Related papers: Sarma-Bogomol'nyi equations in superconductivity
Motivated by the geometric character of spin Hall conductance, the topological invariants of generic superconductivity are discussed based on the Bogoliuvov-de Gennes equation on lattices. They are given by the Chern numbers of degenerate…
We study mean-field states resulting from the pairing of electrons in time-reversal broken fractal Hofstadter bands, which arise in two-dimensional lattices where the unit cell traps magnetic flux $\Phi = (p/q)\Phi_0$ comparable to the flux…
Using the Ginzburg-Landau theory extended to the next-to-leading order we determine numerically the healing lengths of the two order parameters at the two-gap superconductor/normal metal interface. We demonstrate on several examples that…
Solutions of the Bogoliubov-de Gennes equations for the two-dimensional self-consistent Hubbard t-U-V model of superconductors with $d_{x^2-y^2}$ symmetry of the order parameter in the presence of a magnetic field are found. It is shown…
A variational model is proposed to describe the magnetic properties of type-II superconductors in the entire field range between $H_{c1}$ and $H_{c2}$ for any values of the Ginzburg-Landau parameter $\kappa>1/\sqrt{2}$. The hexagonal unit…
The Abelian Higgs model with or without external particles is considered in curved space. Using the dual transformation, we rewrite the model in terms of dual gauge fields and derive the Bogomol'nyi-type bound. We examine cylindrically…
Following Bogomolnyi's classical treatment of vortices, we develop a method for finding rigorous lower bounds to the Landau-Ginzburg free energy describing unconventional superconductors in the absence of external magnetic fields. This…
This Ph.D. thesis investigates effective field and string theories in which supersymmetry is realized and broken in various ways. Chapter 1 addresses effective theories with nonlinearly realized supersymmetry, constructed using the…
Several experimental studies have shown the presence of spatially inhomogeneous phase coexistence of superconducting and non superconducting domains in low dimensional organic superconductors. The superconducting properties of these systems…
A new symmetry of $(1,0)$ supersymmetric non-linear $\sigma$-models in two dimensions with Fermi and mass sectors is introduced. It is a generalisation of the so-called special holonomy $W$-symmetry of Howe and Papadopoulos associated with…
A topological mechanism is a zero elastic-energy deformation of a mechanical structure that is robust against smooth changes in system parameters. Here, we map the nonlinear elasticity of a paradigmatic class of topological mechanisms onto…
As shown by Taubes, in the Bogomol'nyi-Prasad-Sommerfield limit the SU(2) Yang-Mills-Higgs model possesses smooth finite energy solutions, which do not satisfy the first order Bogomol'nyi equations. We construct numerically such a…
Geometric Langlands duality relates a representation of a simple Lie group $G^\vee$ to the cohomology of a certain moduli space associated with the dual group $G$. In this correspondence, a principal $SL_2$ subgroup of $G^\vee$ makes an…
We study superconductors with $n$-fold rotational invariance both in the presence and in the absence of spin-orbit interactions. More specifically, we classify the non-interacting Hamiltonians by defining a series of $Z$-numbers for the…
There have been several proposals for platforms sustaining topological superconductivity in high temperature superconductors, in order to make use of the larger superconducting gap and the expected robustness of Majorana zero modes towards…
We investigate string solutions to the classical equations of motion ("classical QCD strings") for a dual Ginzburg-Landau model corresponding to SU(3) gluodynamics in an abelian projection. For a certain relation between couplings of the…
In his seminal 1934 paper on Brownian motion and the theory of gases Kolmogorov introduced a second order evolution equation which displays some challenging features. In the opening of his 1967 hypoellipticity paper H\"ormander discussed a…
We give model-independent arguments, valid in nearly any number of spacetime dimensions, that topological solitons and instantons satisfy Bogomol'nyi-type bounds and, when these bounds are saturated, satisfy self-duality equations. In the…
We study N=2 supersymmetric Born-Infeld-Higgs theory in 3 dimensions and derive Bogomol'nyi relations in its bosonic sector. A peculiar coupling between the Higgs and the gauge field (with dynamics determined by the Born-Infeld action) is…
In this paper we consider axisymmetric black holes in supergravity and address the general issue of defining a first order description for them. The natural setting where to formulate the problem is the De Donder-Weyl-Hamilton-Jacobi theory…