Inverse flux quantum periodicity in the amplitudes of commensurability oscillations in two-dimensional lateral surface superlattices

Chowdhury, Soumi Roy; Long, A. R.; Skuras, E.; Davies, John H.; Lister, Kevin; Pennelli, Giovanni; Stanley, CR

doi:10.1103/physrevb.69.035330

Cited by 9 publications

(10 citation statements)

References 19 publications

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“…Because σ dif νν ≪ σ col νν , the difference in the total resistivity is very small between the two sets of modulation strengths. However, the oscillation amplitudes in ρ col µµ are higher in the present case and ρ xx increases more slowly with B as observed [8]. Upon closer inspection we see that the prominent peaks, marked by the integral values of α, result entirely from the collisional contribution σ col νν .…”

Section: Numerical Resultssupporting

confidence: 73%

“…As a result, when 2πℓ 2 /a x a y = Φ 0 /Φ is an integer, the second and third terms in the argument of the δ function in Eq. ( 25) vanish and entail n = n ′ , i. e., the response is strongest when one flux quantum passes through an integral number of cells as observed [8,14]. In this case the factor [(...) 2 + Γ 2 ] in Eq.…”

Section: B Analytical Evaluationsmentioning

confidence: 86%

“…To date most of the experimental results pertinent to 2D modulations [7]- [9] with square or hexagonal symmetry have indicated strongly that the predicted [10] fine structure of the Landau levels is not resolved. Magnetotransport theories pertinent to this case are rather limited [4], [7,8] in contrast with those for 1D modulations.…”

Section: Introductionmentioning

confidence: 99%

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Inverse flux quantum periodicity of magnetoresistance oscillations in two-dimensional short-period surface superlattices

2004

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Transport properties of the two-dimensional electron gas (2DEG) are considered in the presence of a perpendicular magnetic field B and of a weak two-dimensional (2D) periodic potential modulation in the 2DEG plane. The symmetry of the latter is rectangular or hexagonal. The wellknown solution of the corresponding tight-binding equation shows that each Landau level splits into several subbands when a rational number of flux quanta h/e pierces the unit cell and that the corresponding gaps are exponentially small. Assuming the latter are closed due to disorder gives analytical wave functions and simplifies considerably the evaluation of the magnetoresistivity tensor ρ µν . The relative phase of the oscillations in ρ xx and ρ yy depends on the modulation periods involved. For a 2D modulation with a short period ≤ 100 nm, in addition to the Weiss oscillations the collisional contribution to the conductivity and consequently the tensor ρ µν show prominent peaks when one flux quantum h/e passes through an integral number of unit cells in good agreement with recent experiments. For periods 300 − 400 nm long used in early experiments, these peaks occur at fields 10 − 25 times smaller than those of the Weiss oscillations and are not resolved.

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Section: Numerical Resultssupporting

confidence: 73%

Section: B Analytical Evaluationsmentioning

confidence: 86%

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Inverse flux quantum periodicity of magnetoresistance oscillations in two-dimensional short-period surface superlattices

2004

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“…2,3,4,5,6,7,8,9,10,11,12,13,14,15 and Refs. 16,17,18,19,20 (and references therein) for 1D and 2D LSLs, respectively].…”

Section: Introductionmentioning

confidence: 99%

Fourier analyses of commensurability oscillations in Fibonacci lateral superlattices

Endo

Iye

2008

Phys. Rev. B

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Magnetotransport measurements have been performed on Fibonacci lateral superlattices (FLSLs) -two-dimensional electron gases subjected to a weak potential modulation arranged in the Fibonacci sequence, LSLLSLS..., with L/S=τ (the golden ratio). Complicated commensurability oscillation (CO) is observed, which can be accounted for as a superposition of a series of COs each arising from a sinusoidal modulation representing the characteristic length scale of one of the selfsimilar generations in the Fibonacci sequence. Individual CO components can be separated out from the magnetoresistance trace by performing a numerical Fourier band-pass filter. From the analysis of the amplitude of a single-component CO thus extracted, the magnitude of the corresponding Fourier component in the potential modulation can be evaluated. By examining all the Fourier contents observed in the magnetoresistance trace, the profile of the modulated potential seen by the electrons can be reconstructed with some remaining ambiguity about the interrelation of the phase between different components.

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“…One of the earliest examples is the observation of Weiss oscillations in conventional two-dimensional electron gas (2DEG) in GaAs/AlGaAs subject to a one-dimensional periodic static electric potential, created by parallel fringes or metallic strip arrays, and a perpendicular homogeneous magnetic field [36], which is due to the commensuration between the cyclotron radius and the period of the electric potential [37][38][39][40]. 2D periodic electric potentials on 2DEG [41][42][43][44][45], with different symmetries [46][47][48], were also realized, which show Hofstadter butterfly spectra under moderate homogeneous magnetic fields. In parallel, spatially periodic (orbital) magnetic fields in 1D [49][50][51][52], 2D [53][54][55][56], and Zeeman fields [57] have been experimentally realized using periodic arrays of superconducting or ferromagnetic strips or dots.…”

Section: Introductionmentioning

confidence: 99%

Emergent flat band lattices in spatially periodic magnetic fields

Tahir,

Pinaud,

Chen

2018

Preprint

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Motivated by the recent discovery of Mott insulating phase and unconventional superconductivity due to the flat bands in twisted bilayer graphene, we propose more generic ways of getting twodimensional (2D) emergent flat band lattices using either 2D Dirac materials or ordinary electron gas (2DEG) subject to moderate periodic orbital magnetic fields with zero spatial average. Employing both momentum-space and real-space numerical methods to solve the eigenvalue problems, we find stark contrast between Schrödinger and Dirac electrons, i.e., the former show recurring "magic" values of the magnetic field when the lowest band becomes flat, while for the latter the zero-energy bands are asymptotically flat without magicness. By examining the Wannier functions localized by the smooth periodic magnetic fields, we are able to explain these nontrivial behaviors using minimal tight-binding models on a square lattice. The two cases can be interpolated by varying the g-factor or effective mass of a 2DEG and by taking into account the Zeeman coupling, which also leads to flat bands with nonzero Chern numbers for each spin. Our work provides flexible platforms for exploring interaction-driven phases in 2D systems with on-demand superlattice symmetries.

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Inverse flux quantum periodicity in the amplitudes of commensurability oscillations in two-dimensional lateral surface superlattices

Cited by 9 publications

References 19 publications

Inverse flux quantum periodicity of magnetoresistance oscillations in two-dimensional short-period surface superlattices

Inverse flux quantum periodicity of magnetoresistance oscillations in two-dimensional short-period surface superlattices

Fourier analyses of commensurability oscillations in Fibonacci lateral superlattices

Emergent flat band lattices in spatially periodic magnetic fields

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