Linear Criterion for an Upper Bound on the Bardeen-Cooper-Schrieffer Critical Temperature
arXiv:2407.00796 · doi:10.1063/5.0230179
Abstract
Since Bardeen-Cooper-Schrieffer theory of superconductivity is non-linear, it is difficult to study superconducting properties analytically. There is a more tractable linear criterion which determines a temperature below which the system is superconducting. Here, we observe that there is a similar linear criterion which gives a temperature above which no superconductivity occurs. We provide examples of translation invariant systems where as well as systems where . Furthermore, we estimate for half-spaces and show that it is exponentially small in the weak coupling limit, exhibiting the same asymptotics as the critical temperature for full space.
20 pages, 1 figure
References in corpus (15)
- Critical Temperature and Energy Gap for the BCS Equation
- The BCS Functional for General Pair Interactions
- The BCS functional of superconductivity and its mathematical properties
- A Nonlinear Model for Relativistic Electrons at Positive Temperature
- The external field dependence of the BCS critical temperature
- Boundary Superconductivity in the BCS Model
- Temperature Effects in a Fermi Gas with Population Imbalance
- The BCS gap equation for spin-polarized fermions
- The BCS critical temperature in a weak homogeneous magnetic field
- Persistence of translational symmetry in the BCS model with radial pair interaction
- Universal and nonuniversal features of Bardeen-Cooper-Schrieffer theory with finite-range interactions
- Universality in low-dimensional BCS theory
- Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field
- Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields
- First-order phase transition by a spin-flip potential in BCS superconductivity