scholarly journals Tidal surface states as fingerprints of non-Hermitian nodal knot metals

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Xiao Zhang ◽  
Guangjie Li ◽  
Yuhan Liu ◽  
Tommy Tai ◽  
Ronny Thomale ◽  
...  
Keyword(s):  
Layer Structure ◽  
Tight Binding ◽  
Surface States ◽  
Explicit Construction ◽  
Real Space ◽  
Energy Bands ◽  
Torus Knots ◽  
Topological Surface ◽  
Berry Phases ◽  
Complex Valued

AbstractNon-Hermitian nodal knot metals (NKMs) contain intricate complex-valued energy bands which give rise to knotted exceptional loops and new topological surface states. We introduce a formalism that connects the algebraic, geometric, and topological aspects of these surface states with their parent knots. We also provide an optimized constructive ansatz for tight-binding models for non-Hermitian NKMs of arbitrary knot complexity and minimal hybridization range. Specifically, various representative non-Hermitian torus knots Hamiltonians are constructed in real-space, and their nodal topologies studied via winding numbers that avoid the explicit construction of generalized Brillouin zones. In particular, we identify the surface state boundaries as “tidal” intersections of the complex band structure in a marine landscape analogy. Beyond topological quantities based on Berry phases, we further find these tidal surface states to be intimately connected to the band vorticity and the layer structure of their dual Seifert surface, and as such provide a fingerprint for non-Hermitian NKMs.

scholarly journals Tidal surface states as fingerprints of non-Hermitian nodal knot metals

2020 ◽  
Author(s):  
Ching Hua Lee ◽  
Guangjie Li ◽  
Yuhan Liu ◽  
Tommy Tai ◽  
Ronny Thomale ◽  
...  
Keyword(s):  
Surface State ◽  
Layer Structure ◽  
Tight Binding ◽  
Surface States ◽  
Seifert Surface ◽  
Energy Bands ◽  
Binding Models ◽  
Topological Surface ◽  
Complex Valued ◽  
Topological Surface State

Abstract The paradigm of metals has undergone a revision and diversification from the viewpoint of topology. Non-Hermitian nodal knot metals (NKMs) constitute a class of matter without Hermitian analog, where the intricate structure of complex-valued energy bands gives rise to knotted lines of exceptional points and new topological surface state phenomena. We introduce a formalism that connects the algebraic, geometric, and topological aspects of these surface states with their underlying parent knots, and complement our results by an optimized constructive ansatz that provides tight-binding models for non-Hermitian NKMs of arbitrary knot complexity and minimal hybridization range. In particular, we identify the surface state boundaries as ``tidal' intersections of the complex band structure in a marine landscape analogy. We further find these tidal surface states to be intimately connected to the band vorticity and the layer structure of their dual Seifert surface, and as such provide a fingerprint for non-Hermitian NKMs.

scholarly journals Machine learning method for tight-binding Hamiltonian parameterization from ab-initio band structure

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Zifeng Wang ◽  
Shizhuo Ye ◽  
Hao Wang ◽  
Jin He ◽  
Qijun Huang ◽  
...  
Keyword(s):  
Machine Learning ◽  
Ab Initio ◽  
Large Scale ◽  
Tight Binding ◽  
Real Space ◽  
Machine Learning Method ◽  
Learning Method ◽  
Energy Bands ◽  
Physical Problems ◽  
Machine Learning Applications

AbstractThe tight-binding (TB) method is an ideal candidate for determining electronic and transport properties for a large-scale system. It describes the system as real-space Hamiltonian matrices expressed on a manageable number of parameters, leading to substantially lower computational costs than the ab-initio methods. Since the whole system is defined by the parameterization scheme, the choice of the TB parameters decides the reliability of the TB calculations. The typical empirical TB method uses the TB parameters directly from the existing parameter sets, which hardly reproduces the desired electronic structures quantitatively without specific optimizations. It is thus not suitable for quantitative studies like the transport property calculations. The ab-initio TB method derives the TB parameters from the ab-initio results through the transformation of basis functions, which achieves much higher numerical accuracy. However, it assumes prior knowledge of the basis and may encompass truncation error. Here, a machine learning method for TB Hamiltonian parameterization is proposed, within which a neural network (NN) is introduced with its neurons acting as the TB matrix elements. This method can construct the empirical TB model that reproduces the given ab-initio energy bands with predefined accuracy, which provides a fast and convenient way for TB model construction and gives insights into machine learning applications in physical problems.

scholarly journals Selective trapping of hexagonally warped topological surface states in a triangular quantum corral

2019 ◽  
Vol 5 (5) ◽  
pp. eaaw3988 ◽  
Author(s):  
Mu Chen ◽  
Ye-Ping Jiang ◽  
Junping Peng ◽  
Huimin Zhang ◽  
Cui-Zu Chang ◽  
...  
Keyword(s):  
Surface Defects ◽  
Three Dimensional ◽  
Surface States ◽  
Real Space ◽  
Dirac Fermions ◽  
Selection Rules ◽  
Potential Barriers ◽  
Topological Surface ◽  
Spin Texture ◽  
Complicated Surface

The surface of a three-dimensional topological insulator (TI) hosts two-dimensional massless Dirac fermions (DFs), the gapless and spin-helical nature of which leads to their high transmission through surface defects or potential barriers. Here, we report the behaviors of topological surface states (TSS) in a triangular quantum corral (TQC) which, unlike a circular corral, is supposed to be totally transparent for DFs. By real-space mapping of the electronic structure of TQCs, both the trapping and detrapping behaviors of the TSS are observed. The selection rules are found to be governed by the geometry and spin texture of the constant energy contour of TSS upon the strong hexagonal warping in Bi2Te3. Our work indicates the extended nature of TSS and elucidates the selection rules of the trapping of TSS in the presence of a complicated surface state structure, giving insights into the effective engineering of DFs in TIs.

Self-Consistent Calculation of Surface States in Real Space

1997 ◽  
Vol 11 (09) ◽  
pp. 1187-1193 ◽  
Author(s):  
Chih-Kai Yang
Keyword(s):  
Scanning Tunneling Microscope ◽  
Local Density ◽  
Tight Binding ◽  
Surface States ◽  
Real Space ◽  
Scanning Tunneling ◽  
Local Density Of States ◽  
Ab Initio Method ◽  
Surface Electronic Structure ◽  
Self Consistency

An ab initio method is developed to calculate the surface electronic structure. The method is based on the tight-binding linear muffin-tin orbitals and real-space recursive Green's function and can achieve self-consistency efficiently. Sample calculations include Fe(001)and Cr(001) systems and are compared with recent experiments using scanning tunneling microscope and photoemission. From the calculated local density of states several prominent surface states above and below the Fermi level are identified and found to agree well with the experimental results.

Large Damping Enhancement in Dirac‐Semimetal–Ferromagnetic‐Metal Layered Structures Caused by Topological Surface States

2021 ◽  
pp. 2008411
Author(s):  
Jinjun Ding ◽  
Chuanpu Liu ◽  
Yuejie Zhang ◽  
Vijaysankar Kalappattil ◽  
Rui Yu ◽  
...  
Keyword(s):  
Surface States ◽  
Layered Structures ◽  
Ferromagnetic Metal ◽  
Dirac Semimetal ◽  
Topological Surface

scholarly journals Discovery of a weak topological insulating state and van Hove singularity in triclinic RhBi2

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Kyungchan Lee ◽  
Gunnar F. Lange ◽  
Lin-Lin Wang ◽  
Brinda Kuthanazhi ◽  
Thaís V. Trevisan ◽  
...  
Keyword(s):  
Time Reversal ◽  
Topological Insulators ◽  
Dirac Point ◽  
Saddle Points ◽  
Surface States ◽  
Van Hove Singularity ◽  
Space Group ◽  
Topological Materials ◽  
Topological Surface ◽  
Optimal Space

AbstractTime reversal symmetric (TRS) invariant topological insulators (TIs) fullfil a paradigmatic role in the field of topological materials, standing at the origin of its development. Apart from TRS protected strong TIs, it was realized early on that more confounding weak topological insulators (WTI) exist. WTIs depend on translational symmetry and exhibit topological surface states only in certain directions making it significantly more difficult to match the experimental success of strong TIs. We here report on the discovery of a WTI state in RhBi2 that belongs to the optimal space group P$$\bar{1}$$ 1 ¯ , which is the only space group where symmetry indicated eigenvalues enumerate all possible invariants due to absence of additional constraining crystalline symmetries. Our ARPES, DFT calculations, and effective model reveal topological surface states with saddle points that are located in the vicinity of a Dirac point resulting in a van Hove singularity (VHS) along the (100) direction close to the Fermi energy (EF). Due to the combination of exotic features, this material offers great potential as a material platform for novel quantum effects.

scholarly journals Vortex states in an acoustic Weyl crystal with a topological lattice defect

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qiang Wang ◽  
Yong Ge ◽  
Hong-xiang Sun ◽  
Haoran Xue ◽  
Ding Jia ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Lattice Defect ◽  
Three Dimensional ◽  
Surface States ◽  
Real Space ◽  
Lattice Defects ◽  
One Dimensional ◽  
Topological Features ◽  
Topological Lattice

AbstractCrystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

Fermi level tuning and the robustness of topological surface states against impurity doping in Sn doped Sb2Te2Se

2021 ◽  
Vol 118 (15) ◽  
pp. 154001
Author(s):  
Debarghya Mallick ◽  
Shoubhik Mandal ◽  
R. Ganesan ◽  
P. S. Anil Kumar
Keyword(s):  
Fermi Level ◽  
Surface States ◽  
Impurity Doping ◽  
Topological Surface

scholarly journals 2D weak anti-localization in thin films of the topological semimetal Pd$$_{3}$$Bi$$_{2}$$S$$_{2}$$

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Shama ◽  
R. K. Gopal ◽  
Goutam Sheet ◽  
Yogesh Singh
Keyword(s):  
Thin Films ◽  
Phonon Scattering ◽  
Surface States ◽  
Relaxation Mechanism ◽  
Transport Studies ◽  
Bulk Carriers ◽  
Topological Semimetal ◽  
Topological Surface ◽  
First Time ◽  
Electron Phonon Scattering

AbstractPd$$_{3}$$ 3 Bi$$_{2}$$ 2 S$$_{2}$$ 2 (PBS) is a recently proposed topological semimetal candidate. However, evidence for topological surface states have not yet been revealed in transport measurements due to the large mobility of bulk carriers. We report the growth and magneto-transport studies of PBS thin films where the mobility of the bulk carriers is reduced by two orders of magnitude, revealing for the first time, contributions from the 2-dimensional (2D) topological surface states in the observation of the 2D weak anti-localization (WAL) effect in magnetic field and angle dependent conductivity measurements. The magnetotransport data is analysed within the 2D Hikami-Larkin-Nagaoka (HLN) theory. The analysis suggests that multiple conduction channels contribute to the transport. It is also found that the temperature dependence of the dephasing length can’t be explained only by electron-electron scattering and that electron-phonon scattering also contributes to the phase relaxation mechanism in PBS films.

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