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postgraduate thesis: Theoretical studies of PT symmetric topological gapless photonic crystals
Title  Theoretical studies of PT symmetric topological gapless photonic crystals 

Authors  
Advisors  Advisor(s):Wang, Z 
Issue Date  2017 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Xie, B. [解碧野]. (2017). Theoretical studies of PT symmetric topological gapless photonic crystals. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. 
Abstract  Topological gapless materials such as topological semimetals and topological metals have attracted lots of attention in recent years due to their unique topological transport properties and topologically protected surface states. As a kind of the representatives, the Weyl semimetals, which have gapless points in the bulk energy band structures, allow us to realize Weyl fermions which have not been observed in high energy physics. Such gapless modes especially gapless points in solidstate materials broaden the scope of the type of elementary particles in high energy physics. Although it is not difficult to realize band degeneracies in electronic materials, to ensure that the Fermi levels are exactly located at the degenerate points is not easy. This is one of the main obstacles to realize the theoretically predicted topological gapless models in electronic materials.
Fortunately, photonic crystals(PhCs) which are periodically arranged materials can be artificially manufactured. Actually, they can be used to simulate and study the topological gapless and gapped band structures. Due to the existence of translational symmetry, PhCs possess photonic band structures which can be used to control the propagation of electromagnetic fields in these materials. Traditional photonic band structures with a photonic band gap in PhCs have been theoretically and experimentally studied for decades. The difficulty in realizing certain types of topological band structures in electronic materials has disappeared when we simulate them in PhCs since the frequencies of electromagnetic fields propagating in PhCs can be controlled. Previous simulations on topological gapped systems result in topological protected oneway edge states in PhCs which can be used to achieve unidirectional backscatter free waveguides.
Classification of topological gapped and gapless systems with respect to time reversal symmetry, particlehole symmetry, chiral symmetry and several spatial symmetries has been fully conducted in theory and partially achieved in experiments. Discrete symmetries always lead to degenerate bands in the band structures of periodic materials. Therefore the gapless modes in both electronic materials and PhCs are always protected by discrete symmetries. Previously people have studied PhCs with time reversal symmetry and inversion symmetry(sometimes called parity symmetry in high energy physics). Here we consider a new type of symmetry, which is the combination of time reversal symmetry(T) and parity symmetry(P), the PT symmetry. A Hamiltonian, or more generally a linear operator, which has PT symmetry is not necessarily to be Hermitian. Although the operator itself is not Hermitian, its eigenvalues are kept to be real as long as the operator is invariant under PT symmetry. Thus it represents a real physical system. We find that a twodimensional PhC with hexagonal lattice structure which has PT symmetry will have gapless points in bulk band structure even both T symmetry and P symmetry are broken down. Furthermore, these gapless points are topologically protected by PT symmetry and characterized by a Z2 topological charge. As a matter of fact, they are stable against local perturbations as long as the perturbations do not break PT symmetry.

Degree  Doctor of Philosophy 
Subject  Photonic crystals Symmetry (Physics) Topological dynamics 
Dept/Program  Physics 
Persistent Identifier  http://hdl.handle.net/10722/255010 
DC Field  Value  Language 

dc.contributor.advisor  Wang, Z   
dc.contributor.author  Xie, Biye   
dc.contributor.author  解碧野   
dc.date.accessioned  20180621T03:41:55Z   
dc.date.available  20180621T03:41:55Z   
dc.date.issued  2017   
dc.identifier.citation  Xie, B. [解碧野]. (2017). Theoretical studies of PT symmetric topological gapless photonic crystals. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.   
dc.identifier.uri  http://hdl.handle.net/10722/255010   
dc.description.abstract  Topological gapless materials such as topological semimetals and topological metals have attracted lots of attention in recent years due to their unique topological transport properties and topologically protected surface states. As a kind of the representatives, the Weyl semimetals, which have gapless points in the bulk energy band structures, allow us to realize Weyl fermions which have not been observed in high energy physics. Such gapless modes especially gapless points in solidstate materials broaden the scope of the type of elementary particles in high energy physics. Although it is not difficult to realize band degeneracies in electronic materials, to ensure that the Fermi levels are exactly located at the degenerate points is not easy. This is one of the main obstacles to realize the theoretically predicted topological gapless models in electronic materials. Fortunately, photonic crystals(PhCs) which are periodically arranged materials can be artificially manufactured. Actually, they can be used to simulate and study the topological gapless and gapped band structures. Due to the existence of translational symmetry, PhCs possess photonic band structures which can be used to control the propagation of electromagnetic fields in these materials. Traditional photonic band structures with a photonic band gap in PhCs have been theoretically and experimentally studied for decades. The difficulty in realizing certain types of topological band structures in electronic materials has disappeared when we simulate them in PhCs since the frequencies of electromagnetic fields propagating in PhCs can be controlled. Previous simulations on topological gapped systems result in topological protected oneway edge states in PhCs which can be used to achieve unidirectional backscatter free waveguides. Classification of topological gapped and gapless systems with respect to time reversal symmetry, particlehole symmetry, chiral symmetry and several spatial symmetries has been fully conducted in theory and partially achieved in experiments. Discrete symmetries always lead to degenerate bands in the band structures of periodic materials. Therefore the gapless modes in both electronic materials and PhCs are always protected by discrete symmetries. Previously people have studied PhCs with time reversal symmetry and inversion symmetry(sometimes called parity symmetry in high energy physics). Here we consider a new type of symmetry, which is the combination of time reversal symmetry(T) and parity symmetry(P), the PT symmetry. A Hamiltonian, or more generally a linear operator, which has PT symmetry is not necessarily to be Hermitian. Although the operator itself is not Hermitian, its eigenvalues are kept to be real as long as the operator is invariant under PT symmetry. Thus it represents a real physical system. We find that a twodimensional PhC with hexagonal lattice structure which has PT symmetry will have gapless points in bulk band structure even both T symmetry and P symmetry are broken down. Furthermore, these gapless points are topologically protected by PT symmetry and characterized by a Z2 topological charge. As a matter of fact, they are stable against local perturbations as long as the perturbations do not break PT symmetry.   
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  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.subject.lcsh  Photonic crystals   
dc.subject.lcsh  Symmetry (Physics)   
dc.subject.lcsh  Topological dynamics   
dc.title  Theoretical studies of PT symmetric topological gapless photonic crystals   
dc.type  PG_Thesis   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Physics   
dc.description.nature  published_or_final_version   
dc.date.hkucongregation  2018   
dc.identifier.mmsid  991044014363203414   