57 citations · 236 across the 14 of their papers we have counts for
6 papers · 1 filter
Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface
Kazuki Ikeda, Shoto Aoki, Yoshiyuki Matsuki
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 in…
Fractal defect states in the Hofstadter butterfly
Yoshiyuki Matsuki, Kazuki Ikeda, Mikito Koshino
We investigate the electronic properties in the Bloch electron on a square lattice with vacancies in the uniform magnetic field. We show that a single vacancy site introduced to th…
Topological Aspects of Matters and Langlands Program
Kazuki Ikeda
The Langlands program is a vast mathematical projection linking number theory and geometry. In high-energy physics, a connection with mirror symmetry has been suggested in string t…
Comments on the Fractal Energy Spectrum of Honeycomb Lattice with Defects
Yoshiyuki Matsuki, Kazuki Ikeda
We address the energy spectrum of honeycomb lattice with various defects or impurities under a perpendicular magnetic field. We use a tight-binding Hamiltonian including interactio…
Quantum Hall Effect and Langlands Program
Kazuki Ikeda
Recent advances in the Langlands program shed light on a vast area of modern mathematics from an unconventional viewpoint, including number theory, gauge theory, representation, kn…
Hofstadter's Butterfly and Langlands Duality
Kazuki Ikeda
We dig out a deeper mathematical structure of the quantum Hall system from a perspective of the Langlands program. An algebraic expression of the Hamiltonian with the quantum group…