scholarly journals Orbital magnetization and Chern number in a supercell framework: Singlek-point formula

2007 ◽  
Vol 76 (1) ◽  
Author(s):  
Davide Ceresoli ◽  
Raffaele Resta
Keyword(s):  
Chern Number ◽  
Orbital Magnetization

scholarly journals Chiral topological superconducting state with Chern number C = −2 in Pb3Bi/Ge(111)

2021 ◽  
Vol 103 (23) ◽  
Author(s):  
Shuwen Sun ◽  
Wei Qin ◽  
Leiqiang Li ◽  
Zhenyu Zhang
Keyword(s):  
Superconducting State ◽  
Chern Number

scholarly journals Many-Body Chern Number from Statistical Correlations of Randomized Measurements

2021 ◽  
Vol 126 (5) ◽  
Author(s):  
Ze-Pei Cian ◽  
Hossein Dehghani ◽  
Andreas Elben ◽  
Benoît Vermersch ◽  
Guanyu Zhu ◽  
...  
Keyword(s):  
Chern Number ◽  
Many Body ◽  
Statistical Correlations

Spin and orbital magnetization in self-assembled Co clusters on Au(111)

1999 ◽  
Vol 59 (2) ◽  
pp. R701-R704 ◽  
Author(s):  
H. A. Dürr ◽  
S. S. Dhesi ◽  
E. Dudzik ◽  
D. Knabben ◽  
G. van der Laan ◽  
...  
Keyword(s):  
Orbital Magnetization ◽  
Self Assembled

scholarly journals Measuring Chern numbers in Hofstadter strips

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Samuel Mugel ◽  
Alexandre Dauphin ◽  
Pietro Massignan ◽  
Leticia Tarruell ◽  
Maciej Lewenstein ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary Conditions ◽  
Chern Number ◽  
Open Boundary ◽  
Topological Invariants ◽  
Transverse Displacement ◽  
Open Boundary Conditions ◽  
Open Questions ◽  
Chern Numbers ◽  
Spatial Dimensions

Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems with open boundary conditions and limited spatial extension. Here, we consider transport in Hofstadter strips, that is, two-dimensional lattices pierced by a uniform magnetic flux which extend over few sites in one of the spatial dimensions. As we show, an atomic wave packet exhibits a transverse displacement under the action of a weak constant force. After one Bloch oscillation, this displacement approaches the quantized Chern number of the periodic system in the limit of vanishing tunneling along the transverse direction. We further demonstrate that this scheme is able to map out the Chern number of ground and excited bands, and we investigate the robustness of the method in presence of both disorder and harmonic trapping. Our results prove that topological invariants can be measured in Hofstadter strips with open boundary conditions and as few as three sites along one direction.

scholarly journals Chern Class Inequalities on Polarized Manifolds and Nef Vector Bundles

2020 ◽  
Author(s):  
Ping Li ◽  
Fangyang Zheng
Keyword(s):  
Chern Class ◽  
Vector Bundles ◽  
Euler Number ◽  
Type Inequality ◽  
Chern Number ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Bisectional Curvature ◽  
Chern Numbers ◽  
Nef Vector Bundles

Abstract This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our 1st main result is a family of sharp Chern class inequalities. Among them the 1st one is a variant of a classical result and the equality case of the 2nd one is a characterization of hypersurfaces. The 2nd main result is a Chern number inequality on it, which includes a reverse Miyaoka–Yau-type inequality. The 3rd main result is that the Chern numbers of a nef vector bundle over a compact Kähler manifold are bounded below by the Euler number. As an application, we classify compact Kähler manifolds with nonnegative bisectional curvature whose Chern numbers are all positive. A conjecture related to the Euler number of compact Kähler manifolds with nonpositive bisectional curvature is proposed, which can be regarded as a complex analogue to the Hopf conjecture.

scholarly journals DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Paul Eugenio ◽  
Ceren Dag
Keyword(s):  
Magnetic Field ◽  
Time Reversal ◽  
Ground States ◽  
Bilayer Graphene ◽  
Chern Number ◽  
Strong Interactions ◽  
Time Reversal Symmetry ◽  
Density Matrix Renormalization ◽  
Topological Quantum ◽  
Twisted Bilayer Graphene

Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern=\pm1=±1), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at half-filling: (i) LLL’s with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL’s with the same magnetic field. In the first scenario – which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene – the opposite Chern LLL’s are Kramer pairs, and thus there exists time-reversal symmetry (\mathbb{Z}_2ℤ2). Turning on repulsive interactions drives the system to spontaneously break time-reversal symmetry – a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern |{++\cdots+}\rangle|++⋯+⟩ or all negative |{--\cdots-}\rangle|−−⋯−⟩. If instead, interactions are taken between electrons of like-Chern number, the ground state is an SU(2)SU(2) ferromagnet, with total spin pointing along an arbitrary direction, as with the \nu=1ν=1 spin-\frac{1}{2}12 quantum Hall ferromagnet. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.

scholarly journals X-Ray Detected Magnetic Resonance: A Unique Probe of the Precession Dynamics of Orbital Magnetization Components

2011 ◽  
Vol 12 (12) ◽  
pp. 8797-8835 ◽  
Author(s):  
José Goulon ◽  
Andrei Rogalev ◽  
Gérard Goujon ◽  
Fabrice Wilhelm ◽  
Jamal Ben Youssef ◽  
...  
Keyword(s):  
Magnetic Resonance ◽  
X Ray ◽  
Unique Probe ◽  
Orbital Magnetization
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