Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916139278270464 |
|---|---|
| author | Ikeda, Kazuki Aoki, Shoto Matsuki, Yoshiyuki |
| author_facet | Ikeda, Kazuki Aoki, Shoto Matsuki, Yoshiyuki |
| contents | 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 (cQED), 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, by which 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_13314 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface Ikeda, Kazuki Aoki, Shoto Matsuki, Yoshiyuki Mesoscale and Nanoscale Physics High Energy Physics - Theory Mathematical Physics Algebraic Geometry Quantum Physics 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 (cQED), 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, by which 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. |
| title | Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface |
| topic | Mesoscale and Nanoscale Physics High Energy Physics - Theory Mathematical Physics Algebraic Geometry Quantum Physics |
| url | https://arxiv.org/abs/2104.13314 |