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postgraduate thesis: Numerical study of topological insulators and semimetals
Title  Numerical study of topological insulators and semimetals 

Authors  
Advisors  Advisor(s):Shen, S 
Issue Date  2011 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Abstract  Topological insulators(TIs) constitute a novel state of quantum matter which possesses nontrivial topological properties. Although discovered only in the recent few years, TIs have attracted intensive interest among the community of condensed matter physics and material science. TIs are insulating in the bulk but have conductive gapless edge or surface states on the boundaries, which have their origin in the nontrivial bulk band topology that is induced by the strong spinorbital interactions in the materials. Existing in all dimensions, TIs exhibit a variety of exotic physics such as quantum spin Hall effect, momentumspin locked surface states, Dirac fermion transport, quantized anomalous Hall effect, Majorana fermions, etc. In this thesis,
I study the transport properties of 2D and 3D TIs by numerical approaches. As an introduction, a brief review of TIs is given. A detailed description of the numerical methods is also presented. The results can be summarized in four aspects. First, disorder is found be able to induce a nontrivial TI from an originally trivial band insulator, where the conductance of a two terminal device drops to nearly zero and then rises to form an anomalous plateau as disorder strength is increased, and finally all the states become localized. The real space Chern number calculation as well as the effective medium theory suggests that disorder is fundamentally responsible for the emerging of the extended helical edge states in this system. We also present a levitation and pair annihilation picture of the extended states for this model. Second, by making the 2D TIs into singly connected quantum point contacts(QPCs), I show a coherent and fast AharonovBohm oscillation of conductance caused by the quantum interference of the helical edge states. This oscillation not only happens against weak magnetic field but also against the gate voltage in the zerofield condition.
This results in a giant edge magnetoresistance of the device in weak magnetic fields. The amplitude of the magnetoresistance is controllable by adjusting either the
QPCs' slit width or the interference loop size in the device. The oscillation is found robust against disorder. Third, by applying a uniform spinsplitting Zeeman field in the bulk of the 3D TI whose surface states can be viewed as massless Dirac fermions,
I find chiral edge states on the gapped surfaces of the 3D TI, which can be considered as interface states between domains of massive and massless Dirac fermions.
Effectively these states are result of splitting of a perfect interface conducting channel. This picture is confirmed by the LandauerB?ttiker calculations in fourterminal Hall bars. Finally, I propose the concept of topological semimetals. By calculating the local density of states on the surfaces, I demonstrate that surface states and the gapless
Dirac cone already exist in the system although the bulk is not gapped. We show how the uniaxial strain induces an insulating band gap and turn the semimetal into true TI. We predict existence of quantum spin Hall effect in the thin films made of these materials, which can be significantly enhanced by disorders. 
Degree  Doctor of Philosophy 
Subject  Condensed matter. Semimetals. 
Dept/Program  Physics 
DC Field  Value  Language 

dc.contributor.advisor  Shen, S   
dc.contributor.author  Chu, Ruilin.   
dc.contributor.author  储瑞林.   
dc.date.issued  2011   
dc.description.abstract  Topological insulators(TIs) constitute a novel state of quantum matter which possesses nontrivial topological properties. Although discovered only in the recent few years, TIs have attracted intensive interest among the community of condensed matter physics and material science. TIs are insulating in the bulk but have conductive gapless edge or surface states on the boundaries, which have their origin in the nontrivial bulk band topology that is induced by the strong spinorbital interactions in the materials. Existing in all dimensions, TIs exhibit a variety of exotic physics such as quantum spin Hall effect, momentumspin locked surface states, Dirac fermion transport, quantized anomalous Hall effect, Majorana fermions, etc. In this thesis, I study the transport properties of 2D and 3D TIs by numerical approaches. As an introduction, a brief review of TIs is given. A detailed description of the numerical methods is also presented. The results can be summarized in four aspects. First, disorder is found be able to induce a nontrivial TI from an originally trivial band insulator, where the conductance of a two terminal device drops to nearly zero and then rises to form an anomalous plateau as disorder strength is increased, and finally all the states become localized. The real space Chern number calculation as well as the effective medium theory suggests that disorder is fundamentally responsible for the emerging of the extended helical edge states in this system. We also present a levitation and pair annihilation picture of the extended states for this model. Second, by making the 2D TIs into singly connected quantum point contacts(QPCs), I show a coherent and fast AharonovBohm oscillation of conductance caused by the quantum interference of the helical edge states. This oscillation not only happens against weak magnetic field but also against the gate voltage in the zerofield condition. This results in a giant edge magnetoresistance of the device in weak magnetic fields. The amplitude of the magnetoresistance is controllable by adjusting either the QPCs' slit width or the interference loop size in the device. The oscillation is found robust against disorder. Third, by applying a uniform spinsplitting Zeeman field in the bulk of the 3D TI whose surface states can be viewed as massless Dirac fermions, I find chiral edge states on the gapped surfaces of the 3D TI, which can be considered as interface states between domains of massive and massless Dirac fermions. Effectively these states are result of splitting of a perfect interface conducting channel. This picture is confirmed by the LandauerB?ttiker calculations in fourterminal Hall bars. Finally, I propose the concept of topological semimetals. By calculating the local density of states on the surfaces, I demonstrate that surface states and the gapless Dirac cone already exist in the system although the bulk is not gapped. We show how the uniaxial strain induces an insulating band gap and turn the semimetal into true TI. We predict existence of quantum spin Hall effect in the thin films made of these materials, which can be significantly enhanced by disorders.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.rights  Creative Commons: Attribution 3.0 Hong Kong License   
dc.source.uri  http://hub.hku.hk/bib/B47163252   
dc.subject.lcsh  Condensed matter.   
dc.subject.lcsh  Semimetals.   
dc.title  Numerical study of topological insulators and semimetals   
dc.type  PG_Thesis   
dc.identifier.hkul  b4716325   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Physics   
dc.description.nature  published_or_final_version   
dc.identifier.doi  10.5353/th_b4716325   
dc.date.hkucongregation  2012   