Multi-component Ginzburg-Landau theory: microscopic derivation and examples
نویسندگان
چکیده
This paper consists of three parts. In part I, we microscopically derive Ginzburg– Landau (GL) theory from BCS theory for translation-invariant systems in which multiple types of superconductivity may coexist. Our motivation are unconventional superconductors. We allow the ground state of the effective gap operator KTc + V to be n-fold degenerate and the resulting GL theory then couples n order parameters. In part II, we study examples of multi-component GL theories which arise from an isotropic BCS theory. We study the cases of (a) pure d-wave order parameters and (b) mixed (s+ d)-wave order parameters, in two and three dimensions. In part III, we present explicit choices of spherically symmetric interactions V which produce the examples in part II. In fact, we find interactions V which produce ground state sectors of KTc +V of arbitrary angular momentum, for open sets of of parameter values. This is in stark contrast with Schrödinger operators −∇2 + V , for which the ground state is always non-degenerate. Along the way, we prove the following fact about Bessel functions: At its first maximum, a half-integer Bessel function is strictly larger than all other half-integer Bessel functions.
منابع مشابه
Microscopic Derivation of Two-Component Ginzburg-Landau Model and Conditions of its Applicability in Two-Band Systems
متن کامل
Exact solutions of the 2D Ginzburg-Landau equation by the first integral method
The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to non integrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the 2D Ginzburg-Landau equation.
متن کاملSome new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equation
In this paper, we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method, homogeneous balance method, extended F-expansion method. By using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...
متن کاملA Rigorous Derivation of a Free-Boundary Problem Arising in Superconductivity
We study the Ginzburg-Landau energy of superconductors submitted to a possibly non-uniform magnetic eld, in the limit of a large Ginzburg-Landau parameter. We prove that the induced magnetic elds associated to minimizers of the energy-functional converge as ! +1 to the solution of a free-boundary problem. This free boundary-problem has a nontrivial solution only when the applied magnetic eld is...
متن کاملhigh-Tc superconductors from isothermal magnetization data. Influence of a temperature dependent Ginzburg-Landau parameter
We show that the scaling procedure, recently proposed for the evaluation of the temperature variation of the normalized upper critical field of type-II superconductors, may easily be modified in order to take into account a possible temperature dependence of the Ginzburg-Landau parameter κ. As an example we consider κ(T ) as it follows from the microscopic theory of superconductivity.
متن کامل