3,212 research outputs found
Berry Curvature in Graphene: A New Approach
In the present paper we have directly computed the Berry curvature terms
relevant for Graphene in the presence of an \textit{inhomogeneous} lattice
distortion. We have employed the generalized Foldy Wouthuysen framework,
developed by some of us \cite{ber0,ber1,ber2}. We show that a non-constant
lattice distortion leads to a valley-orbit coupling which is responsible to a
valley-Hall effect. This is similar to the valley-Hall effect induced by an
electric field proposed in \cite{niu2} and is the analogue of the spin-Hall
effect in semiconductors \cite{MURAKAMI, SINOVA}. Our general expressions for
Berry curvature, for the special case of homogeneous distortion, reduce to the
previously obtained results \cite{niu2}. We also discuss the Berry phase in the
quantization of cyclotron motion.Comment: Slightly modified version, to appear in EPJ
From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics
In 1990, Dyson published a proof due to Feynman of the Maxwell equations
assuming only the commutation relations between position and velocity. With
this minimal assumption, Feynman never supposed the existence of Hamiltonian or
Lagrangian formalism. In the present communication, we review the study of a
relativistic particle using ``Feynman brackets.'' We show that Poincar\'e's
magnetic angular momentum and Dirac magnetic monopole are the consequences of
the structure of the Lorentz Lie algebra defined by the Feynman's brackets.
Then, we extend these ideas to the dual momentum space by considering
noncommutative quantum mechanics. In this context, we show that the
noncommutativity of the coordinates is responsible for a new effect called the
spin Hall effect. We also show its relation with the Berry phase notion. As a
practical application, we found an unusual spin-orbit contribution of a
nonrelativistic particle that could be experimentally tested. Another practical
application is the Berry phase effect on the propagation of light in
inhomogeneous media.Comment: Presented at the 3rd Feynman Festival (Collage Park, Maryland,
U.S.A., August 2006
Spin Hall effect of Photons in a Static Gravitational Field
Starting from a Hamiltonian description of the photon within the set of
Bargmann-Wigner equations we derive new semiclassical equations of motion for
the photon propagating in static gravitational field. These equations which are
obtained in the representation diagonalizing the Hamiltonian at the order
, present the first order corrections to the geometrical optics. The
photon Hamiltonian shows a new kind of helicity-magnetotorsion coupling.
However, even for a torsionless space-time, photons do not follow the usual
null geodesic as a consequence of an anomalous velocity term. This term is
responsible for the gravitational birefringence phenomenon: photons with
distinct helicity follow different geodesics in a static gravitational field.Comment: 6 page
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