scholarly journals Confinement Properties of the 3D Topological Insulators Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃

2021 ◽  
Author(s):  
◽  
Markus Kotulla
Keyword(s):  
Magnetic Field ◽  
Topological Insulators ◽  
Surface States ◽  
Cold Atom ◽  
Zeeman Splitting ◽  
Dirac Fermion ◽  
Topological Phases ◽  
Edge States ◽  
Experimental Realization ◽  
Band Inversion

<p>Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators have conductive surface or edge states but are insulating in the bulk. How the signatures of topological behavior evolve when the system size is reduced is noteworthy from both a fundamental and an application-oriented point of view, as such understanding may form the basis for tailoring systems to be in specific topological phases. This thesis investigates the softly confined topological insulator family of Bi₂Se₃ and its properties when subjected to an in-plane magnetic field. The model system provides a useful platform for systematic study of the transition between the normal and the topological phases, including the development of band inversion and the formation of massless-Dirac-fermion surface states. The effects of bare size quantization, two-dimensional-subband mixing, and electron-hole asymmetry are disentangled and their corresponding physical consequences elucidated.  When a magnetic field is present, it is found that the Dirac cone which is formed in surface states, splits into two cones separated in momentum space and that these cones exhibit properties of Weyl fermions. The effective Zeeman splitting is much larger for the surface states than for the bulk states. Furthermore, the g-factor of the surface states depends on the size of the material. The mathematical model presented here may be realizable experimentally in the frame of optical lattices in ultra cold atom gases.</p>

scholarly journals Confinement Properties of the 3D Topological Insulators Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃

2021 ◽  
Author(s):  
◽  
Markus Kotulla
Keyword(s):  
Magnetic Field ◽  
Topological Insulators ◽  
Surface States ◽  
Cold Atom ◽  
Zeeman Splitting ◽  
Dirac Fermion ◽  
Topological Phases ◽  
Edge States ◽  
Experimental Realization ◽  
Band Inversion

<p>Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators have conductive surface or edge states but are insulating in the bulk. How the signatures of topological behavior evolve when the system size is reduced is noteworthy from both a fundamental and an application-oriented point of view, as such understanding may form the basis for tailoring systems to be in specific topological phases. This thesis investigates the softly confined topological insulator family of Bi₂Se₃ and its properties when subjected to an in-plane magnetic field. The model system provides a useful platform for systematic study of the transition between the normal and the topological phases, including the development of band inversion and the formation of massless-Dirac-fermion surface states. The effects of bare size quantization, two-dimensional-subband mixing, and electron-hole asymmetry are disentangled and their corresponding physical consequences elucidated.  When a magnetic field is present, it is found that the Dirac cone which is formed in surface states, splits into two cones separated in momentum space and that these cones exhibit properties of Weyl fermions. The effective Zeeman splitting is much larger for the surface states than for the bulk states. Furthermore, the g-factor of the surface states depends on the size of the material. The mathematical model presented here may be realizable experimentally in the frame of optical lattices in ultra cold atom gases.</p>

scholarly journals Topological gaps by twisting

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Matheus I. N. Rosa ◽  
Massimo Ruzzene ◽  
Emil Prodan
Keyword(s):  
Magnetic Field ◽  
Quantum Hall Effect ◽  
Twist Angle ◽  
Quantum Hall ◽  
Topological Phases ◽  
Edge States ◽  
Layered Systems ◽  
Virtual Laboratories ◽  
Higher Dimensional ◽  
Chern Numbers

AbstractTwisted bilayered systems such as bilayered graphene exhibit remarkable properties such as superconductivity at magic angles and topological insulating phases. For generic twist angles, the bilayers are truly quasiperiodic, a fact that is often overlooked and that has consequences which are largely unexplored. Herein, we uncover that twisted n-layers host intrinsic higher dimensional topological phases, and that those characterized by second Chern numbers can be found in twisted bi-layers. We employ phononic lattices with interactions modulated by a second twisted lattice and reveal Hofstadter-like spectral butterflies in terms of the twist angle, which acts as a pseudo magnetic field. The phason provided by the sliding of the layers lives on 2n-tori and can be used to access and manipulate the edge states. Our work demonstrates how multi-layered systems are virtual laboratories for studying the physics of higher dimensional quantum Hall effect, and can be employed to engineer topological pumps via simple twisting and sliding.

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.

scholarly journals Large discrete jumps observed in the transition between Chern states in a ferromagnetic topological insulator

2016 ◽  
Vol 2 (7) ◽  
pp. e1600167 ◽  
Author(s):  
Minhao Liu ◽  
Wudi Wang ◽  
Anthony R. Richardella ◽  
Abhinav Kandala ◽  
Jian Li ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Metastable State ◽  
Large Fraction ◽  
Surface States ◽  
Anomalous Hall Effect ◽  
Escape Rate ◽  
Zero Magnetic Field ◽  
Hall Resistance ◽  
Edge States ◽  
Longitudinal Resistance

A striking prediction in topological insulators is the appearance of the quantized Hall resistance when the surface states are magnetized. The surface Dirac states become gapped everywhere on the surface, but chiral edge states remain on the edges. In an applied current, the edge states produce a quantized Hall resistance that equals the Chern numberC= ±1 (in natural units), even in zero magnetic field. This quantum anomalous Hall effect was observed by Changet al. With reversal of the magnetic field, the system is trapped in a metastable state because of magnetic anisotropy. We investigate how the system escapes the metastable state at low temperatures (10 to 200 mK). When the dissipation (measured by the longitudinal resistance) is ultralow, we find that the system escapes by making a few very rapid transitions, as detected by large jumps in the Hall and longitudinal resistances. Using the field at which the initial jump occurs to estimate the escape rate, we find that raising the temperature strongly suppresses the rate. From a detailed map of the resistance versus gate voltage and temperature, we show that dissipation strongly affects the escape rate. We compare the observations with dissipative quantum tunneling predictions. In the ultralow dissipation regime, two temperature scales (T1~ 70 mK andT2~ 145 mK) exist, between which jumps can be observed. The jumps display a spatial correlation that extends over a large fraction of the sample.

scholarly journals Electronic properties of the topological insulators Bi₂Se₃ and Bi₂Te₃

2021 ◽  
Author(s):  
◽  
Robin Gühne
Keyword(s):  
Electronic Properties ◽  
Single Crystals ◽  
Topological Insulators ◽  
Three Dimensional ◽  
Surface States ◽  
Quantitative Agreement ◽  
Model Systems ◽  
Electronic Spin ◽  
Band Inversion ◽  
A Charge

<p>The three-dimensional topological insulators Bi₂Se₃ and Bi₂Te₃ are model systems of a new class of materials with an insulating bulk and gapless surface states. Their small band gaps and the heavy elements are essential for the topologically non-trivial band structure, but these features are similarly responsible for other remarkable properties, such as their high thermoelectric performance.  This thesis investigates the electronic properties of the topological insulators Bi₂Se₃ and Bi₂Te₃ with a broad range of experimental methods. Ferromagnetism in Mn doped Bi₂Te₃ is shown to disappear under sample sintering. A surprisingly large magnetoresistance and a charge carrier independent change in the sign of the thermopower with increasing Mn content are discussed.¹²⁵Te nuclear magnetic resonance (NMR) of Bi₂Te₃ single crystals suggest an unusual electronic spin susceptibility and complex NMR shifts. The quadrupole interaction of ²⁰⁹Bi nuclei in Bi₂Se₃ single crystals is shown to be a signature of the band inversion in quantitative agreement with first-principle calculations. Furthermore, it is proposed that the strong spin-orbit coupling of conduction electrons causes a non-trivial orientation dependent quadrupole splitting of the ²⁰⁹Bi resonance.</p>

scholarly journals Four-band non-Abelian topological insulator and its experimental realization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Tianshu Jiang ◽  
Qinghua Guo ◽  
Ruo-Yang Zhang ◽  
Zhao-Qing Zhang ◽  
Biao Yang ◽  
...  
Keyword(s):  
Topological Insulators ◽  
Edge State ◽  
Topological Classification ◽  
Symmetric System ◽  
Edge States ◽  
Experimental Realization ◽  
Topological Features ◽  
Significant Difference ◽  
Clifford Tori ◽  
Topological Charges

AbstractVery recently, increasing attention has been focused on non-Abelian topological charges, e.g., the quaternion group Q8. Different from Abelian topological band insulators, these systems involve multiple entangled bulk bandgaps and support nontrivial edge states that manifest the non-Abelian topological features. Furthermore, a system with an even or odd number of bands will exhibit a significant difference in non-Abelian topological classification. To date, there has been scant research investigating even-band non-Abelian topological insulators. Here, we both theoretically explore and experimentally realize a four-band PT (inversion and time-reversal) symmetric system, where two new classes of topological charges as well as edge states are comprehensively studied. We illustrate their difference in the four-dimensional (4D) rotation sense on the stereographically projected Clifford tori. We show the evolution of the bulk topology by extending the 1D Hamiltonian onto a 2D plane and provide the accompanying edge state distributions following an analytical method. Our work presents an exhaustive study of four-band non-Abelian topological insulators and paves the way towards other even-band systems.

In-plane magnetic field induced helicity dependent photogalvanic effect on the surface states of topological insulators (BixSb1−x)2Te3

2021 ◽  
Vol 130 (8) ◽  
pp. 085305
Author(s):  
Shenzhong Chen ◽  
Jinling Yu ◽  
Kejing Zhu ◽  
Xiaolin Zeng ◽  
Yonghai Chen ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Topological Insulators ◽  
Surface States ◽  
Photogalvanic Effect

scholarly journals Four-band non-Abelian topological insulator and its experimental realization

2021 ◽  
Author(s):  
Tianshu Jiang ◽  
Qinghua Guo ◽  
Ruo-Yang Zhang ◽  
Zhao-Qing Zhang ◽  
Biao Yang ◽  
...  
Keyword(s):  
Topological Insulators ◽  
Edge State ◽  
Symmetric System ◽  
Edge States ◽  
Experimental Realization ◽  
Topological Features ◽  
Significant Difference ◽  
Clifford Tori ◽  
Exhaustive Study ◽  
Topological Charges

Abstract Very recently, increasing attention has been focused on non-Abelian topological charges, e.g. the quaternion group Q8. Different from Abelian topological band insulators, these systems involve multiple tangled bulk bandgaps and support non-trivial edge states that manifest the non-Abelian topological features. Furthermore, a system with even or odd number of bands will exhibit significant difference in non-Abelian topological classifications. Up to now, there is scant research investigating the even-band non-Abelian topological insulators. Here, we both theoretically explored and experimentally realized a four-band PT (inversion and time-reversal) symmetric system, where two new classes of topological charges as well as edge states are comprehensively studied. We illustrate their difference from four-dimensional rotation senses on the stereographically projected Clifford tori. We show the evolution of bulk topology by extending the 1D Hamiltonian onto a 2D plane and provide the accompanying edge state distributions following an analytical method. Our work presents an exhaustive study of four-band non-Abelian topological insulators and paves the way to other even band systems.

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