Abstract
We study superconductivity in a family of one dimensional incommensurate system with $s$-wave pairing interaction. The incommensurate potential can alter the spatial characteristics of electrons in the normal state, leading to either extended, critical, or localized wave functions. We find that superconductivity is significantly enhanced when the electronic wave function exhibits a critical multifractal structure. This criticality also manifests itself in the power-law dependence of superconducting temperature on the pairing strength. As a consequence, an extended superconducting domain is expected to exist around the localization-delocalization transition, which can be induced by either tuning the amplitude of the incommensurate potential, or by varying the chemical potential across a mobility edge. Our results thus suggest a novel approach to enhance superconducting transition temperature through engineering of incommensurate potential.
Highlights
An electronically incommensurate potential appears in many condensed matter systems
First we show the Bogoliubov–de Gennes (BdG) calculation results for the one-dimensional (1D) s-wave superconductor under incommensurate potential Ui = J cos(2π Qxi )
As shown in Appendix E, the normal state density of state (DOS) at Fermi energy is modified by the incommensurate potential, and affects Tc
Summary
An electronically incommensurate potential appears in many condensed matter systems. Prominent examples include quasicrystals, broken symmetry with incommensurate order parameters, and the Moiré superlattice in twisted van der Waals heterostructures. An incommensurate potential can render the electronic wave functions localized or critical [1]. The electronic states can be categorized into extended, localized, and critical states depending on the spatial characteristics of the wave functions. While a better phase coherence can be maintained by an extended wave function, delocalized electrons in such a state do not take full advantage of the short-range pairing interaction. The superconducting transition temperature Tc is exponentially weak according to the BCS theory This implies that Tc may be enhanced in the case of critical states by optimizing the local pairing interaction while maintaining the long-range phase coherence. N where γn† and γn are the creation and annihilation operators for the Bogoliubov quasiparticle at state n and the prime sign means the sum is over all positive quasiparticle states En > 0
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
