tunability within the BCS–BEC crossover regime.
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.
The condensation of paired fermions into superfluid states changes progressively depending on the coupling strength. At the midpoint of the crossover between Bardeen-Cooper-Schrieffer (BCS) weak-coupling and Bose-Einstein condensate (BEC) strong-coupling limits, paired fermions condensate most robustly, thereby leading to the emergence of a pseudogap due to enhanced pairing fluctuations. In the case of electrons in solids, excessively strong interactions often induce competing electronic orders instead of strong-coupling superconductivity, and experimental comprehension of the pseudogap remains incomplete. In this study, we provide experimental evidence demonstrating the opening of a pseudogap, marking the incipient stage of the BCS-BEC crossover in the organic system $\ensuremath{\kappa}\text{\ensuremath{-}}(\mathrm{BEDT}\text{\ensuremath{-}}{\mathrm{TTF})}_{2}X$. By controlling electron correlations, we investigate the thermodynamic properties of the BCS-BEC crossover and pseudogap phase. Since the superconductivity of $\ensuremath{\kappa}\text{\ensuremath{-}}{(\text{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}X$ arises from a simple Fermi liquid that does not exhibit any other electronic orders, our study sheds light on the inherent nature of the BCS-BEC crossover.