Superconductivity

Motivated by the recently developed classical spin model for Migdal-Eliashberg theory, we develop new numerical and analytical methods based on this spin-chain representation and apply these methods to the Bogoliuov-Tomachov-Morel-Anderson pairing potential, which incorporates the phonon-mediated attraction and Coulomb repulsion. We show that the Monte Carlo method with heat bath updates can efficiently obtain the gap functions even for the situations challenging for the iterative solvers, suggesting an unprecedented robust approach for solving the full nonlinear Migdal-Eliashberg theory. Moreover, we derive the renormalization of all the couplings by tracing out the high-frequency spins in the partition function. The derived analytical renormalization equations produce the well-known μ^∗ effect for the Bogoliuov-Tomachov-Morel-Anderson pairing potential and can be generalized to other superconductivity problems. We further point out that several interesting features (e.g., sign changing in the frequency-dependent gap function) can be intuitively understood using the classical spin-chain representation for Migdal-Eliasherg theory. Our results show the advantage of using the spin-chain representation for solving Migdal-Eliashberg theory and provide new ways for tackling general superconductivity problems.

Phys. Rev. B 109, 054514 (2024)

Motivated by a recent experiment (Y. Zhang et al., arXiv:2205.05087), we investigate a possible mechanism that enhances superconductivity in hole-doped Bernal bilayer graphene due to a proximate WSe2 monolayer. We show that the virtual tunneling between WSe2 and Bernal bilayer graphene, which is known to induce Ising spin-orbit coupling, can generate an additional attraction between two holes, providing a potential explanation for enhancing superconductivity in Bernal bilayer graphene. Using microscopic interlayer tunneling, we derive the Ising spin-orbit coupling and the effective attraction as functions of the twist angle between Bernal bilayer graphene and the WSe2 monolayer. Our theory provides an intuitive and physical explanation for the intertwined relation between Ising spin-orbit coupling and superconductivity enhancement, which should motivate future studies.

Phys. Rev. B 106, L180502 (2022)

Motivated by the discovery of superconductivity in ABC-stacked trilayer graphene, we investigate electron-acoustic-phonon coupling as a possible pairing mechanism. Because of the SU(2)*SU(2) symmetry in the electron-acoustic phonon coupling, the resulting superconductivity has a spin-singlet-spin-triplet degeneracy. The low-energy bands further restrict the sublattice structures in the pairing states such that the s-wave and f-wave dominate. We demonstrate that superconductivity prevails in a wide range of doping, suggesting that superconductivity is likely to be induced by the acoustic phonon. Our theory paves the way for the understanding of superconductivity in graphene-based systems.

 Phys. Rev. Lett. 127, 187001 (2021); Editors' Suggestion

In addition, superconductivity in Bernal bilayer graphene can also be explained by acoustic-phonon-mediated pairing. In this case, Coulomb suppression is not negligible.

Phys. Rev. B 105, L100503 (2022)

We further analyze the graphene crystalline multilayers incorporating the Coulomb suppression (mu^* effect). 

Phys. Rev. B 106, 024507 (2022)

We present a simple model that captures the key aspects of the competition between superconducting and insulating states in twisted bilayer graphene. Within this model, the superconducting phase is primary and arises at generic fillings but is interrupted by the insulator at commensurate fillings. Notably, the insulator forms because of electron-electron interactions, but the model is agnostic as to the superconducting pairing mechanism, which need not originate with electron-electron interactions. The model comprises a collection of crossed one-dimensional quantum wires whose intersections form a superlattice.  We place a locally superconducting puddle at each superlattice point that can exchange Cooper pairs with the quantum wires. We analyze this model assuming weak wire-puddle and wire-wire couplings. We show that for a range of repulsive intrawire interactions, the system is superconducting at `generic' incommensurate fillings, with the superconductivity being `interrupted' by an insulating phase at commensurate fillings. We further show that the gapped insulating states at commensurate fillings give way to gapless states upon application of external Zeeman fields. Despite the distinct microscopic details, these features are consistent with experimental observations in magic-angle twisted bilayer graphenes. We further study the complete phase diagram of this model and discover that it contains several distinct correlated insulating states, which we characterize herein.

Phys. Rev. B 100, 115128 (2019) 

In 2013, a THz pump-probe experiment demonstrated Higgs amplitude mode oscillation in around ten picoseconds duration. The results are reminiscent of the well-studied interaction quench of the BCS model. However, the microscopic mechanisms are quite distinct. We construct a model for simulating the pulse effect and demonstrate that the THz-pumped BCS superconductors can be viewed as a quantum quench problem. The concrete mathematical connection is the Lax reduction method which classifies post-quench steady states into phases I, II, and III. We further predict the existence of phase I for sufficiently intense pump pulses. Moreover, we also compute optical conductivity, superfluid stiffness, and excess energies for the nonequilibrium steady state. This work provides a simplified way to study THz-pumped superconductors.

Phys. Rev. B 95, 104507 (2017); Editors' suggestion