Ginzburg-Landau Coherence Length Research Articles

Test for BCS-BEC crossover in the cuprate superconductors

AbstractIn this paper we address the question of whether high-temperature superconductors have anything in common with BCS-BEC crossover theory. Towards this goal, we present a proposal and related predictions which provide a concrete test for the applicability of this theoretical framework. These predictions characterize the behavior of the Ginzburg-Landau coherence length, $${\xi }_{0}^{{{{\rm{coh}}}}}$$ ξ 0 coh , near the transition temperature Tc, and across the entire superconducting Tc dome in the phase diagram. That we are lacking a systematic characterization of $${\xi }_{0}^{{{{\rm{coh}}}}}$$ ξ 0 coh in the entire class of cuprate superconductors is perhaps surprising, as it is one of the most fundamental properties of any superconductor. This paper is written to motivate further experiments and, thus, address this shortcoming. Here we show how measurements of $${\xi }_{0}^{{{{\rm{coh}}}}}$$ ξ 0 coh contain direct indications for whether or not the cuprates are associated with BCS-BEC crossover and, if so, where within the crossover spectrum a particular superconductor lies.

Competing length scales and 2D versus 3D dimensionality in relatively thick superconducting NbN films

Magneto-transport characteristics of 2D and 3D superconducting layers, in particular, temperature and angular dependences of the upper critical field Hc2, are usually considered to be fundamentally different. In the work, using non-local resistance measurements at temperatures near the normal-to-superconducting transition, we probed an effective dimensionality of nm-thick NbN films. It was found that in relatively thick NbN layers, the thicknesses of which varied from 50 to 100 nm, the temperature effect on Hc2 certainly pointed to the three-dimensionality of the samples, while the angular dependence of Hc2 revealed behavior typical for 2D samples. The seeming contradiction is explained by an intriguing interplay of three length scales in the dimensionally confined superconducting films: the thickness, the Ginzburg–Landau coherence length, and the magnetic-field penetration depth. Our results provide new insights into the physics of superconducting films with an extremely large ratio of the London penetration depth to the Ginzburg–Landau coherence length exhibiting simultaneously 3D isotropic superconducting properties and the 2D transport regime.

Tuning metal/superconductor to insulator/superconductor coupling via control of proximity enhancement between NbSe2 monolayers

The interplay between charge transfer and electronic disorder in transition-metal dichalcogenide multilayers gives rise to superconductive coupling driven by proximity enhancement, tunneling and superconducting fluctuations, of a yet unwieldy variety. Artificial spacer layers introduced with atomic precision change the density of states by charge transfer. Here, we tune the superconductive coupling between monolayers from proximity-enhanced to tunneling-dominated. We correlate normal and superconducting properties in tailored multilayers with varying SnSe layer thickness (). From high-field magnetotransport the critical fields yield Ginzburg–Landau coherence lengths with an increase of cross-plane (), trending towards two-dimensional superconductivity for . We show cross-overs between three regimes: metallic with proximity-enhanced coupling (), disordered-metallic with intermediate coupling () and insulating with Josephson tunneling (). Our results demonstrate that stacking metal mono- and dichalcogenides allows to convert a metal/superconductor into an insulator/superconductor system, prospecting the control of two-dimensional superconductivity in embedded layers.

Structural and Superconducting Proximity Effect of SnPb Bimetallic Nanoalloys

We report the superconducting properties between a conventional strong-coupled Pb and weak-coupled Sn superconductor. A series of SnrPb1-r nanoalloys with various compositions r were synthesized, and their superconducting properties were measured using superconducting quantum interference devices (SQUIDs) magnetometer. Our results reveal a superconducting proximity effect (SPE) between immiscible Sn and Pb granules in the range of r = 0.2~0.9, as a weak superconducting coupling can be established with the coexistence of phonon hardening and increased Ginzburg-Landau coherence length. Furthermore, our results provide new insights into improving the study of the superconducting proximity effect introduced by Sn doping.

Absence of hexagonal-to-square lattice transition in LiFeAs vortex matter

We investigated magnetic vortices in two stoichiometric LiFeAs samples by means of scanning tunneling microscopy and spectroscopy. The vortices were revealed by measuring the local electronic density of states (LDOS) at zero bias conductance of samples in magnetic fields between 0.5 and 12 T. From single vortex spectroscopy we extract the Ginzburg-Landau coherence length of both samples as $4.4\pm0.5$ nm and $4.1\pm0.5$ nm, in accordance with previous findings. However, in contrast to previous reports, our study reveals that the reported hexagonal to square-like vortex lattice transition is absent up to 12 T both in field-cooling and zero-field-cooling processes. Remarkably, a highly ordered zero field cooled hexagonal vortex lattice is observed up to 8 T. We argue that several factors are likely to determine the structure of the vortex lattice in LiFeAs such as (i) details of the cooling procedure (ii) sample stoichiometry that alters the formation of nematic fluctuations, (iii) details of the order parameter and (iv) magnetoelastic coupling.

Evidence for isotropic s-wave superconductivity in high-entropy alloys

High-entropy alloys (HEA) form through the random arrangement of five or more chemical elements on a crystalline lattice. Despite the significant amount of resulting compositional disorder, a subset of HEAs enters a superconducting state below critical temperatures, T_{text{c}}<10, K. The superconducting properties of the known HEAs seem to suffice a Bardeen–Cooper–Schrieffer (BCS) description, but little is known about their superconducting order parameter and the microscopic role of disorder. We report on magnetic susceptibility measurements on films of the superconducting HEA (TaNb)_{1-x}(ZrHfTi)_{x} for characterizing the lower and upper critical fields H_{text{c,1}}(T) and H_{text{c,2}}(T), respectively as a function of temperature T. Our resulting analysis of the Ginzburg–Landau coherence length and penetration depth demonstrates that HEAs of this type are single-band isotropic s-wave superconductors in the dirty limit. Despite a significant difference in the elemental composition between the x=0.35 and x=0.71 films, we find that the observed T_{text{c}} variations cannot be explained by disorder effects.

Disorder-induced 2D superconductivity in a NbTiN film grown on Si by ultrahigh-vacuum magneton sputtering

We report on the growth and characterization of a niobium titanium nitride (NbTiN) film on a Si substrate prepared by ultrahigh vacuum sputtering. We show that the superconducting transition temperature is lower than those of high-quality NbTiN films. Interestingly, even though the zero-temperature Ginzburg-Landau coherence length (=9.77 nm) is significantly shorter than the film thickness (=86 nm), we are still able to observe the Berezinskii-Kosterlitz-Thouless-like transition, indicating the two-dimensional (2D) signature of our three-dimensional (3D) sample. We propose that the mechanism of hidden 2D superconducting property is similar to the recently reported results of the disordered induced 3D to 2D superconductor transition. We suggest further theoretical work is required for studying our new experimental results.

Negligible oxygen vacancies, low critical current density, electric-field modulation, in-plane anisotropic and high-field transport of a superconducting Nd0.8Sr0.2NiO2/SrTiO3 heterostructure

The emerging Ni-based superconducting oxide thin films are rather intriguing to the entire condensed matter physics. Here we report some brief experimental results on transport measurements for a 14-nm-thick superconducting Nd0.8Sr0.2NiO2/SrTiO3 thin-film heterostructure with an onset transition temperature of ~9.5 K. Photoluminescence measurements reveal that there is negligible oxygen vacancy creation in the SrTiO3 substrate during thin-film deposition and post chemical reduction for the Nd0.8Sr0.2NiO2/SrTiO3 heterostructure. It was found that the critical current density of the Nd0.8Sr0.2NiO2/SrTiO3 thin-film heterostructure is relatively small, ~4x10^3 A/cm2. Although the surface steps of SrTiO3 substrates lead to an anisotropy for in-plane resistivity, the superconducting transition temperatures are almost the same. The out-of-plane magnetotransport measurements yield an upper critical field of ~11.4 T and an estimated in-plane Ginzburg-Landau coherence length of ~5.4 nm. High-field magnetotransport measurements up to 50 T reveal anisotropic critical fields at 1.8 K for three different measurement geometries and a complicated Hall effect. An electric field applied via the SrTiO3 substrate slightly varies the superconducting transition temperature. These experimental results could be useful for this rapidly developing field.

Resistivity, Hall effect, and anisotropic superconducting coherence lengths of HgBa2CaCu2O6 thin films with different morphology

Thin films of the high-temperature superconductor HgBa2CaCu2O6 have been prepared on SrTiO3 substrates by pulsed-laser deposition of precursor films and subsequent annealing in mercury-vapor atmosphere. The microstructural properties of such films can vary considerably and have been analyzed by x-ray analysis and atomic force microscopy. Whereas the resistivity is significantly enhanced in samples with coarse-grained structure, the Hall effect shows little variation. This disparity is discussed based on models for transport properties in granular materials. We find that, despite of the morphological variation, all samples have similar superconducting properties. The critical temperatures T c ∼ 121.2 K …122.0 K, resistivity, and Hall data indicate that the samples are optimally doped. The analyses of superconducting order parameter fluctuations in zero and finite magnetic fields yield the in-plane ξ ab (0) ∼ 2.3 nm …2.8 nm and out-of-plane ξ c (0) ∼ 0.17 nm …0.24 nm Ginzburg–Landau coherence lengths at zero temperature. Hall measurements provide estimates of carrier scattering defects in the normal state and vortex pinning properties in the superconducting state inside the grains.

Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene.

Moiré superlattices1,2 have recently emerged as a platform upon which correlated physics and superconductivity can be studied with unprecedented tunability3-6. Although correlated effects have been observed in several other moiré systems7-17, magic-angle twisted bilayer graphene remains the only one in which robust superconductivity has been reproducibly measured4-6. Here we realize a moiré superconductor in magic-angle twisted trilayer graphene (MATTG)18, which has better tunability of its electronic structure and superconducting properties than magic-angle twisted bilayer graphene. Measurements of the Hall effect and quantum oscillations as a function of density and electric field enable us to determine the tunable phase boundaries of the system in the normal metallic state. Zero-magnetic-field resistivity measurements reveal that the existence of superconductivity is intimately connected to the broken-symmetry phase that emerges from two carriers per moiré unit cell. We find that the superconducting phase is suppressed and bounded at the Van Hove singularities that partially surround the broken-symmetry phase, which is difficult to reconcile with weak-coupling Bardeen-Cooper-Schrieffer theory. Moreover, the extensive in situ tunability of our system allows us to reach the ultrastrong-coupling regime, characterized by a Ginzburg-Landau coherence length that reaches the average inter-particle distance, and very large TBKT/TF values, in excess of 0.1 (where TBKT and TF are the Berezinskii-Kosterlitz-Thouless transition and Fermi temperatures, respectively). These observations suggest that MATTG can be electrically tuned close to the crossover to a two-dimensional Bose-Einstein condensate. Our results establish a family of tunable moiré superconductors that have the potential to revolutionize our fundamental understanding of and the applications for strongly coupled superconductivity.

Extended Ginzburg-Landau equations and Abrikrosov vortex and geometric transition from square to rectangular lattice in a magnetic field

In this study, we have constructed an extended version of Ginzburg-Landau theory of superconductivity starting from the exponential non-standard Lagrangian. An extended Ginzburg-Landau coherence length and an extended Ginzburg-Landau parameter emerge in the theory without affecting the Abrikosov's fluxoid quantization law. We have discussed the Abrikosov's periodic vortex lattice problem and we have observed that plausible solutions give rise to a shrink in the energy levels. We have also found that a transition between a type-II and a type-I superconductor takes place forκ=2/2whereas a transition between a new type-III and a type-I superconductor takes place for κ=ζ2/4 where ζ is a physical parameter. The new effective field of type III puts a supplementary limit for supercooling of the normal phase in superconductors. It was also revealed that a geometric transition from the square lattice to the rectangular lattice, a phenomenon which is detected in a number of superconductor's states.

Distortions to the penetration depth and coherence length of superconductor/normal-metal superlattices

Superconducting ($S$) thin film superlattices composed of Nb and a normal metal spacer ($N$) have been extensively utilized in Josephson junctions given their favorable surface roughness compared to Nb films of comparable thickness. In this work, we characterize the London penetration depth and Ginzburg-Landau coherence lengths of $S/N$ superlattices using polarized neutron reflectometry and electrical transport. Despite the normal metal spacer layers being only approximately 8% of the total superlattice thickness, we surprisingly find that the introduction of these thin $N$ spacers between $S$ layers leads to a dramatic increase in the measured London penetration depth compared to that of a single Nb film of comparable thickness. Using the measured values for the effective in- and out-of-plane coherence lengths, we quantify the induced anisotropy of the superlattice samples and compare to a single Nb film sample. From these results, we find that that the superlattices behave similarly to layered 2D superconductors.

Vortex state study of superconducting Fe(Te, Se) thin films deposited on SrTiO3 substrate by pulsed laser deposition technique

Superconducting thin films of two thicknesses have been fabricated on (100) oriented SrTiO3 (STO) substrates using the target of composition Fe1.05Te0.50Se0.50 by pulsed laser deposition technique. The structural and transport properties of the fabricated thin films have been investigated and the results indicate the enhancement in the superconducting properties with increasing thickness of the thin films. The onset of the superconducting transition temperature of the grown thin films of thicknesses ∼78 nm and ∼177 nm are ∼12.10 and 12.62 K at 0 T magnetic field, respectively. To estimate the upper critical fields HC2(0), thermally activated energy (TAE) and vortex phase diagram, the magnetoresistance measurements have been performed in the magnetic field range of 0 - 8 T. HC2(0) have been calculated by Ginzburg Landau (GL) theory and Werthamer-Helfand-Hohenberg model by taking the criterion of 90%, 50% and 10% of normal state resistivity and the corresponding GL coherence lengths have also been calculated. In the present work, the TAE has been estimated by conventional Arrhenius relation and modified thermally activated flux flow (TAFF) theory. The power law dependence of TAE, shows prominently the possible planer defects in the system. From the modified TAFF model, the values of fitting parameter ‘q’ suggests the 3 dimensional behaviour of the vortices for both the grown thin films. The vortex phase diagram study reveals the transition from the vortex liquid to vortex glass state.

AC Magnetic Susceptibility of Y3Ba5Cu8O18 Substituted by Nd3+ and Ca2+ Ions

Effect of Nd3+ and Ca2+ ion substitutions in Y3Ba5Cu8O18 (Y-358) was studied using X-ray diffraction (XRD), scanning electron microscopy (SEM), electrical resistivity, and ac magnetic susceptibility measurements. Superconducting samples of type Y3 − xNdxBa5 − yCayCu8O18 (with 0 ≤ x, y ≤ 0.4) were synthesized by the standard solid-state reaction technique. XRD patterns revealed that all the samples were mainly composed of Y-358 phase with orthorhombic structure. SEM micrographs showed that Nd3+ and Ca2+ ion substitutions had the ability to alter the grain morphology of Y-358 to irregular randomly oriented grains with smaller average grain sizes. The temperature-dependent electrical resistivity curves indicated that the superconducting transition temperature Tc was decreased from 96.51 to 87.41 K as the substitution contents were increased from 0 to 0.4. Detailed AC magnetic susceptibility measurements were done using a quantum design physical property measurement system (PPMS) at different dc fields (B = 0.5–20 kG) and frequency of 1 kHz. A comparison between electrical resistivity and AC magnetic susceptibility data was performed. It was found that Tcs obtained from AC magnetic susceptibility were much lower than those obtained from the resistivity measurements, for all studied samples. This was discussed in terms of filamentary paths that could produce sharp pronounced drops in diamagnetism. Generally, the depression in Tc was attributed to the decrease in relative volume fraction of Y-358 or due to trapping of mobile holes or other mechanism connected with oxygen vacancy disorder. Werthamer–Helfand–Hohenberg (WHH) theory was employed to study the temperature dependence of the upper critical magnetic field Bc2(T) for the samples. The relative importance of both orbital and paramagnetic effects in the suppression of superconductivity was described with the aid of Maki parameter (κM). The estimated values of the upper critical magnetic field at 0 K, Bc2(0), were found to decrease from 37.3 to 13.5 T as Nd3+ and Ca2+ contents were increased from 0 to 0.4. This decrement was attributed to the weak electron–phonon coupling and to the orbital as well as spin pair breaking mechanisms. Furthermore, Ginzburg–Landau coherence length ξGL of Y3 − xNdxBa5 − yCayCu8O18 was found to increase with the increase of the Nd3+ and Ca2+ contents. Therefore, Nd3+ and Ca2+ ions play an important role in the pair-breaking mechanism and in suppressing superconductivity of the Y-358 phase.

Anomalous mesoscopic kinetics in disordered superconductors

We study anomalous mesoscopic transport effects at the onset of the superconducting transition focusing on the observed large Nernst-Ettinghausen signal in disordered thin films. In the vicinity of the transition, as the Ginzburg-Landau coherence length of preformed Cooper pairs diverges, short-range mesoscopic fluctuations are equivalent to local fluctuations of the critical temperature. As a result, the dynamical susceptibility function of pair propagation acquires a singular mesoscopic component, and consequently, superconducting correlations give rise to enhanced mesoscopic fluctuations of thermodynamic and transport characteristics. In contrast to disordered normal metals, the root-mean-square value of mesoscopic conductivity fluctuations ceases to be universal and displays strong dependence on dimensionality, temperature, and under certain conditions can exceed its quantum normal state value by a large factor. Interestingly, we find different universality as magnetic susceptibility, conductivity, and transverse magnetic thermopower coefficients all display the same temperature dependence. Finally, we discuss an enhancement of mesoscopic effects in the Seebeck thermoelectricity and Hall conductivity fluctuations as mediated by emergent superconductivity.

Nuanced superconductivity in endohedral gallide Mo8Ga41

We report on synthesis and characterization of gallide cluster based Mo8Ga41 superconductor. Transport and magnetization measurements confirm the superconducting transition temperature to be 9.8 K. The upper critical field (Hc2), lower critical field (Hc1), Ginzburg–Landau coherence length ( ξGL) and penetration depth(λ) are estimated to be 11.8 T, 150 G, 5.28 nm, 148 nm respectively. The electronic band structure, density of states and phonon dispersion curve calculations are obtained by using Density Functional Theory. The core level x-ray Photoelectron Spectroscopy (XPS) reveals the binding energy information of the constituting elements Mo and Ga in Mo8Ga41. The valence band spectra from XPS are in good agreement with calculated density of states (DOS). The zero field critical current density (Jc) at T = 2 K is ∼3 × 105 A/cm2 which is indicative of efficient flux pinning in the as grown compound. About two fold enhancement in critical current density with application of external pressure (1.1 GPa) is observed with marginal decrease in transition temperature. The fitting of current density to double exponential model confirms possibility of two gap superconductivity in Mo8Ga41.

Filled skutterudite superconductor CaOs4P12 prepared by high-pressure synthesis

In this paper, we report the transport, thermodynamic, and superconducting properties of a new filled skutterudite ${\mathrm{CaOs}}_{4}{\mathrm{P}}_{12}$ synthesized under high pressure and high temperature. The electrical resistivity of 3.4--4.$8\mathrm{m}\mathrm{\ensuremath{\Omega}}\mathrm{cm}$, carrier concentration of 3.8--6.$1\ifmmode\times\else\texttimes\fi{}\phantom{\rule{4pt}{0ex}}{10}^{20}{\mathrm{cm}}^{\ensuremath{-}3}$, and positive Hall coefficient suggest that ${\mathrm{CaOs}}_{4}{\mathrm{P}}_{12}$ is a semimetal with hole carriers. An anomaly due to low-energy optical modes corresponding to an Einstein temperature of 150 K was observed in the specific heat. Resistivity, dc magnetic susceptibility, and specific heat measurements indicate bulk superconductivity below 2.5 K. The specific heat anomaly at ${T}_{\mathrm{c}},\mathrm{\ensuremath{\Delta}}C/\ensuremath{\gamma}{T}_{\mathrm{c}}\phantom{\rule{4pt}{0ex}}\ensuremath{\approx}1.4$, is in agreement with the Bardeen-Cooper-Schrieffer (BCS) value of 1.43. The electron-phonon coupling constant ${\ensuremath{\lambda}}_{ep}$ is estimated to be 0.47. ${\mathrm{CaOs}}_{4}{\mathrm{P}}_{12}$ is classified as a BCS-type, weakly coupled type-II superconductor with an upper critical field of ${H}_{\mathrm{c}2}\phantom{\rule{4pt}{0ex}}\ensuremath{\approx}22$ kOe and Ginzburg-Landau coherence length of $\ensuremath{\xi}\phantom{\rule{4pt}{0ex}}\ensuremath{\approx}12$ nm.

Superconductive coupling in tailored [(SnSe)1+δ]m(NbSe2)1 multilayers

Ferecrystals are a new artificially layered material system, in which the individual layers are stacked with monolayer precision and are turbostratically disordered. Here, the superconducting coupling of the NbSe2 layers in [(SnSe)1+δ]m[NbSe2]1 ferecrystals with m between 1 and 6 are investigated. The variation of m effectively increases the distance between the superconducting NbSe2 monolayers. We find a systematic decrease of the transition temperature with an increasing number of SnSe layers per repeat unit. For m = 9 a superconducting transition can no longer be observed at temperatures above 250 mK. In order to investigate the superconducting coupling between individual NbSe2 layers, the cross-plane Ginzburg–Landau coherence lengths were determined. Electric transport measurements of the superconducting transition were performed in the presence of a magnetic field, oriented parallel and perpendicular to the layers, at temperatures closely below the transition temperature. A decoupling with increasing distance of the NbSe2 layers is observed. However, ferecrystals with NbSe2 layers separated by up to six layers of SnSe are still considered as three-dimensional superconductors.

Quasi-two-dimensional fluctuations in the magnetization of La1.9Ca1.1Cu2O6+δ superconductors

We report the results of magnetization measurements with the magnetic field applied along the $c$ axis on superconducting $\mathrm{L}{\mathrm{a}}_{1.9}\mathrm{C}{\mathrm{a}}_{1.1}\mathrm{C}{\mathrm{u}}_{2}{\mathrm{O}}_{6+\ensuremath{\delta}}$ single crystals processed under ultrahigh oxygen pressure. Strong fluctuation effects were found in both low- and high-field regimes. Scaling analysis of the high-field magnetization data near the critical temperature $({T}_{c}=53.5\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ region reveals the characteristics of critical fluctuation behavior of quasi-two-dimensional (2D) superconductivity, described by Ginzburg-Landau theory using the lowest Landau level approximation. Low-field magnetic susceptibility data can be successfully explained by the Lawrence-Doniach model for a quasi-2D superconductor, from which we obtained the $ab$ plane Ginzburg-Landau coherence length of this system, ${\ensuremath{\xi}}_{ab}(0)=11.8\ifmmode\pm\else\textpm\fi{}0.9\phantom{\rule{0.16em}{0ex}}\AA{}$. The coherence length along the $c$ axis, ${\ensuremath{\xi}}_{c}(0)$, is estimated to be about 1.65 \AA{}, which is in between those of 2D cuprate systems, such as $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{r}}_{2}\mathrm{C}{\mathrm{a}}_{2}\mathrm{C}{\mathrm{u}}_{3}{\mathrm{O}}_{10}$ and $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{r}}_{2}\mathrm{CaC}{\mathrm{u}}_{2}{\mathrm{O}}_{8}$, and quasi-three-dimensional (3D) cuprate systems, such as overdoped $\mathrm{L}{\mathrm{a}}_{2\ensuremath{-}x}\mathrm{S}{\mathrm{r}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ and $\mathrm{YB}{\mathrm{a}}_{2}\mathrm{C}{\mathrm{u}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$. Our studies suggest a strong interplay among the fluctuation effects, dimensionalities, and the ratios of the interlayer Cu-O plane spacing, $s$, to the c-axis coherence lengths. A high $s/{\ensuremath{\xi}}_{c}(0)$ was observed in the high-pressure oxygenated $\mathrm{L}{\mathrm{a}}_{1.9}\mathrm{C}{\mathrm{a}}_{1.1}\mathrm{C}{\mathrm{u}}_{2}{\mathrm{O}}_{6+\ensuremath{\delta}}$, and that apparently drives this system to behave more like a quasi-2D superconductor.

Numerical Solution of Maxwell Equations for S-Wave Superconductors

The present paper is a sequel to the paper by Karchev (Condensed Matter 20 February 2017). We report the numerical solutions of the system of equations, which describes the electrodynamics of s-wave superconductors without normal quasi-particles for time-independent fields and half-plane superconductor geometry. The results are: (i) the applied magnetic field increases the Ginzburg–Landau (GL) coherence length and suppresses the superconductivity; (ii) the applied electric field decreases GL coherence length and supports the superconductivity; (iii) if the applied magnetic field is fixed and the applied electric field increases, the London penetration depth of the magnetic field decreases. The main conclusion is that by applying electric field at very low temperature where there are no normal quasi-particles one increases the critical magnetic field. This result is experimentally testable.