Topology of two-band superconductors

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Abstract

Two-band superconductivity has a topology different from that in single-band superconductivity. The topology is not always stabilized in an infinitely homogeneous sample. The morphology, grain shape, and pattern of the device (topology of the superconducting materials) is effective in stabilizing the topology. In this report, we discuss a vortex having a small magnetic flux but a large winding number as one plausible topology in a two-band superconductor.

Introduction

Since the 1950s, many two-band superconductors (and multi-band superconductors) have been investigated experimentally and theoretically. These include transition metals such as Nb, graphite intercalation compounds such as KC8, intermetallic rare earth transition metal borocarbides such as YNi2 B2C, multilayer cuprate superconductors such as CuxBa2Ca3Cu4Oy, magnesium diboride, iron-based superconductors such as NdFeAsO1-x, and so on [1], [2].

In two-band superconductors, we can consider that each superconducting condensation on each band has its own superconducting phase. This consideration can be applied when the interband interaction is much smaller than the intraband interaction. Using an extended London approximation, in which we assume that the superconducting pair density can be considered constant and no spatial gradient exists, the properties of the system are governed by the interband phase difference. This situation gives an intuitive image of the physics involved [3], [4].

Section snippets

Model

We substitute two-component order parameter, {|Ψ1|exp(iθ1),|Ψ2|exp(iθ2)} for the usual order parameter, Ψ, used in single-band superconductivity [1], [2], [3], [4], [5], [6], [7], [8], [9]. |Ψν|2 is the pair density on each band index by ν, which is assumed to be constant (an extended London approximation). θν is the quantum phase of each component.

When there is no magnetic field, the current J=en1m1θ1+en2m2θ2 becomes zero (this current can be called the non-inductive current) [2], [4], [5]

Result

At the ground states, θ1=θ2. When there is an interband phase difference soliton, this soliton (or more precisely, the soliton wall) divides the superconductor into two regions having different quantum phases (formation of the soliton is irrelevant to the magnetic field) [1], [4], [6]. The trace of the phase change is shown in Fig. 1a and b under zero magnetic field. Here, we trace one location to another on a continuously connected path in the two-band superconductor. θ1=θ2 corresponds to the

Discussion

When |Ψ1|=|Ψ2|, the phase changes by π when crossing a soliton. This situation is the same as in triplet superconductivity (pseudo-triplet superconductivity) [7], [8]. When we cross another soliton, the phase recovers 2π. Regions where θdomain=θ1=θ2 (the phase of a domain surrounded by the soliton wall) are classified into either θdomain=0 or θdomain=π.

When |Ψ1||Ψ2| we cannot recover the phase even after crossing two soliton walls, unlike in a pseudo-triplet superconductivity. θdomain can take

Summary

In two-band superconductors, an abnormal vortex can be stabilized by the sample’s morphology. This monster vortex can join many soliton walls and have arbitrarily small flux quanta.

Acknowledgments

This work was supported by the Strategic International Cooperative Program of the Japan Science and Technology Agency (JST) and the Department of Science and Technology (India) ‘Feasibility study of the application of multiple-order parameters in materials to information processing’; by a Grant-in-Aid for Specially Promoted Research (2 0 0 0 1 0 0 4) from The Ministry of Education, Culture, Sports, Science and Technology (MEXT); by the National Institute of Advanced Industrial Science and Technology

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