Surface states at Anderson transitions in topological phases

2015 Fiscal Year Final Research Report

• Project/Area Number: 25800213
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Hokkaido University
• Principal Investigator: Obuse Hideaki 北海道大学, 工学(系)研究科(研究院), 助教 (50415121)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: トポロジカル相 / アンダーソン転移 / 量子ウォーク

Outline of Final Research Achievements

We have found that two-dimensional surface states of the three dimensional weak topological insulator with a stacked structure remain delocalized irrespective strength of disorder if hoppings between layers are homogeneous. However, if the hoppings between layers induce dimerization effects, electric states of the surface states show a localized-delocalized transition at a certain strength of disorder, whose universality class belongs to the two-dimensional symplectic class. We have also developed an efficient method to numerically calculate the scaling dimension of descendant operators at the two-dimensional integer quantum Hall transition. Furthermore, we have developed systematic procedures to identify symmetry and calculate topological numbers of time-evolution operators which could exhibit Floquet-topological phases. We have succeeded to explain the robustness of surface states of the one-dimensional quantum walk against disorder by using arguments of topological phases.

Free Research Field

物性理論