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Register a new userStrong-coupling theory of condensate-mediated superconductivity in 2D materials
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We develop a strong-coupling theory of Bose-Einstein condensate-mediated superconductivity in a hybrid system, which consists of a two-dimensional electron gas with either (i) parabolic spectrum or (ii) relativistic Dirac spectrum in the vicinity of a two-dimensional solid-state condensate of indirect excitons. The Eliashberg equations are derived and the expressions for the electron pairing self-energy due to the exchange interaction between electrons mediated by a single Bogoliubov excitation (a bogolon) and the bogolon pairs are found. Furthermore, we find the superconducting order parameter and estimate the critical temperature of the superconducting transition. The critical temperature reveals its linear dependence on the dimensionless coupling constant. It is shown, that the bogolon-pair-mediated interaction is the dominant mechanism of electron pairing in hybrid systems in both the weak and strong coupling regimes. We calculate the effective bogolon-electron interaction constant for both parabolic and linear electron dispersions and examine the dependence of the critical temperature of electron gas superconducting transition on exciton condensate density.
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Recent discovery of Ising superconductivity protected against in-plane magnetic field by spin-orbit coupling (SOC) has stimulated intensive research interests. The effect, however, was only expected to appear in two-dimensional (2D) noncentrosymmetric materials with spin-valley locking. In this work, we proposed a new type of Ising superconductivity in 2D materials with $C_{nz}$ rotational symmetry ($n=3,4,6$). This mechanism, dubbed as type-II Ising superconductivity, is applicable for centrosymmetric materials. Type-II Ising superconductivity relies on the SOC-induced spin-orbital locking characterized by Ising-type Zeeman-like fields displaying opposite signs for opposing orbitals. We found that type-II Ising superconductivity are most prominent around time-reversal invariant momenta and is not sensitive to inversion symmetry breaking. By performing high-throughput first-principles calculations, about one hundred candidate materials were identified. Our work significantly enriches the physics and materials of Ising superconductor, opening new opportunities for fundamental research and practical applications of 2D materials.
I present results from an extended Migdal-Eliashberg theory of electron-phonon interactions and superconductivity. The history of the electron-phonon problem is introduced, and then study of the intermediate parameter regime is justified from the energy scales in the cuprate superconductors. The Holstein model is detailed, and limiting cases are examined to demonstrate the need for an extended theory of superconductivity. Results of the extended approximation are shown, including spectral functions and phase diagrams. These are discussed with reference to Hohenbergs theorem, the Bardeen-Cooper-Schrieffer theory and Coulomb repulsion.
Coupling between $sigma$-bonding electrons and phonons is generally very strong. To metallize $sigma$-electrons provides a promising route to hunt for new high-T$_c$ superconductors. Based on this picture and first-principles density functional calculation with Wannier interpolation for electronic structure and lattice dynamics, we predict that trilayer film LiB$_2$C$_2$ is a good candidate to realize this kind of high-T$_c$ superconductivity. By solving the anisotropic Eliashberg equations, we find that free-standing trilayer LiB$_2$C$_2$ is a phonon-mediated superconductor with T$_c$ exceeding the liquid-nitrogen temperature at ambient pressure. The transition temperature can be further raised to 125 K by applying a biaxial tensile strain.
In order to discuss superconductivity in orbital degenerate systems, a microscopic Hamiltonian is introduced. Based on the degenerate model, a strong-coupling theory of superconductivity is developed within the fluctuation exchange (FLEX) approximation where spin and orbital fluctuations, spectra of electron, and superconducting gap function are self-consistently determined. Applying the FLEX approximation to the orbital degenerate model, it is shown that the $d_{x^2-y^2}$-wave superconducting phase is induced by increasing the orbital splitting energy which leads to the development and suppression of the spin and orbital fluctuations, respectively. It is proposed that the orbital splitting energy is a controlling parameter changing from the paramagnetic to the antiferromagnetic phase with the $d_{x^2-y^2}$-wave superconducting phase in between.
In flat bands, superconductivity can lead to surprising transport effects. The superfluid mobility, in the form of the superfluid weight $D_s$, does not draw from the curvature of the band but has a purely band-geometric origin. In a mean-field description, a non-zero Chern number or fragile topology sets a lower bound for $D_s$, which, via the Berezinskii-Kosterlitz-Thouless mechanism, might explain the relatively high superconducting transition temperature measured in magic-angle twisted bilayer graphene (MATBG). For fragile topology, relevant for the bilayer system, the fate of this bound for finite temperature and beyond the mean-field approximation remained, however, unclear. Here, we use numerically exact Monte Carlo simulations to study an attractive Hubbard model in flat bands with topological properties akin to those of MATBG. We find a superconducting phase transition with a critical temperature that scales linearly with the interaction strength. We then investigate the robustness of the superconducting state to the addition of trivial bands that may or may not trivialize the fragile topology. Our results substantiate the validity of the topological bound beyond the mean-field regime and further stress the importance of fragile topology for flat-band superconductivity.
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