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 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 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.

scholarly journals Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Max Geier ◽  
Ion Cosma Fulga ◽  
Alexander Lau
Keyword(s):  
Topological Insulators ◽  
Three Dimensions ◽  
Topological Phases ◽  
Rotation Symmetry ◽  
First Order ◽  
Zero Modes ◽  
Symmetry Classes ◽  
Topological Lattice ◽  
Rotation Symmetric ◽  
Translation Symmetry

We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct d-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to (d-2)-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.

scholarly journals ON EXOTIC SPHERE FIBRATIONS, TOPOLOGICAL PHASES, AND EDGE STATES IN PHYSICAL SYSTEMS

2013 ◽  
Vol 27 (19) ◽  
pp. 1350107 ◽  
Author(s):  
HAI LIN ◽  
SHING-TUNG YAU
Keyword(s):  
Topological Insulators ◽  
Condensed Matter ◽  
Topological Phases ◽  
Edge States ◽  
Geometric Phases ◽  
Magnetoelectric Effects ◽  
Physical Systems ◽  
Chern Numbers ◽  
Weyl Semimetals ◽  
Exotic Sphere

We suggest that exotic sphere fibrations can be mapped to band topologies in condensed matter systems. These fibrations can correspond to geometric phases of two double bands or state vector bases with second Chern numbers m+n and -n, respectively. They can be related to topological insulators, magnetoelectric effects, and photonic crystals with special edge states. We also consider time-reversal symmetry breaking perturbations of topological insulator, and heterostructures of topological insulators with normal insulators and with superconductors. We consider periodic TI/NI/TI/NI′ heterostructures, and periodic TI/SC/TI/SC′ heterostructures. They also give rise to models of Weyl semimetals which have thermal and electrical transports.

Some remarks on topological phases and topological insulators

2016 ◽  
Vol 13 (Supp. 1) ◽  
pp. 1650100 ◽  
Author(s):  
Manuel Asorey
Keyword(s):  
Magnetic Fields ◽  
Time Reversal ◽  
Topological Insulators ◽  
Topological Phases ◽  
Edge States ◽  
Quantum Phases ◽  
Simple Quantum ◽  
Mechanical Models ◽  
Characteristic Effect ◽  
The Magnetic Field

The remarkable properties of topological phases and topological insulators are analyzed in very simple quantum mechanical models. A characteristic effect of magnetic fields on quantum systems is the appearance of degenerate ground states. The level of degeneracy of the corresponding quantum phases depends on the strength of the magnetic field and the topology of the configuration space. In topological insulators, in absence of magnetic fields, the essential ingredients are time reversal symmetry, the existence of edge states and a non-trivial topological structure of the Jacobian space (Brillouin zone). In both cases the main features are encoded by topological indices. In topological phases induced by magnetic fields, the index is a topological invariant that depends on the Chern class of the magnetic fields and the topology of the space. In topological insulators the topological index is given by the number of edge levels crossing the Fermi surface that remains invariant under time reversal invariant perturbations. The robustness of the corresponding effects under perturbations follows from the topological nature of both phenomena.

scholarly journals Non-Hermiticity and topological invariants of magnon Bogoliubov–de Gennes systems

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Hiroki Kondo ◽  
Yutaka Akagi ◽  
Hosho Katsura
Keyword(s):  
Hall Effect ◽  
Topological Insulators ◽  
Three Dimensional ◽  
Surface States ◽  
Theoretical Models ◽  
Topological Invariant ◽  
Topological Invariants ◽  
Topological Phases ◽  
Ideal Candidate ◽  
Edge Surface

Abstract Since the theoretical prediction and experimental observation of the magnon thermal Hall effect, a variety of novel phenomena that may occur in magnonic systems have been proposed. We review recent advances in the study of topological phases of magnon Bogoliubov–de Gennes (BdG) systems. After giving an overview of previous works on electronic topological insulators and the magnon thermal Hall effect, we provide the necessary background for bosonic BdG systems, with particular emphasis on their non-Hermiticity arising from the diagonalization of the BdG Hamiltonian. We then introduce definitions of $$ \mathbb{Z}_2 $$ topological invariants for bosonic systems with pseudo-time-reversal symmetry, which ensures the existence of bosonic counterparts of “Kramers pairs.” Because of the intrinsic non-Hermiticity of bosonic BdG systems, these topological invariants have to be defined in terms of the bosonic Berry connection and curvature. We then introduce theoretical models that can be thought of as magnonic analogs of two- and three-dimensional topological insulators in class AII. We demonstrate analytically and numerically that the $$ \mathbb{Z}_2 $$ topological invariants precisely characterize the presence of gapless edge/surface states. We also predict that bilayer CrI$$_3$$ with a particular stacking would be an ideal candidate for the realization of a two-dimensional magnon system characterized by a nontrivial $$ \mathbb{Z}_2 $$ topological invariant. For three-dimensional topological magnon systems, the magnon thermal Hall effect is expected to occur when a magnetic field is applied to the surface.

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