Crystalline Gapless and Gapped Topological Phases from The Global Topology of The Momentum Space

Professor Wang, Zidan   (Principal Investigator (PI))

Dr Zhang Shizhong   (Co-Investigator)

Dr Zhao Yuxin   (Co-Investigator)

36

2017-07-01

472351

Crystalline Gapless and Gapped Topological Phases from The Global Topology of The Momentum Space

Crysalline Topological Phases, Global Topology in The k Space, Quantum Simulations, Real Equivariant K Theory, Topological Metal/Insulator

Physics

Physical Sciences (P)

17305717

General Research Fund (GRF)

2017

Completed

1 We aim to develop the concept of global topology for gapless crystalline topological phases, which may extend the current local topology merely for a single gapless Fermi point to the global one for the whole system of a crystalline (semi)metal. 2 New mathematical techniques would be introduced and developed by us for classifications and characterizations of the crystalline topological phases. In particular, find proper ways to apply the equivariant real K theory for band theories with crystal symmetries, and formulate corresponding topological invariants for topological phases. 3 Our proposed work on crystal-symmetry-enforced topological (semi)metals would deepen our understandings of the relations among the quantum criticality, crystal symmetries, and particularly topology. 4 New fermions are expected to be discovered in this project. In contrast to the Poincaré symmetry for elementary particles in high energy physics, these new fermions may respect certain crystal symmetries and have topological charges, which would lead to exotic structures of internal degrees of freedom, and anomalous responses to external sources including electromagnetic fields, strain, and thermal perturbations. 5 We intend to make theoretical proposals about the simulations of the crystalline topological phases by utilizing cutting-edge technologies for artificial systems, in particular cold atoms and superconducting cirsuits, which may provide persuasive experimental tests with high tunability. Note that physical parameters in real materials are usually restricted in certain ranges which are not very adjustable.