Topological Lifshitz Transition and Novel Edge States Induced by Non-Abelian SU(2) Gauge Field on Bilayer Honeycomb Lattice

2021 ◽  
Author(s):  
Wen-Xiang Guo ◽  
Wu-Ming Liu
Keyword(s):  
Secular Equation ◽  
Universality Class ◽  
Gauge Potential ◽  
Honeycomb Lattice ◽  
The Novel ◽  
Winding Number ◽  
Edge States ◽  
Abelian Gauge ◽  
Fermi Surfaces ◽  
Lifshitz Transition

Abstract We investigate the SU(2) gauge effects on bilayer honeycomb lattice thoroughly. We discover a topological Lifshitz transition induced by the non-Abelian gauge potential. Topological Lifshitz transitions are determined by topologies of Fermi surfaces in the momentum space. Fermi surface consists of N = 8 Dirac points at π-flux point instead of N = 4 in the trivial Abelian regimes. A local winding number is defined to classify the universality class of the gapless excitations. We also obtain the phase diagram of gauge fluxes by solving the secular equation. Furthermore, the novel edge states of biased bilayer nanoribbon with gauge fluxes are also investigated.

scholarly journals Experimental realization of non-Abelian gauge field in circuit system

2020 ◽  
Author(s):  
Rui Yu ◽  
Ziyin Song ◽  
Tianyu Wu ◽  
Wenquan Wu
Keyword(s):  
Gauge Field ◽  
Building Blocks ◽  
The Novel ◽  
Spin Orbit ◽  
Edge States ◽  
Abelian Gauge ◽  
Experimental Realization ◽  
Wide Range ◽  
Exotic Physics ◽  
Spin Texture

Abstract Synthetic gauge field, especially the non-Abelian gauge field, has emerged as a new way to explore exotic physics in a wide range of materials and platforms. Here we present the building blocks, consisting of capacitors and inductors, to implement the non-Abelian tunneling matrices and show that circuit system is an appropriate choice to realize the non-Abelian gauge field. To demonstrate the novel physics enabled by the non-Abelian gauge field, we provide a simple and modular scheme to design the Rashba-Dresselhaus spin-orbit interaction and topological Chern state in circuits. By measuring the spin texture and chiral edge states of the resonant frequency band structures, we confirm the spin-orbit effect and topological Chern state in circuits. Our schemes open a broad avenue to study non-Abelian gauge field and related physics in circuit platform.

scholarly journals Bulk-edge correspondence of classical diffusion phenomena

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tsuneya Yoshida ◽  
Yasuhiro Hatsugai
Keyword(s):  
Temperature Field ◽  
Diffusion Equation ◽  
Edge State ◽  
Lattice System ◽  
Honeycomb Lattice ◽  
Two Dimensional ◽  
Winding Number ◽  
Edge States ◽  
Diffusive Dynamics ◽  
Diffusion Phenomena

AbstractWe elucidate that diffusive systems, which are widely found in nature, can be a new platform of the bulk-edge correspondence, a representative topological phenomenon. Using a discretized diffusion equation, we demonstrate the emergence of robust edge states protected by the winding number for one- and two-dimensional systems. These topological edge states can be experimentally accessible by measuring diffusive dynamics at edges. Furthermore, we discover a novel diffusion phenomenon by numerically simulating the distribution of temperatures for a honeycomb lattice system; the temperature field with wavenumber $$\pi $$ π cannot diffuse to the bulk, which is attributed to the complete localization of the edge state.

scholarly journals TOPOLOGICALLY MASSIVE GAUGE THEORY: A LORENTZIAN SOLUTION

2007 ◽  
Vol 22 (16n17) ◽  
pp. 2961-2976 ◽  
Author(s):  
K. SAYGILI
Keyword(s):  
Field Equation ◽  
Gauge Theory ◽  
Field Strength ◽  
Gauge Transformation ◽  
Global Section ◽  
Gauge Potential ◽  
Abelian Gauge ◽  
Abelian Field ◽  
Hopf Map ◽  
Topological Mass

We obtain a Lorentzian solution for the topologically massive non-Abelian gauge theory on AdS space [Formula: see text] by means of an SU (1, 1) gauge transformation of the previously found Abelian solution. There exists a natural scale of length which is determined by the inverse topological mass ν ~ ng2. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an Abelian gauge transformation. Then we present map [Formula: see text] including the topological mass which is the Lorentzian analog of the Hopf map. This map yields a global decomposition of [Formula: see text] as a trivial [Formula: see text] bundle over the upper portion of the pseudosphere [Formula: see text] which is the Hyperboloid model for the Lobachevski geometry. This leads to a reduction of the Abelian field equation onto [Formula: see text] using a global section of the solution on [Formula: see text]. Then we discuss the integration of the field equation using the Archimedes map [Formula: see text]. We also present a brief discussion of the holonomy of the gauge potential and the dual field strength on [Formula: see text].

scholarly journals Edge states in a honeycomb lattice: Effects of anisotropic hopping and mixed edges

2010 ◽  
Vol 81 (15) ◽  
Author(s):  
Hari P. Dahal ◽  
Zi-Xiang Hu ◽  
N. A. Sinitsyn ◽  
Kun Yang ◽  
A. V. Balatsky
Keyword(s):  
Honeycomb Lattice ◽  
Edge States ◽  
Lattice Effects

scholarly journals Nuclear spin-rotation interaction and non-Abelian gauge potential

1995 ◽  
Vol 84 (3) ◽  
pp. 627-632 ◽  
Author(s):  
Yu.A. Serebrennikov ◽  
U.E. Steiner
Keyword(s):  
Nuclear Spin ◽  
Spin Rotation ◽  
Gauge Potential ◽  
Abelian Gauge

scholarly journals On Spinor Representations in the Weyl Gauge Theory

1997 ◽  
Vol 12 (26) ◽  
pp. 1957-1968 ◽  
Author(s):  
B. M. Barbashov ◽  
A. B. Pestov
Keyword(s):  
Gauge Theory ◽  
Differential Forms ◽  
Current Source ◽  
Gauge Potential ◽  
Spinor Representation ◽  
Abelian Gauge ◽  
Cartan Torsion ◽  
Gauge Space ◽  
Spinor Current ◽  
Spinor Representations

A spinor current-source is found in the Weyl non-Abelian gauge theory which does not contain the abstract gauge space. It is shown that the searched spinor representation can be constructed in the space of external differential forms and it is a 16-component quantity for which a gauge-invariant Lagrangian is determined. The connection between the Weyl non-Abelian gauge potential and the Cartan torsion field, and the problem of a possible manifestation of the considered interactions are considered.

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