scholarly journals GAUGE FIELDS, QUANTIZED FLUXES AND MONOPOLE CONFINEMENT OF THE HONEYCOMB LATTICE

2009 ◽  
Vol 23 (14) ◽  
pp. 3113-3130 ◽  
Author(s):  
MAHITO KOHMOTO
Keyword(s):  
Time Reversal ◽  
Dual Space ◽  
Gauge Fields ◽  
Honeycomb Lattice ◽  
Time Reversal Symmetry ◽  
Hall Conductance ◽  
Jahn Teller ◽  
Jahn Teller Effect ◽  
Hopping Models ◽  
Bloch Electrons

Electron hopping models on the honeycomb lattice are studied. The lattice consists of two triangular sublattices, and it is non-Bravais. The dual space has non-trivial topology. The gauge fields of Bloch electrons have the U(1) symmetry and thus represent superconducting states in the dual space. Two quantized Abrikosov fluxes exist at the Dirac points and have fluxes 2π and -2π, respectively. We define the non-Abelian SO(3) gauge theory in the extended 3d dual space and it is shown that a monopole and anti-monoplole solution is stable. The SO(3) gauge group is broken down to U(1) at the 2d boundary. The Abrikosov fluxes are related to quantized Hall conductance by the topological expression. Based on this, monopole confinement and deconfinement are discussed in relation to time reversal symmetry and QHE. The Jahn–Teller effect is briefly discussed.

scholarly journals Time-reversal symmetry breaking superconducting ground state in the doped Mott insulator on the honeycomb lattice

2013 ◽  
Vol 88 (15) ◽  
Author(s):  
Zheng-Cheng Gu ◽  
Hong-Chen Jiang ◽  
D. N. Sheng ◽  
Hong Yao ◽  
Leon Balents ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Ground State ◽  
Time Reversal ◽  
Mott Insulator ◽  
Honeycomb Lattice ◽  
Time Reversal Symmetry ◽  
Doped Mott Insulator

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.

Theory of Quantum Transport in Two-Dimensional Graphite

2007 ◽  
Vol 21 (08n09) ◽  
pp. 1113-1122 ◽  
Author(s):  
TSUNEYA ANDO
Keyword(s):  
Transport Properties ◽  
Quantum Transport ◽  
Time Reversal ◽  
Zero Mode ◽  
Point Of View ◽  
Honeycomb Lattice ◽  
Time Reversal Symmetry ◽  
Theoretical Point ◽  
Two Dimensional ◽  
Special Time

A brief review is given on electronic and transport properties of a two-dimensional honeycomb lattice from a theoretical point of view. The topics include the symmetry crossover among symplectic, unitary, and orthogonal due to the presence of special time reversal symmetry and the topological anomaly giving rise to various zero-mode anomalies and peculiar magnetotransport.

scholarly journals Visualization of superparamagnetic dynamics in magnetic topological insulators

2015 ◽  
Vol 1 (10) ◽  
pp. e1500740 ◽  
Author(s):  
Ella O. Lachman ◽  
Andrea F. Young ◽  
Anthony Richardella ◽  
Jo Cuppens ◽  
H. R. Naren ◽  
...  
Keyword(s):  
Phase Transition ◽  
Time Reversal ◽  
Quantum Interference ◽  
Topological Insulators ◽  
Quantum Phase Transitions ◽  
Electronic System ◽  
Characteristic Size ◽  
Quantum Phase ◽  
Time Reversal Symmetry ◽  
Hall Conductance

Quantized Hall conductance is a generic feature of two-dimensional electronic systems with broken time reversal symmetry. In the quantum anomalous Hall state recently discovered in magnetic topological insulators, time reversal symmetry is believed to be broken by long-range ferromagnetic order, with quantized resistance observed even at zero external magnetic field. We use scanning nanoSQUID (nano–superconducting quantum interference device) magnetic imaging to provide a direct visualization of the dynamics of the quantum phase transition between the two anomalous Hall plateaus in a Cr-doped (Bi,Sb)2Te3 thin film. Contrary to naive expectations based on macroscopic magnetometry, our measurements reveal a superparamagnetic state formed by weakly interacting magnetic domains with a characteristic size of a few tens of nanometers. The magnetic phase transition occurs through random reversals of these local moments, which drive the electronic Hall plateau transition. Surprisingly, we find that the electronic system can, in turn, drive the dynamics of the magnetic system, revealing a subtle interplay between the two coupled quantum phase transitions.

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