Hall conductivity as topological invariant in phase space

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.

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Hall conductivity as a topological invariant

physica status solidi (b) ◽

10.1002/pssb.200460762 ◽

2005 ◽

Vol 242 (6) ◽

pp. 1199-1203

Author(s):

A. Kunold ◽

M. Torres

Keyword(s):

Topological Invariant ◽

Hall Conductivity

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CANONICAL PHASE, TOPOLOGICAL INVARIANT AND REPRESENTATION THEORY

Modern Physics Letters A ◽

10.1142/s0217732390001013 ◽

1990 ◽

Vol 05 (12) ◽

pp. 917-925 ◽

Cited By ~ 1

Author(s):

HIROSHI KURATSUJI ◽

KEN-ICHI TAKADA

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Mechanics ◽

Phase Space ◽

General Scheme ◽

Geometric Quantization ◽

Topological Invariant ◽

Quantum Field ◽

Compact Lie Groups ◽

Generalized Phase Space

We show that the non-integrable phase defined over the generalized phase space, which is called the canonical phase, yields the topological quantization that reveals the connection with the irreducible representation of a certain class of compact Lie groups. Although this consequence by itself is already known in mathematics under the general scheme named geometric quantization, it has not yet been fully appreciated in physics except for some specific problems. The descriptive technique adopted here seems fresh enough to commit itself to the topological aspect of quantum mechanics even including quantum field theory.

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A one-dimensional self-gravitating stellar gas

Symposium - International Astronomical Union ◽

10.1017/s0074180900105261 ◽

1966 ◽

Vol 25 ◽

pp. 46-48 ◽

Cited By ~ 2

Author(s):

M. Lecar

Keyword(s):

Gravitational Field ◽

Phase Space ◽

Motion Picture ◽

Space Distribution ◽

Two Dimensional ◽

One Dimensional ◽

Phase Space Distribution ◽

Dimensional Phase Space ◽

The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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