scholarly journals Engineering of topological phases in driven thin topological insulators: Structure inversion asymmetry effect

2021 ◽  
Vol 104 (24) ◽  
Author(s):  
S. Sajad Dabiri ◽  
Hosein Cheraghchi
Keyword(s):  
Topological Insulators ◽  
Topological Phases ◽  
Asymmetry Effect ◽  
Inversion Asymmetry ◽  
Structure Inversion

Topological phases of a three-dimensional topological insulator with structure inversion asymmetry

2015 ◽  
Vol 29 (06) ◽  
pp. 1550034 ◽  
Author(s):  
Xiaoyong Guo ◽  
Zaijun Wang ◽  
Qiang Zheng ◽  
Jie Peng
Keyword(s):  
Phase Diagram ◽  
Topological Insulator ◽  
Tight Binding ◽  
Three Dimensional ◽  
Surface States ◽  
Topological Phases ◽  
Zeeman Field ◽  
Surface Modes ◽  
Inversion Asymmetry ◽  
Structure Inversion

We investigate the topological phases of a three-dimensional (3D) topological insulator (TI) without the top–bottom inversion symmetry. We calculate the momentum depended spin Chern number to extract the phase diagram. Various phases are found and we address the dependence of phase boundaries on the strength of inversion asymmetry. Opposite to the quasi-two-dimensional thin film TI, in our 3D system the TI state is stabilized by the structure inversion asymmetry (SIA). With a strong SIA the 3D TI phase can exist even under a large Zeeman field. In a tight-binding form, the surface modes are discussed to confirm with the phase diagram. Particularly we find that the SIA cannot destroy the surface states but open a gap on its spectrum.

scholarly journals Simulating Floquet topological phases in static systems

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Selma Franca ◽  
Fabian Hassler ◽  
Ion Cosma Fulga
Keyword(s):  
Topological Insulators ◽  
Topological Phases ◽  
Topological System ◽  
Reflection Matrix ◽  
Back Scattering ◽  
Scattering Matrices ◽  
Floquet Operator ◽  
Static Systems ◽  
Time Periodic ◽  
External Driving

We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators. We consider D-dimensional HOTIs with gapless corner states which are weakly probed by external waves in a scattering setup. We find that the unitary reflection matrix describing back-scattering from the boundary of the HOTI is topologically equivalent to a (D-1)-dimensional nontrivial Floquet operator. To characterize the topology of the reflection matrix, we introduce the concept of `nested' scattering matrices. Our results provide a route to engineer topological Floquet systems in the lab without the need for external driving. As benefit, the topological system does not suffer from decoherence and heating.

scholarly journals Impact of magnetic dopants on magnetic and topological phases in magnetic topological insulators

2020 ◽  
Vol 102 (20) ◽  
Author(s):  
Thanh-Mai Thi Tran ◽  
Duc-Anh Le ◽  
Tuan-Minh Pham ◽  
Kim-Thanh Thi Nguyen ◽  
Minh-Tien Tran
Keyword(s):  
Topological Insulators ◽  
Topological Phases

scholarly journals The family of topological phases in condensed matter†

2013 ◽  
Vol 1 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Shun-Qing Shen
Keyword(s):  
Topological Insulators ◽  
Condensed Matter ◽  
Quantum States ◽  
Condensed Matter Physics ◽  
Topological Phases ◽  
Important Advance ◽  
Global Properties ◽  
The Family ◽  
Boundary States ◽  
Historic Development

Abstract The discovery of topological insulators and superconductors is an important advance in condensed matter physics. Topological phases reflect global properties of the quantum states in materials, and the boundary states are the characteristic of the materials. Such phases constitute a new branch in condensed matter physics. Here a historic development is briefly introduced, and the known family of phases in condensed matter are summarized.

scholarly journals Topological phases: Isomorphism, homotopy and K-theory

2015 ◽  
Vol 12 (09) ◽  
pp. 1550098 ◽  
Author(s):  
Guo Chuan Thiang
Keyword(s):  
Topological Insulators ◽  
Vector Bundles ◽  
Equivalence Classes ◽  
Topological Phases ◽  
Winding Number ◽  
Symmetry Constraints ◽  
K Theory

Equivalence classes of gapped Hamiltonians compatible with given symmetry constraints, such as those underlying topological insulators, can be defined in many ways. For the non-chiral classes modeled by vector bundles over Brillouin tori, physically relevant equivalences include isomorphism, homotopy, and K-theory, which are inequivalent but closely related. We discuss an important subtlety which arises in the chiral Class AIII systems, where the winding number invariant is shown to be relative rather than absolute as is usually assumed. These issues are then analyzed and reconciled in the language of K-theory.

scholarly journals Realization of quasicrystalline quadrupole topological insulators in electrical circuits

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Bo Lv ◽  
Rui Chen ◽  
Rujiang Li ◽  
Chunying Guan ◽  
Bin Zhou ◽  
...  
Keyword(s):  
Circuit Design ◽  
Topological Insulators ◽  
Topological Phases ◽  
Quadrupole Moments ◽  
Impedance Spectra ◽  
Electrical Circuits ◽  
New Class ◽  
Artificial Materials ◽  
Higher Dimensional ◽  
Topological Boundary

AbstractQuadrupole topological insulators are a new class of topological insulators with quantized quadrupole moments, which support protected gapless corner states. The experimental demonstrations of quadrupole-topological insulators were reported in a series of artificial materials, such as photonic crystals, acoustic crystals, and electrical circuits. In all these cases, the underlying structures have discrete translational symmetry and thus are periodic. Here we experimentally realize two-dimensional aperiodic-quasicrystalline quadrupole-topological insulators by constructing them in electrical circuits, and observe the spectrally and spatially localized corner modes. In measurement, the modes appear as topological boundary resonances in the corner impedance spectra. Additionally, we demonstrate the robustness of corner modes on the circuit. Our circuit design may be extended to study topological phases in higher-dimensional aperiodic structures.

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