Magnetic-electric two-dimensional Euclidean group

Hadjioannou, F. T.; Sarlis, N. V.

doi:10.1103/physrevb.54.5334

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…The dual problem corresponds to a simultaneous reverse in the directions of B and E. We notice that the commutators in the second line of Eq. (8) are part of the Lie algebra of the EM-Galilean two dimensional group [24,25]. This group is obtained when the usual rotation and boost operators of the planar-Galilean group are replaced by their electric-magnetic generalization in which the operators are enlarged by the effect of a gauge transformation.…”

Section: Electric Evolution and Magnetic Translationsmentioning

confidence: 99%

Hofstadter spectrum in electric and magnetic fields

Kunold

Torres

2005

Annals of Physics

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The problem of Bloch electrons in two dimensions subject to magnetic and intense electric fields is investigated. Magnetic translations, electric evolution and energy translation operators are used to specify the solutions of the Schrödinger equation. For rational values of the magnetic flux quanta per unit cell and commensurate orientations of the electric field relative to the original lattice, an extended superlattice can be defined and a complete set of mutually commuting space-time symmetry operators is obtained. Dynamics of the system is governed by a finite difference equation that exactly includes the effects of: an arbitrary periodic potential, an electric field orientated in a commensurable direction of the lattice, and coupling between Landau levels. A weak periodic potential broadens each Landau level in a series of minibands, separated by the corresponding minigaps. The addition of the electric field induces a series of avoided and exact crossing of the quasienergies, for sufficiently strong electric field the 1 spectrum evolves into equally spaced discreet levels, in this "magnetic Stark ladder" the energy separation is an integer multiple of hE/aB, with a the lattice parameter.

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Section: Electric Evolution and Magnetic Translationsmentioning

confidence: 99%

Hofstadter spectrum in electric and magnetic fields

Kunold

Torres

2005

Annals of Physics

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“…The commutators in the second line of Eq. ( 6) are part of the more general Lie algebra of the magnetic-electric Euclidean two dimensional group [8]. Schrödinger's equation and the symmetry operators are expressed in terms of covariant derivatives π µ and O µ , respectively.…”

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confidence: 99%

“…Hence, the meaning of ( 9) is that the ratio of the Stark ladder spacing (bE) to the Brillouin zone for the quasienergy (2πv d /b) is given by the rational number φ = p/q. We henceforth consider that the three conditions ( 7), (8), and (9) hold simultaneously. In this case the three EMB operators: the electric evolution T 0 ≡ T 0 (τ 0 ) and the magnetic translations T L ≡ T L (qb), and T T ≡ T T (b) form a set of mutually commuting symmetry operators.…”

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confidence: 99%