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arXiv:2212.01170

Impact of the electric field on superconductivity in Bose-Einstein Condensation regime

Naoum Karchev

Published Dec 2, 2022• 0 citations
arXivHTMLPDF

Abstract

In the strong coupling Bose-Einstein Condensation (BEC) regime the superconductors have two characteristic temperatures: $T^*$- onset of fermion pairing and $T_{sc}$- onset of superconductivity, such that $T_{sc}T_{sc}$. Important consequence is the fact that arbitrary temperature within the interval ($T_{sc},T^*$) is a critical temperature of superconductor transition if an appropriate electric field is applied. This means that if we set the temperature of the system within the above mentioned interval and increase the applied electric field the system undergoes an electric field induced transition to superconductor. We also show the existence of critical value of the applied electric field at which $T^*=T^E_{sc}$. This means that although the system is in BEC regime, away from the BCS one, we can apply an electric field that moves the system to a state with $T^E_{sc}=T^*$, characteristic of BCS regime. The results indicate that applied electric field experiments are a suitable tool to identify the BEC regime of the superconductors. The experiment can determine $T^*$ as a temperature below which the electric field Bose condenses the Cooper pairs, while above it the electrons screen the field and it cannot penetrate.

DOI
10.48550/arxiv.2212.01170

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In the strong coupling Bose-Einstein Condensation (BEC) regime the superconductors have two characteristic temperatures: T∗T^*T∗- onset of fermion pairing and TscT_{sc}Tsc​- onset of superconductivity, such that TscTscT_{sc}T_{sc}Tsc​Tsc​. Important consequence is the fact that arbitrary temperature within the interval (Tsc,T∗T_{sc},T^*Tsc​,T∗) is a critical temperature of superconductor transition if an appropriate electric field is applied. This means that if we set the temperature of the system within the above mentioned interval and increase the applied electric field the system undergoes an electric field induced transition to superconductor. We also show the existence of critical value of the applied electric field at which T∗=TscET^*=T^E_{sc}T∗=TscE​. This means that although the system is in BEC regime, away from the BCS one, we can apply an electric field that moves the system to a state with TscE=T∗T^E_{sc}=T^*TscE​=T∗, characteristic of BCS regime. The results indicate that applied electric field experiments are a suitable tool to identify the BEC regime of the superconductors. The experiment can determine T∗T^*T∗ as a temperature below which the electric field Bose condenses the Cooper pairs, while above it the electrons screen the field and it cannot penetrate.
In this paper, we address the impact of the electric field on superconductors which are insulators in the normal state, semiconductors at low carrier concentration and ultracold gas of fermions in the strongly interacting regime. The electric field penetrates these systems and effects on the Cooper pairs. We show that if there are Cooper pairs above the superconductor critical temperature, the electric field forces the Cooper pairs to Bose condensate and the onset of the superconductivity, thereby increasing the critical temperature. To study this phenomenon, we numerically solve the Maxwell equations for [Formula: see text]-wave superconductors obtained from the time-dependent Ginzburg–Landau theory. Our investigation designs an experimental way for verification of the pairing of Fermions preceding superconductivity and superfluidity.
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Abstract The superfluid density ns(T)n_{s}(T)ns​(T) n s ( T ) of a superconductor is calculated based on the generalized Bose–Einstein condensation (GBEC) theory that addresses a fully-interacting ternary boson-fermion gas mixture of free electrons as fermions, plus two-electron Cooper pairs (2eCPs) and also, explicitly, two-hole Cooper pairs (2hCPs), both as bosons. Here we consider two special cases (i) 100%–0% (i.e., with no condensed 2hCPs) and (ii) 0%–100% (i.e., with no condensed 2eCPs). Subsumed in GBEC are the Bardeen–Cooper–Schrieffer (BCS) and Bose–Einstein condensation (BEC) theories along with the BCS-BEC crossover theory extended with 2hCPs. We find that in the weak-coupling regime ns(0)n_{s}(0)ns​(0) n s ( 0 ) agrees with data from the Uemura et al. (2004) graph for several elemental SCs by taking in 3D with a quadratic energy-dispersion relation while in 2D with a linear relation are much too far below the data. In the strong-coupling regime the linear behavior of critical temperature TcT_{c}Tc​ T c vs ns(0)n_{s}(0)ns​(0) n s ( 0 ) obtained here is just as Božović et al. (2016) found. However, in 2D with a linear relation accounting for 0%–100%, ns(T)/ns(0)n_{s}(T)/n_{s}(0)ns​(T)/ns​(0) n s ( T ) / n s ( 0 ) compares well with some high- TcT_{c}Tc​ T c -cuprate SC data between the two coupling regimes.
Observed crossover events between different power functions of absolute temperature occurring below about ~1 K in the temperature dependence of the heat capacity or the thermal conductivity of the conventional superconductors are identified as transitions from Maxwell-Boltzmann to Bose-Einstein (BE) statistics of the Cooper-pairs. Because of the low mass of the Cooper pairs of 2me (with me as mass of the electron) and their high density, the BE-condensation temperature, TBE, of the Cooper-pairs is about five orders of magnitude higher than for the dilute alkali atom condensates. The condensation temperature TBE turns out to be proportional to the superconducting transition temperature TSC. From the observed TBE-values it is possible to calculate the density of the Cooper pairs. Assuming that the Cooper pairs form a dense gas of bosons, the diameter of the Cooper-pair orbitals turns out to be equal to the London penetration depth. As a conclusion, due to the large orbital diamagnetism of the Cooper-pairs pairs, only one layer of Cooper-pairs, next to the inner surface of the sample, is sufficient to shield an applied external magnetic field completely.
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
This article gives a detailed review of our current theoretical understanding of the crossover from cooperative Cooper pairing to independent bound-state formation and Bose–Einstein condensation in Fermi systems with increasing attractive interactions. Introduction There are two well-known paradigms for understanding the phenomena of superconductivity and superfluidity: (I) BCS theory [1], in which the normal state is a degenerate Fermi liquid that undergoes a pairing instability at a temperature T c ≪ ε f , the degeneracy scale. The formation of Cooper pairs and their condensation (macroscopic occupation of a single quantum state) both occur simultaneously at the transition temperature T c . (II) Bose–Einstein condensation (BEC) of bosons at a T c of the order of their degeneracy temperature. At a fundamental level these bosons (for example, 4 He or excitons) are invariably composite objects made up of an even number of fermions. The composite particles form at some very high temperature scale of the order of their dissociation temperature T dissoc , and these “pre-formed” bosons then condense at the BEC T c ≪ T dissoc . In most cases of experimental interest the system under consideration clearly falls into one category or the other. For instance, 3 He is a Fermi superfluid described by (I) whereas 4 He is a Bose superfluid (II). Essentially all cases of superconductivity in metals that we understand reasonably well are much closer to (I) than to (II), as evidenced by the existence of fermionic quasiparticles above T c .