scholarly journals Conflicting symmetries in topologically ordered surface states of three-dimensional bosonic symmetry protected topological phases

2014 ◽  
Vol 89 (23) ◽  
Author(s):  
Gil Young Cho ◽  
Jeffrey C. Y. Teo ◽  
Shinsei Ryu
Keyword(s):  
Three Dimensional ◽  
Surface States ◽  
Topological Phases ◽  
Symmetry Protected

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 Three-Dimensional Topological States of Phonons with Tunable Pseudospin Physics

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Yizhou Liu ◽  
Yong Xu ◽  
Wenhui Duan
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Surface States ◽  
Phonon Transport ◽  
Efficient Control ◽  
Topological States ◽  
Topological Surface ◽  
Symmetry Protected ◽  
Energy Information ◽  
Crystalline Symmetry

Efficient control of phonons is crucial to energy-information technology, but limited by the lacking of tunable degrees of freedom like charge or spin. Here we suggest to utilize crystalline symmetry-protected pseudospins as new quantum degrees of freedom to manipulate phonons. Remarkably, we reveal a duality between phonon pseudospins and electron spins by presenting Kramers-like degeneracy and pseudospin counterparts of spin-orbit coupling, which lays the foundation for “pseudospin phononics”. Furthermore, we report two types of three-dimensional phononic topological insulators, which give topologically protected, gapless surface states with linear and quadratic band degeneracies, respectively. These topological surface states display unconventional phonon transport behaviors attributed to the unique pseudospin-momentum locking, which are useful for phononic circuits, transistors, antennas, etc. The emerging pseudospin physics offers new opportunities to develop future phononics.

scholarly journals Tunable Topological Surface States of Three-Dimensional Acoustic Crystals

2021 ◽  
Vol 9 ◽  
Author(s):  
Hua-Shan Lai ◽  
Yu-Li Xu ◽  
Bo He ◽  
Xiao-Chen Sun ◽  
Cheng He ◽  
...  
Keyword(s):  
Domain Wall ◽  
Mirror Symmetry ◽  
Three Dimensional ◽  
Surface States ◽  
Building Blocks ◽  
Quantum Spin ◽  
Quantum Spin Hall Effect ◽  
Breaking Mechanism ◽  
Symmetry Protected ◽  
Complete Bandgap

Topological design for band structures of artificial materials such as acoustic crystals provides a powerful tool to manipulate wave propagating in a robust and symmetry-protected way. In this paper, based on the band folding and breaking mechanism by building blocks with acoustic atoms, we construct a three-dimensional topological acoustic crystal with a large complete bandgap. At a mirror-symmetry domain wall, two gapped symmetry and anti-symmetry surface states can be found in the bandgap, originated from two opposite Su-Schrieffer-Heeger chains. Remarkably, by enforcing a glide symmetry on the domain wall, we can tune the original gapped surface states in a gapless fashion at the boundaries of surface Brillouin zone, acting as omnidirectional acoustic quantum spin Hall effect. Our tunable yet straightforward acoustic crystals offer promising potentials in realizing future topological acoustic devices.

scholarly journals Weyl-like points from band inversions of spin-polarised surface states in NbGeSb

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
I. Marković ◽  
C. A. Hooley ◽  
O. J. Clark ◽  
F. Mazzola ◽  
M. D. Watson ◽  
...  
Keyword(s):  
Mirror Symmetry ◽  
Density Functional ◽  
Three Dimensional ◽  
Surface States ◽  
Nodal Line ◽  
Surface Band ◽  
Spin Orbital ◽  
Band Inversion ◽  
Topological Surface ◽  
Symmetry Protected

AbstractBand inversions are key to stabilising a variety of novel electronic states in solids, from topological surface states to the formation of symmetry-protected three-dimensional Dirac and Weyl points and nodal-line semimetals. Here, we create a band inversion not of bulk states, but rather between manifolds of surface states. We realise this by aliovalent substitution of Nb for Zr and Sb for S in the ZrSiS family of nonsymmorphic semimetals. Using angle-resolved photoemission and density-functional theory, we show how two pairs of surface states, known from ZrSiS, are driven to intersect each other near the Fermi level in NbGeSb, and to develop pronounced spin splittings. We demonstrate how mirror symmetry leads to protected crossing points in the resulting spin-orbital entangled surface band structure, thereby stabilising surface state analogues of three-dimensional Weyl points. More generally, our observations suggest new opportunities for engineering topologically and symmetry-protected states via band inversions of surface states.

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.

scholarly journals Ultrasonic nodal chains in topological granular metamaterials

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Aurélien Merkel ◽  
Johan Christensen
Keyword(s):  
Material Characterization ◽  
Condensed Matter ◽  
Three Dimensional ◽  
Surface States ◽  
Nodal Line ◽  
Topological Phases ◽  
Non Destructive Testing ◽  
Destructive Testing ◽  
Ultrasonic Devices ◽  
Non Destructive

AbstractThree-dimensional (3D) Weyl and Dirac semimetals garner considerable attention in condensed matter physics due to the exploration of entirely new topological phases and related unconventional surface states. Nodal line and ring semimetals, on the other hand, can facilitate 3D band crossings characterized by nontrivial links such as coupled chains and knots that are protected by the underlying crystal symmetry. Experimental complexities and detrimental effects of the spin-orbit interaction, among others, pose great challenges for the advancement that can be overcome with other systems such as bosonic lattices. Here we demonstrate that a 3D mechanical metamaterial made of granular beads hosts multiple intersecting nodal rings in the ultrasonic regime. By unveiling these yet unseen classical topological phases, we discuss the resilience of the associated novel surface states that appear entirely unaffected to the type of crystal termination, making them a promising platform in ultrasonic devices for non-destructive testing and material characterization.

scholarly journals Direct comparison of current-induced spin polarization in topological insulator Bi2Se3 and InAs Rashba states

2016 ◽  
Vol 7 (1) ◽  
Author(s):  
C. H. Li ◽  
O.M.J. van ‘t Erve ◽  
S. Rajput ◽  
L. Li ◽  
B. T. Jonker
Keyword(s):  
Spin Polarization ◽  
Three Dimensional ◽  
Surface States ◽  
Bias Current ◽  
Band Bending ◽  
Potentiometric Measurements ◽  
Dimensional Electron Gas ◽  
Symmetry Protected ◽  
Electrochemical Potentials ◽  
Spin Momentum

Abstract Three-dimensional topological insulators (TIs) exhibit time-reversal symmetry protected, linearly dispersing Dirac surface states with spin–momentum locking. Band bending at the TI surface may also lead to coexisting trivial two-dimensional electron gas (2DEG) states with parabolic energy dispersion. A bias current is expected to generate spin polarization in both systems, although with different magnitude and sign. Here we compare spin potentiometric measurements of bias current-generated spin polarization in Bi2Se3(111) where Dirac surface states coexist with trivial 2DEG states, and in InAs(001) where only trivial 2DEG states are present. We observe spin polarization arising from spin–momentum locking in both cases, with opposite signs of the measured spin voltage. We present a model based on spin dependent electrochemical potentials to directly derive the sign expected for the Dirac surface states, and show that the dominant contribution to the current-generated spin polarization in the TI is from the Dirac surface states.

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