scholarly journals Higher Chern numbers in multilayer Lieb lattices ( N≥2 ): Topological transitions and quadratic band crossing lines

2021 ◽  
Vol 103 (23) ◽  
Author(s):  
Saikat Banerjee ◽  
Avadh Saxena
Keyword(s):  
Chern Numbers ◽  
Topological Transitions ◽  
Band Crossing

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.

Soap-film dynamics and topological transitions under continuous deformation

2016 ◽  
Vol 1 (6) ◽  
Author(s):  
H. K. Moffatt ◽  
Raymond E. Goldstein ◽  
Adriana I. Pesci
Keyword(s):  
Soap Film ◽  
Continuous Deformation ◽  
Topological Transitions

scholarly journals Effect of Deformation on Topological Properties of Cobalt Monosilicide

Crystals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 143
Author(s):  
Sergey Nikolaev ◽  
Dmitry Pshenay-Severin ◽  
Yuri Ivanov ◽  
Alexander Burkov
Keyword(s):  
Band Structure ◽  
Ab Initio Calculations ◽  
Topological Charge ◽  
External Stress ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Topological Properties ◽  
Uniaxial Deformation ◽  
Band Crossing ◽  
Topological Charges

Recently, it was shown that materials with certain crystal structures can exhibit multifold band crossings with large topological charges. CoSi is one such material that belongs to non-centrosymmetric space group P213 (#198) and posseses multifold band crossing points with a topological charge of 4. The change of crystal symmetry, e.g., by means of external stress, can lift the degeneracy and change its topological properties. In the present work, the influence of uniaxial deformation on the band structure and topological properties of CoSi is investigated on the base of ab initio calculations. The k·p Hamiltonian taking into account deformation is constructed on the base of symmetry consideration near the Γ and R points both with and without spin-orbit coupling. The transformation of multifold band crossings into nodes of other types with different topological charges, their shift both in energy and in reciprocal space and the tilt of dispersion around nodes are studied in detail depending on the direction of uniaxial deformation.

scholarly journals Floquet engineering of topological transitions in a twisted transition metal dichalcogenide homobilayer

2021 ◽  
Vol 103 (1) ◽  
Author(s):  
Michael Vogl ◽  
Martin Rodriguez-Vega ◽  
Benedetta Flebus ◽  
Allan H. MacDonald ◽  
Gregory A. Fiete
Keyword(s):  
Transition Metal ◽  
Transition Metal Dichalcogenide ◽  
Topological Transitions

scholarly journals Mirror Chern numbers in the hybrid Wannier representation

2021 ◽  
Vol 103 (19) ◽  
Author(s):  
Tomáš Rauch ◽  
Thomas Olsen ◽  
David Vanderbilt ◽  
Ivo Souza
Keyword(s):  
Chern Numbers

Chern Numbers and Green's Functions in Solid State Physics

1997 ◽  
Vol 11 (11) ◽  
pp. 1389-1410
Author(s):  
Xiao-Rong Wu-Morrow ◽  
Cecile Dewitt-Morette ◽  
Lev Rozansky
Keyword(s):  
Periodic Potential ◽  
Solid State Physics ◽  
Hall Conductance ◽  
Energy Eigenvalues ◽  
Finite Dimensional ◽  
Topological Quantum ◽  
Chern Numbers ◽  
Density Response ◽  
Physical Quantities ◽  
Noninteracting Electron

Using the energy Green's function formulation proposed by Niu 1 for particle densities, we construct and clarify the nature of the topological invariant assigned to the Hall conductance in the Hall system of 2-dimensional noninteracting electron gas; we identify this topological quantum number explicitly as the first Chern number of a complex vector bundle over a 2-torus parametrized by the magnetic potential (a1, a2); the fibres are finite dimensional spaces spanned by eigenfunctions of the system with energy eigenvalues below the Fermi energy. Other cases can be treated by a similar procedure, namely, by recognizing that some physical quantities are integrals of curvatures defined on a nontrivial finite dimensional complex bundle. Therefore, in suitable units, they take integer values. We treat, as an example, the electron density response to a dilation of a periodic potential. The integer in this case is the number of Bloch bands. The quantization of the Hall conductance and density response is also shown in the presence of disorder.

scholarly journals Experimental Observation of Large Chern Numbers in Photonic Crystals

2015 ◽  
Vol 115 (25) ◽  
Author(s):  
Scott A. Skirlo ◽  
Ling Lu ◽  
Yuichi Igarashi ◽  
Qinghui Yan ◽  
John Joannopoulos ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Experimental Observation ◽  
Chern Numbers
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