scholarly journals Surface States of Topological Insulators: The Dirac Fermion in Curved Two-Dimensional Spaces

2009 ◽  
Vol 103 (19) ◽  
Author(s):  
Dung-Hai Lee
Keyword(s):  
Topological Insulators ◽  
Surface States ◽  
Dirac Fermion ◽  
Two Dimensional

Optical properties of surface states in two-dimensional topological insulators

2018 ◽  
Vol 57 (31) ◽  
pp. 9275
Author(s):  
L. S. Huang ◽  
H. M. Dong ◽  
Y. F. Duan ◽  
J. L. Liu ◽  
C. X. Zhao
Keyword(s):  
Optical Properties ◽  
Topological Insulators ◽  
Surface States ◽  
Two Dimensional

scholarly journals Terahertz signatures of ultrafast Dirac fermion relaxation at the surface of topological insulators

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
S. Kovalev ◽  
K.-J. Tielrooij ◽  
J.-C. Deinert ◽  
I. Ilyakov ◽  
N. Awari ◽  
...  
Keyword(s):  
Fermi Level ◽  
Topological Insulators ◽  
Surface States ◽  
Dirac Fermion ◽  
Dirac Fermions ◽  
Bulk Carriers ◽  
Information And Communication ◽  
Protected Surface ◽  
Saturation Effects ◽  
Conversion Efficiencies

AbstractTopologically protected surface states present rich physics and promising spintronic, optoelectronic, and photonic applications that require a proper understanding of their ultrafast carrier dynamics. Here, we investigate these dynamics in topological insulators (TIs) of the bismuth and antimony chalcogenide family, where we isolate the response of Dirac fermions at the surface from the response of bulk carriers by combining photoexcitation with below-bandgap terahertz (THz) photons and TI samples with varying Fermi level, including one sample with the Fermi level located within the bandgap. We identify distinctly faster relaxation of charge carriers in the topologically protected Dirac surface states (few hundred femtoseconds), compared to bulk carriers (few picoseconds). In agreement with such fast cooling dynamics, we observe THz harmonic generation without any saturation effects for increasing incident fields, unlike graphene which exhibits strong saturation. This opens up promising avenues for increased THz nonlinear conversion efficiencies, and high-bandwidth optoelectronic and spintronic information and communication applications.

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 Glide symmetry protected higher-order topological insulators from semimetals with butterfly-like nodal lines

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Xiaoting Zhou ◽  
Chuang-Han Hsu ◽  
Cheng-Yi Huang ◽  
Mikel Iraola ◽  
Juan L. Mañes ◽  
...  
Keyword(s):  
Topological Insulator ◽  
Topological Insulators ◽  
Surface States ◽  
Nodal Line ◽  
Higher Order ◽  
Dirac Fermion ◽  
Space Groups ◽  
Nodal Lines ◽  
Topological Semimetals ◽  
Symmetry Protected

AbstractMost topological insulators (TIs) discovered today in spinful systems can be transformed from topological semimetals (TSMs) with vanishing bulk gap via introducing the spin-orbit coupling (SOC), which manifests the intrinsic links between the gapped topological insulator phases and the gapless TSMs. Recently, we have discovered a family of TSMs in time-reversal invariant spinless systems, which host butterfly-like nodal-lines (NLs) consisting of a pair of identical concentric intersecting coplanar ellipses (CICE). In this Communication, we unveil the intrinsic link between this exotic class of nodal-line semimetals (NLSMs) and a $${{\mathbb{Z}}}_{4}$$ Z 4 = 2 topological crystalline insulator (TCI), by including substantial SOC. We demonstrate that in three space groups (i.e., Pbam (No.55), P4/mbm (No.127), and P42/mbc (No.135)), the TCI supports a fourfold Dirac fermion on the (001) surface protected by two glide symmetries, which originates from the intertwined drumhead surface states of the CICE NLs. The higher order topology is further demonstrated by the emergence of one-dimensional helical hinge states, indicating the discovery of a higher order topological insulator protected by a glide symmetry.

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>

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