Hyperbolic band theory under magnetic field and Dirac cones on a higher genus surface. (22nd September 2021)

• Record Type: Journal Article
• Authors: Ikeda, Kazuki; Aoki, Shoto; Matsuki, Yoshiyuki
• Is Part Of: Journal of physics. Volume 33:Number 48(2021)
• Publication Date: 2021-09-22
• Subjects: hyperbolic -- band -- theories -- magnetic field -- Dirac -- higher -- circuit quantum electrodynamics; Condensed matter -- Periodicals; Matière condensée -- Périodiques; Vaste stoffen; Vloeistoffen; Natuurkunde; Electronic journals; Computer network resources; 530.4105
• DOI: 10.1088/1361-648X/ac24c4
• Languages: English
• ISSNs: 0953-8984

Abstract

Abstract: We explore the hyperbolic band theory under a magnetic field for the first time. Our theory is a general extension of the conventional band theory defined on a Euclidean lattice into the band theory on a general hyperbolic lattice/Riemann surface. Our methods and results can be confirmed experimentally by circuit quantum electrodynamics, which enables us to create novel materials in a hyperbolic space. To investigate the band structures, we construct directly the hyperbolic magnetic Bloch states and find that they form Dirac cones on a coordinate neighborhood. They can be regarded as a global quantum gravity solution detectable in a laboratory. Besides this is the first explicit example of a massless Dirac state on a higher genus surface. Moreover we show that the energy spectrum exhibits an unusual fractal structure refracting the negative curvature, when plotted as a function of a magnetic flux.