2007/10/31 by Mahito Kohmoto, Daijiro Tobe · 39 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Coupling (piping) #Critical line #Duality (order theory) #Lattice (music) #Magnetic properties of thin films #Materials science #Mathematical physics #Mathematics #Phase (matter) #Phase diagram #Physics #Pure mathematics #Quantum mechanics #Quasiperiodic function #Quasiperiodicity #Spin–orbit interaction #Square lattice #Theoretical and Computational Physics #Topological Materials and Phenomena #Wave function #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.77.134204
published in Physical Review B 77(13) (American Physical Society) · 10 pages, 11 figures
arxiv created 2008/03/06 · openalex publication_date 2008/04/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a one-dimensional quasiperiodic system that is obtained from a tight-binding model on the square lattice in a uniform magnetic field with the spin-orbit interaction. A phase diagram with respect to the Harper coupling and the Rashba coupling is proposed from a number of numerical studies, which include a multifractal analysis. There are four phases, i.e., I, II, III, and IV, in this order from weak to strong Harper coupling. In the weak coupling phase I, all of the wave functions are extended, in the intermediate coupling phases II and III, mobility edges exist and, accordingly, both localized and extended wave functions exist, and in the strong Harper coupling phase IV, all of the wave functions are localized. Phases I and IV are related by duality, and phases II and III are related by duality as well. A localized wave function is related to an extended wave function by the duality and vice versa. The boundary between phases II and III is the self-dual line, on which all of the wave functions are critical. In the present model, the duality does not lead to pure spectra in contrast to the case of a Harper equation.