arXiv subjects

Mao Yoshii

Publications and source records attributed to Mao Yoshii.

3 recordsLinked to original sources

arXiv2024

Brillouin zone folding method for quasiperiodic superconductivity in multilayer systems: application to electronic structure and optical responses

We construct an efficient momentum space approach to the superconductivity in quasiperiodic multilayer systems. To this end, we extend the Brillouin zone (BZ) folding method to the superconducting (SC) phases by formulating the gap equation in the momentum space representation with the BZ folding. We show that the physical observables in quasiperiodic multilayers are generally given by so-called quasiperiodic functions. Consequently, there appear SC order parameters with finite momenta in the BZ folding method, which corresponds to the spatial fluctuation of the SC order in quasiperiodic multilayers. We also find a systematic way to compute the physical observables in the BZ folding method with a proper normalization condition using the continued fraction approximation. We apply the BZ folding method to a one-dimensional toy model of quasiperiodic superconductors and demonstrate its numerical efficiency compared to the conventional method based on the real space representation with a large system size. We also study a quasiperiodic bilayer system of Rice-Mele model and an s-wave superconductor to demonstrate an efficient computation of optical responses of a quasiperiodic superconductor with inversion symmetry breaking.

cond-mat.supr-con↗

arXiv2022

Gap labeling theorem for multilayer thin film heterostructures

Quasiperiodic systems show a universal gap structure due to quasiperiodicity which is analogous to gap openings at the Brillouin zone boundary in periodic systems. The integrated density of states (IDoS) below those energy gaps are characterized by a few integers, which is known as the ``gap labeling theorem'' (GLT) for quasiperiodic systems. In this study, focusing on multilayer thin film systems such as twisted bilayer graphene and stacked transition metal dichalcogenides, we extend the GLT for multilayer systems of arbitrary dimensions and number of layers, using an approach based on the algebra called ``a noncommutative torus''. We find that the energy gaps and the associated IDoS are generally characterized by $_{DN}C_D$ integer labels in $N$ layer systems in the $D$ dimensions, when the effect of the interlayer coupling can be approximated by a quasiperiodic intralayer coupling for each layer. We demonstrate that the generalized GLT holds for quasiperiodic 1D tight binding models by numerical simulations.

cond-mat.str-el↗

arXiv2021

Topological charge pumping in quasiperiodic systems characterized by Bott index

We study topological charge pumping in one-dimensional quasiperiodic systems. Since these systems lack periodicity, we cannot use the conventional approach based on the topological Chern number defined in the momentum space. Here, we develop a general formalism based on a real space picture using the so-called Bott index. We extend the Bott index that was previously used to characterize quantum Hall effects in quasiperiodic systems, and apply it to topological charge pumping in quasiperiodic systems. The Bott index allows us to systematically compute topological indices of charge pumping, regardless of the detail of quasiperiodic models. We apply this formalism to the Fibonacci-Rice-Mele model which we made from Fibonacci lattice, a well-known quasiperiodic system, and Rice-Mele model. We find that these quasiperiodic systems show topological charge pumping with a multi-level behavior due to the fractal nature of the Fibonacci lattice. Such multi-level pumping behaviors can be understood by a real space renormalization group analysis.

cond-mat.mes-hall↗