Chern Forms and Chern Numbers

Tubes ◽  
2004 ◽  
pp. 85-115
Author(s):  
Alfred Gray
Keyword(s):  
Chern Numbers ◽  
Chern Forms

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 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

scholarly journals Non-commutative Chern numbers for generic aperiodic discrete systems

2018 ◽  
Vol 51 (23) ◽  
pp. 235202 ◽  
Author(s):  
Chris Bourne ◽  
Emil Prodan
Keyword(s):  
Discrete Systems ◽  
Chern Numbers

scholarly journals Invariant almost complex geometry on flag manifolds: geometric formality and Chern numbers

2016 ◽  
Vol 196 (1) ◽  
pp. 165-200 ◽  
Author(s):  
Lino Grama ◽  
Caio J. C. Negreiros ◽  
Ailton R. Oliveira
Keyword(s):  
Complex Geometry ◽  
Flag Manifolds ◽  
Almost Complex ◽  
Chern Numbers ◽  
Geometric Formality
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