Nematic superconductivity in doped Bi2Se3 topological superconductors

Nematic superconductivity is a novel class of superconductivity characterized by spontaneous rotational-symmetry breaking in the superconducting gap amplitude and/or Cooper-pair spins with respect to the underlying lattice symmetry. Doped Bi2Se3 superconductors, such as CuxBi2Se3, SrxBi2Se3, and NbxBi2Se3, are considered as candidates for nematic superconductors, in addition to the anticipated topological superconductivity. Recently, various bulk probes, such as nuclear magnetic resonance, specific heat, magnetotransport, magnetic torque, and magnetization, have consistently revealed two-fold symmetric behavior in their in-plane magnetic-field-direction dependence, although the underlying crystal lattice possesses three-fold rotational symmetry. More recently, nematic superconductivity is directly visualized using scanning tunneling microscopy and spectroscopy. In this short review, we summarize the current researches on the nematic behavior in superconducting doped Bi2Se3 systems, and discuss issues and perspectives.Comment: 20 pages (incl. 5 pages of reference list), 4 figures; Submitted for the proceedings of Erice Workshop 2018 "Majorana Fermions and Topological Materials Science". Small revisions are made on 14th Dec. Comments are welcom

Coincidence sets in quasilinear elliptic problems of monostable type

This paper concerns the formation of a coincidence set for the positive solution of $p$-Laplacian elliptic problems of monostable type. It is proved that for any small parameter of diffusion term, the solution coincides with the stable zero-function $a(x)$ of reaction term in an open set if $a(x)$ is $p$-harmonic (but, not constant) and a zero of order less than 1. Inversely, it is also shown that the solution is less than $a(x)$ if $a(x)$ is a zero of order greater than or equal to 1. The proof rely on comparison theorems and an energy method for obtaining local comaprison functions.Comment: 18 page

Bose-Einstein condensation in the Rindler space

Based on the Unruh effect, we calculate the critical acceleration of the Bose-Einstein condensation in a free complex scalar field at finite density in the Rindler space. Our model corresponds to an ideal gas performing constantly accelerating motion in a Minkowski space-time at zero-temperature, where the gas is composed of the complex scalar particles and it can be thought to be in a thermal-bath with the Unruh temperature. In the accelerating frame, the model will be in the Bose-Einstein condensation state at low acceleration, on the other hand there will be no condensation at high acceleration by the thermal excitation brought into by the Unruh effect. Our critical acceleration is the one at which the Bose-Einstein condensation begins to appear in the accelerating frame when we decrease the acceleration gradually. To carry out the calculation, we assume that the critical acceleration is much larger than the mass of the particle.Comment: 18 pages, no figure; v2: improvement of the abstract, introduction and remarks, and some minor corrections; v3: mainly, description in the analysis part was improved, v5: accepted versio

Unruh effect in a real scalar field with the Higgs type potential on the de Sitter space

It has been predicted that an accelerating electron performs a Brownian motion in the inertial frame. This Brownian motion in the inertial frame has its roots in the interaction with the thermal excitation given by the Unruh effect in the accelerating frame. If such a prediction is possible, we correspondingly propose a prediction in this study that the thermal radiation appears in the inertial frame from an electron heated by the Unruh effect in the accelerating frame. The point in our prediction is, although the Unruh effect is only in the accelerating frame, if the appearance of the Brownian motion rooted in the Unruh effect in the inertial frame can be predicted, the heat that the particle gets in its body by the Unruh effect in the accelerating frame could survive in the inertial frame. Based on such a prediction, in this paper we investigate phenomena in the neighborhood of an accelerating electron in the inertial frame. The model we consider is the four-dimensional Klein-Gordon real scalar field model with the Higgs type potential term at the finite temperature identified with the Unruh temperature on the de Sitter space-time. We calculate the one-loop effective potential in the inertial frame with the corrections by the thermal radiation rooted in the Unruh effect in the accelerating frame. In this calculation, we take into account that the background space-time is deformed due to the field theory's corrected one-loop effective potential. Based on such an analysis, we illustrate the restoration of the spontaneous symmetry breaking and the variation of the background space-time, and we examine the accelerating particle's world-line and the amount of the energy corresponding to the change of the acceleration.Comment: v3: 16 pages, 8 figures, version after published (description was improved