Quantum geometry encoded to pair potentials

Abstract

Bloch wave functions of electrons have properties called quantum geometry, which has recently attracted much attention as the origin of intriguing physical phenomena. In this paper, we introduce the notion of the quantum-geometric pair potentials (QGPP) based on the generalized band representation and thereby clarify how the quantum geometry of electrons is transferred to the Cooper pairs they form. QGPP quantifies the deviation of multiband superconductors from an assembly of single-band superconductors and has a direct connection to the quantum-geometric corrections to thermodynamic coefficients. We also discuss their potential ability to emulate exotic pair potentials and engineer intriguing superconducting phenomena including topological superconductivity.

arXiv comment12 pages, 2 figures (+8 pages)

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• Ideal quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity
• Quantum geometry in correlated electron phases: from flat band to dispersive band
• Normal state quantum geometry, non-locality and superconductivity
• Quantum geometric tensor in systems with fractional band dispersion
• Distinct topological excitonic insulators characterized by quantum geometry
• Quantum Geometric Helical Superconductivity
• Superconducting magnetoelectric effects in mesoscopic hybrid structures