Journal
JOURNAL OF PHYSICS-CONDENSED MATTER
Volume 33, Issue 48, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-648X/ac24c4
Keywords
hyperbolic; band; theories; magnetic field; Dirac; higher; circuit quantum electrodynamics
Categories
Funding
- PIMS Postdoctoral Fellowship Award
- Japan Society for the Promotion of Science (JSPS) [JP19J20559]
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This study explores the hyperbolic band theory under a magnetic field for the first time, extending traditional band theory to hyperbolic lattice/Riemann surface and proposing a novel method for material creation in a hyperbolic space. Experimental confirmation shows that hyperbolic magnetic Bloch states form Dirac cones and the energy spectrum exhibits a unique fractal structure when plotted as a function of magnetic flux.
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.
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