136 research outputs found
Magnetic translations for a spatially periodic magnetic field
It is shown that in the case of free electron in a spatially periodic
magnetic field the concept of magnetic translations operators is still valid
and, moreover, these operators can be defined in the same way as for a Bloch
electron in a uniform magnetic field. The results can be a useful tool in
investigation of lately observed phenomena in 2DEG with spatially modulated
density.Comment: 8 pages, epsfig, amsfonts, sub. to Acta Phys. Po
Local gauge and magnetic translation groups
The magnetic translation group was introduced as a set of operators
T(R)=\exp[-iR.(p-eA/c)/\hbar]. However,these operators commute with the
Hamiltonian for an electron in a periodic potential and a uniform magnetic
field if the vector potential A (the gauge) is chosen in a symmetric way. It is
showed that a local gauge field A_R(r) on a crystal lattice leads to operators,
which commute with the Hamiltonian for any (global) gauge field A=A(r). Such
choice of the local gauge determines afactor system \omega(R,R')= T(R)T(R')
T(R+R')^{-1}, which depends on a global gauge only. Moreover, for any potential
A a commutator T(R)T(R')T(R)^{-1}T(R')^{-1} depends only on the magnetic field
and not on the gauge.Comment: Latex 2.09, RevTex,3 pages, amsfont
Two-dimensional electron gas in a periodic potential and external magnetic field: states of pairs and three-particle systems
The group-theoretical classification of states of identical particle pairs is
presented. Then obtained states are coupled with those of an antiparticle to
construct states of a three-particle system. Investigations are performed using
products of irreducible projective representations of the 2D translation group.
For a given BvK period N degeneracy of pair states is N, whereas three-particle
states are N^2-fold degenerated. It has to be underlined that the case of even
N is more complicated since pair states are labelled by four inequivalent
irreducible projective representations. The problem of symmetry properties with
respect to particles transposition is briefly discussed.Comment: 8 pages, LaTeX 2
Trions in a periodic potential
The group-theoretical classification of trion states is presented. It is
based on considerations of products of irreducible representations of the 2D
translation group. For a given BvK period N degeneracy of obtained states is
N^2. Trions consist of two identical particles so the symmetrization of states
with respect to particles transposition is considered. Completely antisymmetric
states can be constructed by introducing antisymmetric spin functions. Two
symmetry adapted bases are considered. The third possibility is postponed for
the further investigations.Comment: revtex, 5 p., sub. to Physica
The role of a form of vector potential - normalization of the antisymmetric gauge
Results obtained for the antisymmetric gauge A=[Hy,-Hx]/2 by Brown and Zak
are compared with those based on pure group-theoretical considerations and
corresponding to the Landau gauge A=[0,Hx]. Imposing the periodic boundary
conditions one has to be very careful since the first gauge leads to a factor
system which is not normalized. A period N introduced in Brown's and Zak's
papers should be considered as a magnetic one, whereas the crystal period is in
fact 2N. The `normalization' procedure proposed here shows the equivalence of
Brown's, Zak's, and other approaches. It also indicates the importance of the
concept of magnetic cells. Moreover, it is shown that factor systems (of
projective representations and central extensions) are gauge-dependent, whereas
a commutator of two magnetic translations is gauge-independent. This result
indicates that a form of the vector potential (a gauge) is also important in
physical investigations.Comment: RevTEX, 9 pages, to be published in J. Math. Phy
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