scholarly journals Symmetry fractionalization and anomaly detection in three-dimensional topological phases

2016 ◽  
Vol 94 (19) ◽  
Author(s):  
Xie Chen ◽  
Michael Hermele
Keyword(s):  
Anomaly Detection ◽  
Three Dimensional ◽  
Topological Phases

scholarly journals Engineering topological phases with a three-dimensional nodal-loop semimetal

2017 ◽  
Vol 96 (23) ◽  
Author(s):  
Linhu Li ◽  
Han Hoe Yap ◽  
Miguel A. N. Araújo ◽  
Jiangbin Gong
Keyword(s):  
Three Dimensional ◽  
Topological Phases

scholarly journals Two- and three-dimensional topological phases in BiTeX compounds

2017 ◽  
Vol 96 (15) ◽  
Author(s):  
S. V. Eremeev ◽  
I. A. Nechaev ◽  
E. V. Chulkov
Keyword(s):  
Three Dimensional ◽  
Topological Phases

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 A Method of the Riemann–Hilbert Problem for Zhang’s Conjecture 2 in a Ferromagnetic 3D Ising Model: Topological Phases

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2936
Author(s):  
Zhidong Zhang ◽  
Osamu Suzuki
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
External Magnetic Field ◽  
Hilbert Problem ◽  
Three Dimensional ◽  
Preceding Paper ◽  
Mathematical Structure ◽  
Topological Phases ◽  
Riemann Hilbert Problem ◽  
3D Ising Model

A method of the Riemann–Hilbert problem is employed for Zhang’s conjecture 2 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in a zero external magnetic field. In this work, we first prove that the 3D Ising model in the zero external magnetic field can be mapped to either a (3 + 1)-dimensional ((3 + 1)D) Ising spin lattice or a trivialized topological structure in the (3 + 1)D or four-dimensional (4D) space (Theorem 1). Following the procedures of realizing the representation of knots on the Riemann surface and formulating the Riemann–Hilbert problem in our preceding paper [O. Suzuki and Z.D. Zhang, Mathematics 9 (2021) 776], we introduce vertex operators of knot types and a flat vector bundle for the ferromagnetic 3D Ising model (Theorems 2 and 3). By applying the monoidal transforms to trivialize the knots/links in a 4D Riemann manifold and obtain new trivial knots, we proceed to renormalize the ferromagnetic 3D Ising model in the zero external magnetic field by use of the derivation of Gauss–Bonnet–Chern formula (Theorem 4). The ferromagnetic 3D Ising model with nontrivial topological structures can be realized as a trivial model on a nontrivial topological manifold. The topological phases generalized on wavevectors are determined by the Gauss–Bonnet–Chern formula, in consideration of the mathematical structure of the 3D Ising model. Hence we prove the Zhang’s conjecture 2 (main theorem). Finally, we utilize the ferromagnetic 3D Ising model as a platform for describing a sensible interplay between the physical properties of many-body interacting systems, algebra, topology, and geometry.

scholarly journals Prediction of topological crystalline insulators and topological phase transitions in two-dimensional PbTe films

2017 ◽  
Vol 19 (43) ◽  
pp. 29647-29652 ◽  
Author(s):  
Yi-zhen Jia ◽  
Wei-xiao Ji ◽  
Chang-wen Zhang ◽  
Ping Li ◽  
Shu-feng Zhang ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Three Dimensional ◽  
Topological Phases ◽  
Topological Phase ◽  
Two Dimensional ◽  
Topological Crystalline Insulators ◽  
Topological Phase Transitions

Topological phases, especially topological crystalline insulators (TCIs), have been intensively explored and observed experimentally in three-dimensional (3D) materials.

scholarly journals Global Anomaly Detection in Two-Dimensional Symmetry-Protected Topological Phases

2018 ◽  
Vol 120 (15) ◽  
Author(s):  
Nick Bultinck ◽  
Robijn Vanhove ◽  
Jutho Haegeman ◽  
Frank Verstraete
Keyword(s):  
Anomaly Detection ◽  
Topological Phases ◽  
Two Dimensional ◽  
Global Anomaly ◽  
Symmetry Protected

scholarly journals Universal entanglement signatures of foliated fracton phases

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Wilbur Shirley ◽  
Kevin Slagle ◽  
Xie Chen
Keyword(s):  
Fixed Point ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Topological Phases ◽  
Topological Order ◽  
Two Dimensional ◽  
Adiabatic Evolution ◽  
Universal Properties ◽  
Three Dimensional Models ◽  
Topological Entanglement Entropy

Fracton models exhibit a variety of exotic properties and lie beyond the conventional framework of gapped topological order. In , we generalized the notion of gapped phase to one of foliated fracton phase by allowing the addition of layers of gapped two-dimensional resources in the adiabatic evolution between gapped three-dimensional models. Moreover, we showed that the X-cube model is a fixed point of one such phase. In this paper, according to this definition, we look for universal properties of such phases which remain invariant throughout the entire phase. We propose multi-partite entanglement quantities, generalizing the proposal of topological entanglement entropy designed for conventional topological phases. We present arguments for the universality of these quantities and show that they attain non-zero constant value in non-trivial foliated fracton phases.

scholarly journals Time-periodic corner states from Floquet higher-order topology

2022 ◽  
Vol 13 (1) ◽  
Author(s):  
Weiwei Zhu ◽  
Haoran Xue ◽  
Jiangbin Gong ◽  
Yidong Chong ◽  
Baile Zhang
Keyword(s):  
Three Dimensional ◽  
Higher Order ◽  
Topological Phases ◽  
Time Dynamics ◽  
Topological States ◽  
Acoustic Lattice ◽  
Static Systems ◽  
Time Invariant ◽  
Time Periodic ◽  
Spatial Axis

AbstractThe recent discoveries of higher-order topological insulators (HOTIs) have shifted the paradigm of topological materials, previously limited to topological states at boundaries of materials, to include topological states at boundaries of boundaries, such as corners. So far, all HOTI realisations have been based on static systems described by time-invariant Hamiltonians, without considering the time-variant situation. There is growing interest in Floquet systems, in which time-periodic driving can induce unconventional phenomena such as Floquet topological phases and time crystals. Recent theories have attempted to combine Floquet engineering and HOTIs, but there has been no experimental realisation so far. Here we report on the experimental demonstration of a two-dimensional (2D) Floquet HOTI in a three-dimensional (3D) acoustic lattice, with modulation along a spatial axis serving as an effective time-dependent drive. Acoustic measurements reveal Floquet corner states with double the period of the underlying drive; these oscillations are robust, like time crystal modes, except that the robustness arises from topological protection. This shows that space-time dynamics can induce anomalous higher-order topological phases unique to Floquet systems.

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