New paradigm for a disordered superconductor in a magnetic field

Datta, Anushree; Banerjee, Anurag; Trivedi, Nandini; Ghosal, Amit

doi:10.48550/arxiv.2101.00220

Cited by 8 publications

(15 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Until recently, small-λ region was not attainable for direct numerical simulations of real 2D and 3D systems due to size restrictions. Advances in this field [32][33][34] seem to make such a study possible. The shape of distribution function P (∆) was found to differ considerably from the fat-tail distributions obtained previously in Ref.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Distribution of the order parameter in strongly disordered superconductors: An analytic theory

Khvalyuk,

Feigel'man

2021

Preprint

View full text Add to dashboard Cite

We developed an analytic theory of inhomogeneous superconducting pairing in strongly disordered materials, which are moderately close to superconducting-insulator transition. Single-electron eigenstates are assumed to be Anderson-localized, with a large localization volume. Superconductivity develops due to coherent delocalization of originally localized pre-formed Cooper pairs. The key assumption of the theory is that each such pair is coupled to a large number Z 1 of similar neighboring pairs. We derived integral equations for the probability distribution P (∆) of local superconducting order parameter ∆ (r) and analyzed their solutions in the limit of small dimensionless Cooper coupling constant λ 1. The shape of the order-parameter distribution is found to depend crucially upon the effective number of "nearest neighbors" Zeff = 2ν0∆0Z. The solution we provide is valid both at large and small Zeff; the latter case is nontrivial as the function P (∆) is heavily non-Gaussian. The discovery of a broad parameter range where the distribution function P (∆) is non-Gaussian but also non-critical (in the sense of SIT criticality) is one of our key findings. The analytic results are supplemented by numerical data, and good agreement between them is observed.

show abstract

Section: Discussionmentioning

confidence: 99%

“…As already mentioned, the discussed approximation is valid for κ λ, as follows from analysis of higher order corrections to the expansion (34), see Subsection C 4 for details. The presented results (35)(36)(37) are otherwise accessible by a direct averaging of the original saddle-point equations (4).…”

Section: Extreme Value Statisticsmentioning

confidence: 93%

Distribution of the order parameter in strongly disordered superconductors: An analytic theory

Khvalyuk,

Feigel'man

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…One can also study the multifractal superconducting state that occurs in the system that without superconducting instability is near the interacting metal-insulator transition. Our theory can also be extended to the case of an applied magnetic field that destroys the superconducting state and may produce an intermediate phase with giant magnetoresistance [54] (for studying the giant magnetoresistance near the transition within the NLSM formalism, see Ref. [23]).…”

Section: Discussionmentioning

confidence: 99%

Multifractally-enhanced superconductivity in thin films

Burmistrov,

Gornyi,

Mirlin

2021

Preprint

View full text Add to dashboard Cite

The multifractal superconducting state originates from the interplay of Anderson localization and interaction effects. In this article we overview the recent theory of the superconductivity enhancement by multifractality and extend it to describe the spectral properties of superconductors on the scales of the order of the superconducting gap. Specifically, using the approach based on renormalization group within the nonlinear sigma model, we develop the theory of a multifractal superconducting state in thin films. We derive a modified Usadel equation that incorporates the interplay of disorder and interactions at energy scales larger than the spectral gap and study the effect of such an interplay on the low-energy physics. We determine the spectral gap at zero temperature which occurs to be proportional to the multifracally enhanced superconducting transition temperature. The modified Usadel equation results in the disorder-averaged density of states that, near the spectral gap, resembles the one obtained in the model of a spatially random superconducting order parameter. We reveal strong mesoscopic fluctuations of the local density of states in the superconducting state. Such strong mesoscopic fluctuations imply that the interval of energies in which the superconducting gap establishes is parametrically large in systems with multifractally-enhanced superconductivity.

show abstract

“…The origin of these unexpected features is still under debate [21] though it is believed to be somehow related to residual correlations of the superconducting state [22][23][24][25][26] in the form, for instance, of localized phase-incoherent Cooper's pairs. A more recent explanation of this phenomenon [27], based on an explicit numerical solution of the BdG equations in small lattices, is that there exists a region of magnetic fields where the conductivity still has a gap-like form for low frequencies but the superfluidity density vanishes. As a result, the resistivity becomes very large until larger magnetic fields close the gap completely.…”

Section: Introductionmentioning

confidence: 99%

“…It is important to stress that, with the exception of Refs. [17,27], theoretical research about vortices in disordered superconductors do not employ the microscopic and self-consistent BdG approach where the random potential is the one felt by the electrons that form the Cooper's pair. For instance, in the XY model, describing the phase dynamics, the Josephson couplings are random but they are not directly related to the random potential that model impurities in materials.…”

Section: Introductionmentioning

confidence: 99%

Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors

Fan¹,

García-García²

2022

Preprint

View full text Add to dashboard Cite

The interplay of disorder and magnetic vortices is a recurrent topic of research in the theory of superconductivity. In most of previous approaches, disorder enters in a phenomenological way, namely, it is not the random potential felt by the electrons.Here we address this problem in a fully microscopic model: a two-dimensional disordered superconductor at zero temperature described by the Bogoliubov-de Gennes (BdG) formalism for lattices of sizes up to 100 × 100 where the magnetic field is introduced by the Peierls's substitution. For a not too strong disorder strength, we identify a rich phase diagram in Fourier space as a function of the magnetic field strength. Initially, we observe the expected Abrikosov triangular vortex lattice slightly distorted by disorder. Intriguingly, an increase in the magnetic field leads to an unexpected rectangular lattice which is followed by a vortex glass with only traces of Bragg's peaks but strong vortex repulsion. Finally, a further increases of the field leads to a fully disordered phase where even vortex repulsion is suppressed.We show that these phases can coexist with global phase coherence. Disorder also enhances the critical magnetic field with respect to the clean limit with a maximum for strong disorder strength on the metallic side of the transition.

show abstract

New paradigm for a disordered superconductor in a magnetic field

Cited by 8 publications

References 45 publications

Distribution of the order parameter in strongly disordered superconductors: An analytic theory

Distribution of the order parameter in strongly disordered superconductors: An analytic theory

Multifractally-enhanced superconductivity in thin films

Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors

Contact Info

Product

Resources

About