This vortex flow parallel to the supercurrent has never been observed experimentally, but in the case of superfluidity of charge neutral bosons of 4He, the parallel vortex flow was nicely demonstrated in the movie of ref. 1a) brings about vortex flow parallel or antiparallel to the supercurrent flow. Hence, the dissipationless nature of the vortex core in the BEC regime (Fig. In the BEC regime, the motion of vortices antiparallel (parallel) to the background current density J (superfluid velocity) can be understood as follows: The vortex motion in the presence of the magnetic field B induces the macroscopic electric field \(\) follows. ![]() 1b, arrows), while the vortex in the BEC regime moves parallel to the superfluid velocity, i.e., anti-parallel to the net supercurrent (Fig. The above difference results in contrasting vortex motions: the vortex in the BCS regime moves perpendicularly to the net supercurrent (Fig. This large level spacing renders the vortex motion dissipationless since the quasiparticles in the core cannot be scattered. In the BEC limit, on the other hand, the energy level spacing is large enough to form a single quantized level 13 (Fig. 1b), and thus the quasiparticles in the core are easily scattered, resulting in energy dissipative vortex motion. ![]() In the BCS limit, Δ 2/ E F is so small that the energy spectrum is almost continuous (Fig. According to the Caroli-de Gennes-Matricon picture 12, the energy level spacing is in the order of Δ 2/ E F. Inside the vortex core, the quasiparticle states are confined and quantized. Figure 1a, b shows a comparison of the energy levels inside the vortices for the BEC and BCS limit. One of the intriguing phenomena related to the enhancement of Δ/ E F is the dynamics of superconducting vortices. By approaching the crossover towards the BEC-limit, the coupling strength described as the ratio of superconducting gap Δ to Fermi energy E F increased 9. Since T c/ T F = 1/8 is the upper limit for 2D systems 10, 11 in the crossover, it confirms the successful approach of the 2D BCS-BEC crossover. In fact, both systems approached the crossover regime by reducing the carrier density and reached T c/ T F~1/8, where T c and T F are the critical temperature and the Fermi temperature, respectively. The tunable carrier density is highly advantageous to observe how the system evolves from the BCS- to the BEC-limit. The two BCS-BEC crossover systems, twisted trilayer graphene and Li xZrNCl, are highly two-dimensional (2D), and the carrier density can be controlled by a gate voltage. The first experimental realization of the BCS-BEC crossover was achieved in ultracold atomic gases 4 starting from the BEC side, while the approach with superconductors from the BCS side 5 has become active since recent discoveries of suitable materials including FeSe 6, twisted graphene 7, 8, and Li xZrNCl 9. ![]() The crossover between the two limiting ground states of Fermion systems-the BCS and BEC state-has attracted continuous interest both theoretically and experimentally from the communities of ultracold atomic gases and superconductors 1, 2, 3. These results demonstrate that gate-controlled superconductors are ideal platforms towards investigations of unexplored properties in BEC superconductors. Li xZrNCl 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. 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. Here we report the study of vortex dynamics within the crossover using their Hall effect as a probe in Li xZrNCl. These superconductors offer new opportunities to clarify the nature of charged-particles transport towards the BEC regime. For superconductors, ultra-low doping systems like graphene and Li xZrNCl successfully approached the crossover starting from the BCS-side. ![]() 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.
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