Hall Conductivity as the Topological Invariant in the Phase Space in the Presence of Interactions and a Nonuniform Magnetic Field

JETP Letters ◽  
2019 ◽  
Vol 110 (7) ◽  
pp. 487-494 ◽  
Author(s):  
C. X. Zhang ◽  
M. A. Zubkov
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Topological Invariant ◽  
Hall Conductivity ◽  
Nonuniform Magnetic Field

scholarly journals Hall conductivity as topological invariant in phase space

2020 ◽  
Vol 95 (6) ◽  
pp. 064003
Author(s):  
I V Fialkovsky ◽  
M Suleymanov ◽  
Xi Wu ◽  
C X Zhang ◽  
M A Zubkov
Keyword(s):  
Phase Space ◽  
Topological Invariant ◽  
Hall Conductivity

scholarly journals Hall conductivity of strained ℤ 2 crystals

2021 ◽  
pp. 2044034
Author(s):  
I. V. Fialkovsky ◽  
M. A. Zubkov
Keyword(s):  
Magnetic Field ◽  
Mechanical Stress ◽  
Topological Invariant ◽  
Hall Conductivity ◽  
Spatially Varying ◽  
2D And 3D

We establish topological nature of Hall conductivity of graphene and other [Formula: see text] crystals in 2D and 3D in the presence of inhomogeneous perturbations. To this end the lattice Weyl–Wigner formalism is employed. The nonuniform mechanical stress is considered, along with the spatially varying magnetic field. The relation of the obtained topological invariant to level counting is clarified.

scholarly journals Double layers in the downward current region of the aurora

2003 ◽  
Vol 10 (1/2) ◽  
pp. 45-52 ◽  
Author(s):  
R. E. Ergun ◽  
L. Andersson ◽  
C. W. Carlson ◽  
D. L. Newman ◽  
M. V. Goldman
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Phase Space ◽  
Electric Field ◽  
Electric Fields ◽  
Double Layers ◽  
Parallel Electric Field ◽  
Electrostatic Waves ◽  
Current Region ◽  
Decisive Evidence

Abstract. Direct observations of magnetic-field-aligned (parallel) electric fields in the downward current region of the aurora provide decisive evidence of naturally occurring double layers. We report measurements of parallel electric fields, electron fluxes and ion fluxes related to double layers that are responsible for particle acceleration. The observations suggest that parallel electric fields organize into a structure of three distinct, narrowly-confined regions along the magnetic field (B). In the "ramp" region, the measured parallel electric field forms a nearly-monotonic potential ramp that is localized to ~ 10 Debye lengths along B. The ramp is moving parallel to B at the ion acoustic speed (vs) and in the same direction as the accelerated electrons. On the high-potential side of the ramp, in the "beam" region, an unstable electron beam is seen for roughly another 10 Debye lengths along B. The electron beam is rapidly stabilized by intense electrostatic waves and nonlinear structures interpreted as electron phase-space holes. The "wave" region is physically separated from the ramp by the beam region. Numerical simulations reproduce a similar ramp structure, beam region, electrostatic turbulence region and plasma characteristics as seen in the observations. These results suggest that large double layers can account for the parallel electric field in the downward current region and that intense electrostatic turbulence rapidly stabilizes the accelerated electron distributions. These results also demonstrate that parallel electric fields are directly associated with the generation of large-amplitude electron phase-space holes and plasma waves.

COLLECTIVE FIELD THEORY TO MAGNETIC-FIELD-INDUCED SPIN-DENSITY-WAVE-STATE IN BECHGAARD SALTS, (TMTSF)2X

1993 ◽  
Vol 07 (19) ◽  
pp. 3415-3421 ◽  
Author(s):  
ALEXANDRE S. ROZHAVSKY
Keyword(s):  
Magnetic Field ◽  
Spin Density ◽  
Chemical Potential ◽  
Density Wave ◽  
Spin Density Wave ◽  
Hall Conductivity ◽  
Chiral Anomaly ◽  
Threshold Field ◽  
Wave State ◽  
Extended States

A field description of spin-density-wave (SDW) in a quasi-two-dimensional metal with open Fermi surface in magnetic field, is proposed. The SDW transition temperature, T c (H), and the Hall conductivity σxy, are calculated. The dependence T c (H) is found to be different from that of the Bardeen-Cooper-Schrieffer model, in particular, a threshold field, H c , found its natural explanation. It is proved that the quantized Hall conductivity arises from the chiral anomaly terms in the effective action provided there is pinning of chemical potential in the gap of extended states.

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