Role of the Berry curvature on BCS-type superconductivity in two-dimensional materials

Abstract

We theoretically investigate how the Berry curvature, which arises in multi-band structures when the electrons can be described by an effective single-band Hamiltonian, affects the superconducting properties of two-dimensional electronic systems. Generically the Berry curvature is coupled to electric fields beyond those created by the periodic crystal potential. A potential source of such electric fields, which vary slowly on the lattice scale, is the mutual interaction between the electrons. We show that the Berry curvature provides additional terms in the Hamiltonian describing interacting electrons within a single band. When these terms are taken into account in the framework of the usual BCS weak-coupling treatment of a generic attractive interaction that allows for the formation of Cooper pairs, the coupling constant is modified. In pure singlet and triplet superconductors, we find that the Berry curvature generally lowers the coupling constant and thus the superconducting gap and the critical temperature as a function of doping. From an experimental point of view, a measured deviation from the expected BCS critical temperature upon doping, e.g. in doped two-dimensional transition-metal dichalcogenides, may unveil the strength of the Berry curvature.

arXiv comment14 pages, 3 figures

References in corpus (29)

• Topological Insulators
• Topological insulators and superconductors
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Berry Phase Effects on Electronic Properties
• Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS2
• Topological superconductors: a review
• Colloquium: Topological Band Theory
• Tightly bound excitons in monolayer WSe2
• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• Black phosphorus: narrow gap, wide applications
• Superfluidity in topologically nontrivial flat bands
• Superfluidity and Quantum Geometry in Twisted Multilayer Systems
• Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models
• All Topological Bands of All Nonmagnetic Stoichiometric Materials
• Anomalous Hall effect in paramagnetic two dimensional systems
• Towards a field theory of the fractional quantum Hall states
• Berry phase modification to the energy spectrum of excitons
• Topological and geometrical aspects of band theory
• Quantum Metric and Correlated States in Two-dimensional Systems
• Pairing symmetry of twisted bilayer graphene: a phenomenological synthesis
• Optical Absorption by Dirac Excitons in Single-Layer Transition-Metal Dichalcogenides
• Model Prediction of Self-Rotating Excitons in Two-Dimensional Transition-Metal Dichalcogenides
• Semiclassical Dynamics of Electrons in Magnetic Bloch Bands: a Hamiltonian Approach
• Measure of Diracness in two-dimensional semiconductors
• Charged exctions in two-dimensional transition-metal dichalcogenides - semiclassical calculation of Berry-curvature effects
• Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution
• Unconventional singlet-triplet superconductivity

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