On Mathematical Aspects of the Theory of Topological Insulators  

作　　者：Innocenti MARESIN Armen SERGEEV Egor TEPLYAKOV 

机构地区：[1]Department of Complex Analysis,Steklov Mathematical Institute,119991,Gubkina 8,Moscow,Russia [2]Moscow Institute of Physics and Technology,141701,Institute per.9,Dolgoprudny,Moscow Region,Russia

出　　处：《Acta Mathematica Sinica,English Series》2024年第1期81-106,共26页数学学报（英文版）

基　　金：Supported by RFBR(Grant Nos.19-01-00474,20-51-05006)。

摘　　要：This review is devoted to one of the most interesting and actively developing fields in condensed matter physics—theory of topological insulators.Apart from its importance for theoretical physics,this theory enjoys numerous connections with modern mathematics,in particular,with topology and homotopy theory,Clifford algebras,K-theory and non-commutative geometry.From the physical point of view topological invariance is equivalent to adiabatic stability.Topological insulators are characterized by the broad energy gap,stable under small deformations,which motivates application of topological methods.A key role in the study of topological ob jects in the solid state physics is played by their symmetry groups.There are three main types of symmetries—time reversion symmetry,preservation of the number of particles(charge symmetry)and PH-symmetry(particle-hole symmetry).Based on the study of symmetry groups and representation theory of Clifford algebras Kitaev proposed a classification of topological ob jects in solid state physics.In this review we pay special attention to the topological insulators invariant under time reversion.

关 键 词：Topological insulators Bloch theory fermionic Fock spaces Kramers degeneration Maiorana states 

分 类 号：O469[理学—凝聚态物理]