Quantum Hall effect in a<i>p</i>-type heterojunction with a lateral surface superlattice

Demikhovskiǐ, V. Ya.; Khomitskiy, D. V.

doi:10.1103/physrevb.68.165301

Cited by 6 publications

(3 citation statements)

References 33 publications

(71 reference statements)

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“…In the tight-binding limit, it is known that the Hall conductance of the entire band is always zero, although if inner gaps are opened by the periodic modulation, they can have different Hall conductances. By explicitly counting the number of zeros (and their vorticities) of the Bloch wave function inside the magnetic Brillouin zone u k (r) = e −ik⋅r ψ k (r) [23][24][25] , we have verified that the Hall conductance of the sub-bands follow this expected behavior in both limits of the Hofstadter problem (see Fig. 3).…”

supporting

confidence: 56%

Manipulating spin and charge in magnetic semiconductors using superconducting vortices

Berciu

Rappoport

Jankó

2005

Nature

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The magnetic properties of SC and DMS are vastly different. When placed in a magnetic field, a type-II SC allows the field to penetrate in a non-uniform fashion, as Abrikosov vortices -the field lines are bundled up into flux quanta surrounded by superfluid eddy currents 5 . The length scale characterizing the field inhomogeneity is the decay length of the superfluid eddy currents surrounding the core of an isolated vortex. This is known as the

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supporting

confidence: 56%

Manipulating spin and charge in magnetic semiconductors using superconducting vortices

Berciu

Rappoport

Jankó

2005

Nature

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“…Fractal energy band structures are believed to play an important role for a number of effects like the quantum Hall effect induced by magnetic fields in strongly correlated electron systems [14,18]. Therefore it is desirable to study the Hofstadter butterfly experimentally under well defined conditions.…”

Section: Introductionmentioning

confidence: 99%

Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms

2003

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We investigate the dynamics of neutral atoms in a 2D optical lattice which traps two distinct internal states of the atoms in different columns. Two Raman lasers are used to coherently transfer atoms from one internal state to the other, thereby causing hopping between the different columns. By adjusting the laser parameters appropriately we can induce a non vanishing phase of particles moving along a closed path on the lattice. This phase is proportional to the enclosed area and we thus simulate a magnetic flux through the lattice. This setup is described by a Hamiltonian identical to the one for electrons on a lattice subject to a magnetic field and thus allows us to study this equivalent situation under very well defined controllable conditions. We consider the limiting case of huge magnetic fields -which is not experimentally accessible for electrons in metals -where a fractal band structure, the Hofstadter butterfly, characterizes the system.

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“…In two dimensions, the TKNN equations for generalized Dirac-Harper operators have been worked out in [29]. Analyses of higher-dimensional situations are contained in [11,14,6,27,15].…”

Section: Introductionmentioning

confidence: 99%

Singular Geometry of the Momentum Space: From wire networks to quivers and monopoles

Kaufmann

Khlebnikov²,

Wehefritz-Kaufmann

2016

jsing

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Abstract.A new nano-material in the form of a double gyroid has motivated us to study (non)-commutative C * geometry of periodic wire networks and the associated graph Hamiltonians.Here we present a general more abstract framework, which is given by certain quiver representations, with special attention to the original case of the gyroid as well as related cases, such as graphene. The resulting effective C * -geometry is that of the momentum space, which parameterizes the quasi-momenta.This geometry is usually singular, where the singularities describe so-called band intersections in physics. We give geometric and algebraic methods to study these intersections; their origin being singularity theory and representation theory. A technique we newly apply to this situation is the use of topological invariants, which we formalize and explain in the paper. This uses K-theory and Chern classes as well as "slicing methods" for their computation. In this method the invariants can be computed using Berry's connection in the momentum space. This brings monopole charges and issues of topological stability into the picture.Adding a constant magnetic field or allowing projective representations makes the C * geometry non-commutative. In this case, we can also use K-theory, albeit in a different way, to make statements about the band structure using gap labeling.

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Quantum Hall effect in ap-type heterojunction with a lateral surface superlattice

Cited by 6 publications

References 33 publications

Manipulating spin and charge in magnetic semiconductors using superconducting vortices

Manipulating spin and charge in magnetic semiconductors using superconducting vortices

Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms

Singular Geometry of the Momentum Space: From wire networks to quivers and monopoles

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