Quantization of Edge Currents Along Magnetic Interfaces: A K-Theory Approach

被引：0
作者：
De Nittis, Giuseppe [1 ,2 ]
Gutierrez, Esteban [1 ]
机构：
[1] Pontificia Univ Catolica Chile, Fac Matemat, Santiago, Chile
[2] Pontificia Univ Catolica Chile, Inst Fis, Santiago, Chile
来源：
ACTA APPLICANDAE MATHEMATICAE | 2021年 / 175卷 / 01期
关键词：
Magnetic interfaces; Iwatsuka Hamiltonian; Edge currents; K-theory; QUANTUM; TRANSPORT; ALGEBRAS; STATES;
D O I：
10.1007/s10440-021-00428-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The purpose of this paper is to investigate the propagation of topological currents along magnetic interfaces (also known as magnetic walls) of a two-dimensional material. We consider tight-binding magnetic models associated to generic magnetic multi-interfaces and describe the K-theoretical setting in which a bulk-interface duality can be derived. Then, the (trivial) case of a localized magnetic field and the (non trivial) case of the Iwatsuka magnetic field are considered in full detail. This is a pedagogical preparatory work that aims to anticipate the study of more complicated multi-interface magnetic systems.
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页数：58
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共 64 条
  • [1] Conceptions of topological transitivity
    Akin, Ethan
    Carlson, Jeffrey D.
    [J]. TOPOLOGY AND ITS APPLICATIONS, 2012, 159 (12) : 2815 - 2830
  • [2] [Anonymous], 1998, MATH SCI RES I PUBLI
  • [3] [Anonymous], 1990, ALGEBRAS OPERATOR TH
  • [4] Arici F., 2020, GEOMETRIC METHODS PH, VXXXVIII
  • [5] Arveson W., 1976, INVITATION ALGEBRAS, DOI [10.1007/978-1-4612-6371-5, DOI 10.1007/978-1-4612-6371-5]
  • [6] CHARGE DEFICIENCY, CHARGE-TRANSPORT AND COMPARISON OF DIMENSIONS
    AVRON, JE
    SEILER, R
    SIMON, B
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 159 (02) : 399 - 422
  • [7] K-Theory for Group C*-algebras
    Baum, Paul F.
    Sanchez-Garcia, Ruben J.
    [J]. TOPICS IN ALGEBRAIC AND TOPOLOGICAL K-THEORY, 2011, 2008 : 1 - 43
  • [8] Spectral continuity for aperiodic quantum systems I. General theory
    Beckus, Siegfried
    Bellissard, Jean
    De Nittis, Giuseppe
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2018, 275 (11) : 2917 - 2977
  • [9] Bellissard J., 1986, Statistical Mechanics and Field Theory: Mathematical Aspects. Proceedings of the International Conference, P99
  • [10] THE NONCOMMUTATIVE GEOMETRY OF THE QUANTUM HALL-EFFECT
    BELLISSARD, J
    VANELST, A
    SCHULZBALDES, H
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 1994, 35 (10) : 5373 - 5451
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