Influence of an external electric field on high-Tc superconductivity

Lee, W.D.; Chen, J.L.; Yang, Tzong–Jer; Chiou, Bi–Shiou

doi:10.1016/0921-4534(96)00128-1

Cited by 11 publications

(14 citation statements)

References 19 publications

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“…where C is independent of ∆. In this order of expansion in small φ 1 , the additional electrostatic field energy in (19) coincides with the standard expression. The linear term ∼ ρ 1 φ 0 describes a gate effect on superconductivity, which in this approach we see to be related to the ∆-dependence of the equilibrium potential φ 0 .…”

Section: Mean-field Modelsupporting

confidence: 71%

Superconducting size effect in thin films under electric field: Mean-field self-consistent model

2019

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We consider effects of an externally applied electrostatic field on superconductivity, selfconsistently within a BCS mean field model, for a clean 3D metal thin film. The electrostatic change in superconducting condensation energy scales as µ −1 close to subband edges as a function of the Fermi energy µ, and follows 3D scaling µ −2 away from them. We discuss nonlinearities beyond gate effect, and contrast results to recent experiments.

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Section: Mean-field Modelsupporting

confidence: 71%

Superconducting size effect in thin films under electric field: Mean-field self-consistent model

2019

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“…Although there is a long history of experimental and theoretical investigation of the control of superconductivity with electric fields beginning with Glover and Sherill, 61 there has been no significant tuning of superconductivity in metallic systems, and models based on the BCS theory 62,63,64 only treat the effect on the transition temperature of changes in the density of states in response to changes in the carrier concentration. They do not include an issue that is relevant here, the apparent insulator to metal transition that accompanies the superconductor to insulator transition.…”

Section: Discussionmentioning

confidence: 99%

Electrostatic and parallel-magnetic-field tuned two-dimensional superconductor-insulator transitions

2006

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The two-dimensional superconductor-insulator transition in disordered ultrathin amorphous bismuth films has been tuned both by electrostatic electron doping using the electric field effect and by the application of parallel magnetic fields. Electrostatic doping was carried out in both zero and nonzero magnetic fields, and magnetic tuning was conducted at multiple strengths of electrostatically induced superconductivity. The various transitions were analyzed using finite size scaling to determine their critical exponent products. For the electrostatically tuned transition the exponent product νz = 0.7 ± 0.1, using data from intermediate temperatures down to 60 mK. Here ν is the correlation length exponent and z is the dynamical critical exponent. In the case of electrostatically tuned transitions in field, and the field-tuned transtions at various values of electrostatically induced superconductivity, from intermediate temperatures down to about 100 to 150 mK scaling was successful with νz = 0.65 ± 0.1. The parallel critical magnetic field, Bc, increased with electron transfer as (∆nc − ∆n) 0.33 , and the critical resistance decreased linearly with ∆n. However at lower temperatures, in the insulating regime, the resistance became larger than expected from extrapolation of its temperature dependence at higher temperatures, and scaling failed. These observations imply that although the electrostatic-and parallel magnetic field-tuned superconductor-insulator transitions would appear to belong to the same universality class and to be delineated by a robust phase boundary that can be crossed either by tuning ∆n or B, in the case of the field-tuned transition at the lowest temperatures, some different type of physical behavior turns on in the insulating regime.

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“…Formula (15) differs from Shapiro's formula (9) only by a factor due to the impurity limited coherence length assumed in Ref. 15.…”

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confidence: 94%

“…A heuristic derivation of the fieldeffect from the GL equation cannot cover this factor. 9 It is advantageous to express the effective potential U s via the usual parameters of the GL theory. First we employ the BCS relation for the critical temperature…”

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confidence: 99%

Ginzburg-Landau theory of superconducting surfaces under the influence of electric fields

et al. 2006

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A boundary condition for the Ginzburg-Landau wave function at surfaces biased by a strong electric field is derived within the de Gennes approach. This condition provides a simple theory of the field effect on the critical temperature of superconducting layers.The critical temperature of a thin superconducting layer is increased or lowered by an electric field applied perpendicular to the layer. [1][2][3][4][5] Similarly to the conductivity of inverse layers in semiconductors, superconductivity of thin metallic layers can thus be controlled by a gate voltage, which makes these structures attractive for applications.In this paper we show that the phase transition in a thin metallic layer is conveniently described by the Ginzburg-Landau (GL) theory, where the electric field E enters the GL boundary condition asBriefly, the logarithmic derivative of the GL function ψ or the gap function ∆ at the surface is a sum of the zerofield part 1/b 0 and the field induced correction E/U s . The zero-field part has been derived by de Gennes 6 from the BCS theory. A typical value b 0 ∼ 1 cm is large on the scale of the GL coherence length, therefore this contribution is usually neglected. This approximation, 1/b 0 ≈ 0, corresponds to the original GL condition ∇ψ = 0.Here we employ the de Gennes approach to derive the field induced correction E/U s . The correction becomes important for the above mentioned experiments, where fields of the order of 10 7 V/cm are realized. Small electric fields appearing e.g. in Josephson junctions do not require such corrections.We start from the conditionderived by de Gennes (Eq. (7-62) in Ref. 6). Here N 0 is the density of states of a bulk material, V is the BCS interaction, and N (x) is the local density of states at position x. The actual gap function ∆(x) has a nontrivial profile close to the surface at x = 0, but it has only slow variation at distances exceeding the BCS coherence length ξ 0 = 0.18hv F /k B T c . For x ∼ ξ 0 it is crudely linear ∆(x) ≈ ∆ 0 (1 + x/b), so that ∆ 0 is not the true surface value but the extrapolation of the gap function towards the surface. In Eq. (2) we have used the GL coherence length at zero temperature ξ(0) = 0.74 ξ 0 for pure metals. In measurements of the field effect on the transition temperature, the zero-field term b 0 is included in the reference zero-bias transition temperature. Accordingly, we can assume a model of the crystal for which 1/b 0 = 0. The simplest model of this kind is a semi-infinite jellium, where for zero field the density of states is steplike, N (x) = N 0 for x > 0 and N (x) = 0 elsewhere. Using that the gap function is restricted to the crystal, ∆(x) = 0 for x < 0, one can check that from (2) follows 1/b 0 = 0. Now we include the electric field. According to the Anderson theorem 7 , the electric field does not change the thermodynamical properties directly but only via the density of states. The change of the density of states is also indirect. The penetrating electric field induces a deviation δn of the electron density. The den...

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Influence of an external electric field on high-Tc superconductivity

Cited by 11 publications

References 19 publications

Superconducting size effect in thin films under electric field: Mean-field self-consistent model

Superconducting size effect in thin films under electric field: Mean-field self-consistent model

Electrostatic and parallel-magnetic-field tuned two-dimensional superconductor-insulator transitions

Ginzburg-Landau theory of superconducting surfaces under the influence of electric fields

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