scholarly journals The Cayley transform in complex, real and graded K-theory

2020 ◽  
Vol 31 (09) ◽  
pp. 2050074
Author(s):  
Chris Bourne ◽  
Johannes Kellendonk ◽  
Adam Rennie
Keyword(s):  
Real Structure ◽  
Computational Techniques ◽  
Topological Phases ◽  
Cayley Transform ◽  
K Theory ◽  
Topological Phases Of Matter ◽  
Special Case

We use the Cayley transform to provide an explicit isomorphism at the level of cycles from van Daele [Formula: see text]-theory to [Formula: see text]-theory for graded [Formula: see text]-algebras with a real structure. Isomorphisms between [Formula: see text]-theory and complex or real [Formula: see text]-theory for ungraded [Formula: see text]-algebras are a special case of this map. In all cases, our map is compatible with the computational techniques required in physical and geometrical applications, in particular, index pairings and Kasparov products. We provide applications to real [Formula: see text]-theory and topological phases of matter.

scholarly journals Half-Dirac Semimetal and Quantum Anomalous Hall Effect in Kagome Cd2N3 Lattice

2020 ◽  
Author(s):  
Xinyang Li ◽  
Weixiao Ji ◽  
Peiji Wang ◽  
Chang-wen Zhang
Keyword(s):  
Hall Effect ◽  
Quantum State ◽  
Anomalous Hall Effect ◽  
Topological Phases ◽  
Dirac Semimetal ◽  
Quantum Anomalous Hall Effect ◽  
Dirac Materials ◽  
Low Dimensionality ◽  
Dirac Semimetals ◽  
Topological Phases Of Matter

Half-Dirac semimetals (HDSs), which possess 100% spin-polarizations for Dirac materials, are highly desirable for exploring various topological phases of matter, as low-dimensionality opens unprecedented opportunities for manipulating the quantum state...

scholarly journals Non-Hermitian route to higher-order topology in an acoustic crystal

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
He Gao ◽  
Haoran Xue ◽  
Zhongming Gu ◽  
Tuo Liu ◽  
Jie Zhu ◽  
...  
Keyword(s):  
Higher Order ◽  
Order Topology ◽  
Topological Phases ◽  
Edge States ◽  
Experimental Realization ◽  
Artificial Materials ◽  
Intrinsic Loss ◽  
Topological Phases Of Matter ◽  
Hierarchical Features ◽  
Nontrivial Topology

AbstractTopological phases of matter are classified based on their Hermitian Hamiltonians, whose real-valued dispersions together with orthogonal eigenstates form nontrivial topology. In the recently discovered higher-order topological insulators (TIs), the bulk topology can even exhibit hierarchical features, leading to topological corner states, as demonstrated in many photonic and acoustic artificial materials. Naturally, the intrinsic loss in these artificial materials has been omitted in the topology definition, due to its non-Hermitian nature; in practice, the presence of loss is generally considered harmful to the topological corner states. Here, we report the experimental realization of a higher-order TI in an acoustic crystal, whose nontrivial topology is induced by deliberately introduced losses. With local acoustic measurements, we identify a topological bulk bandgap that is populated with gapped edge states and in-gap corner states, as the hallmark signatures of hierarchical higher-order topology. Our work establishes the non-Hermitian route to higher-order topology, and paves the way to exploring various exotic non-Hermiticity-induced topological phases.

Topological Phases of Matter

2021 ◽  
Author(s):  
Roderich Moessner ◽  
Joel E. Moore
Keyword(s):  
Topological Phases ◽  
Topological Phases Of Matter

scholarly journals Electrically tunable low-density superconductivity in a monolayer topological insulator

Science ◽  
2018 ◽  
Vol 362 (6417) ◽  
pp. 926-929 ◽  
Author(s):  
Valla Fatemi ◽  
Sanfeng Wu ◽  
Yuan Cao ◽  
Landry Bretheau ◽  
Quinn D. Gibson ◽  
...  
Keyword(s):  
Ground State ◽  
Field Effect ◽  
Field Effect Transistor ◽  
Quantum Spin ◽  
Topological Phases ◽  
Critical Temperatures ◽  
Topological States ◽  
Effect Transistor ◽  
Topological Phases Of Matter

Turning on superconductivity in a topologically nontrivial insulator may provide a route to search for non-Abelian topological states. However, existing demonstrations of superconductor-insulator switches have involved only topologically trivial systems. Here we report reversible, in situ electrostatic on-off switching of superconductivity in the recently established quantum spin Hall insulator monolayer tungsten ditelluride (WTe2). Fabricated into a van der Waals field-effect transistor, the monolayer’s ground state can be continuously gate-tuned from the topological insulating to the superconducting state, with critical temperaturesTcup to ~1 kelvin. Our results establish monolayer WTe2as a material platform for engineering nanodevices that combine superconducting and topological phases of matter.

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