New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field

1993 ◽  
Vol 71 (17) ◽  
pp. 2777-2780 ◽  
Author(s):  
G. Ortiz ◽  
D. M. Ceperley ◽  
R. M. Martin
Keyword(s):  
Magnetic Field ◽  
Time Reversal ◽  
Stochastic Method ◽  
Time Reversal Symmetry

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 Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4

Science ◽  
2020 ◽  
Vol 367 (6480) ◽  
pp. 895-900 ◽  
Author(s):  
Yujun Deng ◽  
Yijun Yu ◽  
Meng Zhu Shi ◽  
Zhongxun Guo ◽  
Zihan Xu ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Quantum Transport ◽  
Topological Insulator ◽  
Time Reversal ◽  
Magnetic Order ◽  
Anomalous Hall Effect ◽  
Time Reversal Symmetry ◽  
Zero Field ◽  
Exotic States ◽  
Ferromagnetic Layers

In a magnetic topological insulator, nontrivial band topology combines with magnetic order to produce exotic states of matter, such as quantum anomalous Hall (QAH) insulators and axion insulators. In this work, we probe quantum transport in MnBi2Te4 thin flakes—a topological insulator with intrinsic magnetic order. In this layered van der Waals crystal, the ferromagnetic layers couple antiparallel to each other; atomically thin MnBi2Te4, however, becomes ferromagnetic when the sample has an odd number of septuple layers. We observe a zero-field QAH effect in a five–septuple-layer specimen at 1.4 kelvin, and an external magnetic field further raises the quantization temperature to 6.5 kelvin by aligning all layers ferromagnetically. The results establish MnBi2Te4 as an ideal arena for further exploring various topological phenomena with a spontaneously broken time-reversal symmetry.

scholarly journals FLUCTUATION THEOREMS WITHOUT TIME-REVERSAL SYMMETRY

2014 ◽  
Vol 28 (07) ◽  
pp. 1430003 ◽  
Author(s):  
CHENJIE WANG ◽  
D. E. FELDMAN
Keyword(s):  
Magnetic Field ◽  
Time Reversal ◽  
Topological States Of Matter ◽  
Transport Coefficients ◽  
Theoretical Research ◽  
Time Reversal Symmetry ◽  
Nonlinear Transport ◽  
Open Problems ◽  
Fluctuation Theorems ◽  
Fluctuation Relations

Fluctuation theorems establish deep relations between observables away from thermal equilibrium. Until recently, the research on fluctuation theorems was focused on time-reversal-invariant systems. In this review we address some newly discovered fluctuation relations that hold without the time-reversal symmetry, in particular, in the presence of an external magnetic field. One family of relations connects nonlinear transport coefficients in the opposite magnetic fields. Another family relates currents and noises at a fixed direction of the magnetic field in chiral systems, such as the edges of some quantum Hall liquids. We review the recent experimental and theoretical research, including the controversy about the microreversibility without the time-reversal symmetry, consider the applications of fluctuation theorems to the physics of topological states of matter, and discuss open problems.

Time-reversal symmetry for systems in a constant external magnetic field

2017 ◽  
Vol 96 (1) ◽  
Author(s):  
Sara Bonella ◽  
Alessandro Coretti ◽  
Lamberto Rondoni ◽  
Giovanni Ciccotti
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Constant External Magnetic Field

scholarly journals Advances in synthetic gauge fields for light through dynamic modulation

2018 ◽  
Vol 5 (4) ◽  
pp. 172447 ◽  
Author(s):  
Daniel Hey ◽  
Enbang Li
Keyword(s):  
Magnetic Field ◽  
Gauge Field ◽  
Time Reversal ◽  
Higher Dimensions ◽  
Gauge Fields ◽  
Time Reversal Symmetry ◽  
Topological Properties ◽  
Dynamic Modulation ◽  
Recent Developments ◽  
Synthetic Gauge Fields

Photons are weak particles that do not directly couple to magnetic fields. However, it is possible to generate a photonic gauge field by breaking reciprocity such that the phase of light depends on its direction of propagation. This non-reciprocal phase indicates the presence of an effective magnetic field for the light itself. By suitable tailoring of this phase, it is possible to demonstrate quantum effects typically associated with electrons, and, as has been recently shown, non-trivial topological properties of light. This paper reviews dynamic modulation as a process for breaking the time-reversal symmetry of light and generating a synthetic gauge field, and discusses its role in topological photonics, as well as recent developments in exploring topological photonics in higher dimensions.

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