Detection of a Landau Band-Coupling-Induced Rearrangement of the Hofstadter Butterfly

Geisler, Martin; Smet, J. H.; Umansky, V.; Klitzing, K. von; Naundorf, B.; Ketzmerick, Roland; Schweizer, H.

doi:10.1103/physrevlett.92.256801

Cited by 124 publications

(93 citation statements)

References 11 publications

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“…Here, e is the charge of the electron. Although this can be overcome by using superlattice structures [45,62], defects or impurities are inevitable in a real crystal. In contrast, the optical lattice setup allows for a virtually defect-free implementation of the quantum Hall Hamiltonian, and values up to α ∼ 1 can be achieved [34,35,36,50].…”

Section: Hamiltonianmentioning

confidence: 99%

Optical lattice quantum Hall effect

2008

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We explore the behavior of interacting bosonic atoms in an optical lattice subject to a large artificial magnetic field. We extend earlier investigations of this system where the number of magnetic flux quanta per unit cell α is close to a simple rational number [Phys. Rev. Lett. 96, 180407 (2006)].Interesting topological states such as the Laughlin and Read-Rezayi states can occur even if the atoms experience a weak trapping potential in one direction. An explicit numerical calculation near α = 1/2 shows that the system exhibits a striped vortex lattice phase of one species, which is analogous to the behavior of a two-species system for small α. We also investigate methods to probe the encountered states. These include spatial correlation functions and the measurement of noise correlations in time-of-flight expanded atomic clouds. Characteristic differences arise which allow for an identification of the respective quantum Hall states. We furthermore discuss that a counterintuitive flow of the Hall current occurs for certain values of α.

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Section: Hamiltonianmentioning

confidence: 99%

Optical lattice quantum Hall effect

2008

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“…A periodic potential modulation of the 2DEG can be obtained by either patterning a metallic layer deposited onto the sample used as a top gate 15,16,17,18 or by etching the sample surface, creating an array of nano-dots 11,12,13,14,19,20 . The first approach presents challenges in the control of the potential amplitude perceived by the electrons of the 2DEG, which decreases with increasing distance from the gate.…”

Section: Methodsmentioning

confidence: 99%

Fabrication of artificial graphene in a GaAs quantum heterostructure

Scarabelli¹,

Wang²,

Pinczuk³

et al. 2015

Journal of Vacuum Science &Amp; Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phen

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The unusual electronic properties of graphene, which are a direct consequence of its twodimensional (2D) honeycomb lattice, have attracted a great deal of attention in recent years. Creation of artificial lattices that recreate graphene's honeycomb topology, known 2 as artificial graphene, can facilitate the investigation of graphene-like phenomena, such as the existence of massless Dirac fermions, in a tunable system. In this work, we present the fabrication of artificial graphene in an ultra-high quality GaAs/AlGaAs quantum well, with lattice period as small as 50 nm, the smallest reported so far for this type of system. Electron-beam lithography is used to define an etch mask with honeycomb geometry on the surface of the sample, and different methodologies are compared and discussed. An optimized anisotropic reactive ion etching process is developed to transfer the pattern into the AlGaAs layer and create the artificial graphene. The achievement of such highresolution artificial graphene should allow the observation for the first time of massless Dirac fermions in an engineered semiconductor.

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“…To observe the fractal pattern in a reasonable range of the magnetic field, the important requirement is that the lattice structure has a large period. This can be achieved in artificial superlattices based on semiconductor nanostructures [6]. Observation of a clear fractal pattern remained a challenge however.…”

Section: Introductionmentioning

confidence: 99%

Fractal butterflies in buckled graphenelike materials

Apalkov

Chakraborty

2015

Phys. Rev. B

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We study theoretically the properties of buckled graphene-like materials, such as silicene and germanene, in a strong perpendicular magnetic field and a periodic potential. We analyze how the spin-orbit interaction and the perpendicular electric field influences the energy spectra of these systems. When the magnetic flux through a unit cell of the periodic potential measured in magnetic flux quantum is a rational number, α = p/q, then in each Landau level the energy spectra have a band structure, which is characterized by the corresponding gaps. We study the dependence of those gaps on the parameters of the buckled graphene-like materials. Although some gaps have weak dependence on the magnitude of the spin-orbit coupling and the external electric field, there are gaps that show strong nonomonotic dependence on these parameters. For α = 1/2, the spin-orbit interaction also opens up a gap at one of the Landau levels. The magnitude of the gap increases with spin-orbit coupling and decreases with the applied electric field.

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Detection of a Landau Band-Coupling-Induced Rearrangement of the Hofstadter Butterfly

Cited by 124 publications

References 11 publications

Optical lattice quantum Hall effect

Optical lattice quantum Hall effect

Fabrication of artificial graphene in a GaAs quantum heterostructure

Fractal butterflies in buckled graphenelike materials

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