Magnetoresistance oscillations in a periodically modulated two-dimensional electron gas: The magnetic-breakdown approach

Gvozdikov, V. M.

doi:10.1103/physrevb.75.115106

Cited by 9 publications

(7 citation statements)

References 31 publications

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“…Magneto-plasmons in far-infrared transmission [15] and commensurability oscillations [16] in a modulated 2DEG can be largely explained without invoking quantum mechanics [17,18]. On the other hand, SLs under strong magnetic fields, which leads to magnetic breakdown [19,20], as well as other more complex systems [21][22][23], require quantum-mechanical ingredients (Bohr-Sommerfeld quantization and tunnelling between semiclassical orbits).…”

Section: Introductionmentioning

confidence: 99%

From laterally modulated two-dimensional electron gas towards artificial graphene

Nádvorník

Орлита

Goncharuk³

et al. 2012

New J. Phys.

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Cyclotron resonance has been measured in far-infrared transmission of GaAs/Al x Ga 1−x As heterostructures with an etched trigonal lateral superlattice intended to mimic graphene with lattice constant of the order of 100 nm (about 1000 times larger than that of natural graphene). Nonlinear dependence of the resonance position on magnetic field was observed, as well as its splitting into several modes. Our explanation, based on a perturbative calculation, describes the observed phenomena as a weak effect of the lateral potential on the twodimensional electron gas. Using this approach, we found a correlation between parameters of the lateral patterning and the created effective potential and obtained thus insights into how the electronic miniband structure has been tuned. The miniband dispersion was calculated using a simplified model and allowed us to formulate four basic criteria that have to be satisfied to reach graphene-like physics in such systems.

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Section: Introductionmentioning

confidence: 99%

From laterally modulated two-dimensional electron gas towards artificial graphene

Nádvorník

Орлита

Goncharuk³

et al. 2012

New J. Phys.

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“…Further theoretical work on this model may reveal these symmetries. Our model also provides a convenient inroad towards a semiclassical understanding of the Hofstadter spectrum, and connections to magnetic breakdown in real materials [19].The most promising experimental realization of our model is in optical lattices [18]. Optical lattice experiments can study both bosonic and fermionic quantum Hall states, and allow us in principle to study much larger fluxes than can be achieved with real magnetic fields.…”

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confidence: 96%

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confidence: 97%

Exact Parent Hamiltonian for the Quantum Hall States in a Lattice

2010

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We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wavefunctions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wavefunction is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.PACS numbers: 03.75. Lm,67.85.Hj,03.75.Hh, The interplay between periodic potentials and magnetic fields is an important topic [1][2][3][4][5]. In the tight binding limit, the lattice broadens the Landau levels into a series of finite bandwidth "Hofstadter bands" which can be represented as a self-similar fractal. Since the original band-gaps persist, the integer quantum Hall effects are robust against the lattice. The split degeneracy, however, invalidates many of the analytic arguments used to explain the fractional quantum Hall effect [6][7][8][9], and questions remain about the nature of the interacting system. Here, by adding longer range hoppings to a Hubbard model, we produce a Hamiltonian for which several Hofstadter bands coalesce into a single degenerate manifold. Adding local repulsion between the particles, we show that at appropriate filling factors the Laughlin wavefunction becomes an exact ground-state.In a uniform magnetic field, the most general hopping Hamiltonian on a two-dimensional square lattice iswhere the position of the j'th lattice site is written in complex notation as z j = x j + iy j , and z = z k − z j . The operators a j annihilate an atom at site j. The phase factor z j z * − z * j z φ = 2i (x j y − y j x) φ, corresponds to a uniform magnetic field in the symmetric gauge, with flux φ through each plaquette. This flux is only defined modulo 1, and having a full flux quantum through each plaquette is gauge equivalent to no flux. We will explicitly assume 0 ≤ φ ≤ 1, and take φ = p/q to be the ratio of two relatively prime integers. If one chooses W to be −t for nearest neighbors and zero otherwise, one reproduces the Hofstadter spectrum [1]. We show that if instead we chooseG (z) ≡ (−1) x+y+xy , the lowest p Hofstadter bands collapses to a single fully degenerate Landau level. Although we work in the symmetric gauge A = (B/2) (xŷ − yx), converting our results to other gauges is trivial: under a gauge transformation A(r) → A(r) + ∇Λ(r) and c j → c j e iΛ(r j ) . The flux is measured in units of φ 0 = h/e, where h is Planck's constant, and e is the electric charge. Our derivation of this Hamiltonian is similar to one...

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“…The most prominent example is the Weiss oscillations observed in periodically modulated 2D electron gas. [34][35][36] In our case, the average velocity within the delocalized stripe Eq. ͑10͒ is determined by the variable-range-hopping mechanism and does not oscillate.…”

Section: Shubnikov-de Haas Oscillations Of the Conductivitymentioning

confidence: 86%

Incoherence, metal-to-insulator transition, and magnetic quantum oscillations of interlayer resistance in an organic conductor

Gvozdikov

2007

Phys. Rev. B

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An analytic theory is developed for the conductivity across the layers zz in a layered conductor in perpendicular magnetic field under the conditions of interlayer incoherence. The latter assumes a small hopping integral between the layers t Ӷប/ and the presence of localized states in the tails of broadened Landau levels ͑LLs͒ ͑ is the electron scattering time within the layers͒. In the incoherent regime, zz strongly depends on the in-plane conductivity mechanisms because electrons spend most of their time within the weakly coupled layers. At high fields ⍀ ӷ 1, an integer quantum Hall effect ͑IQHE͒ within the layers develops which changes dramatically magnetic quantum oscillations in the zz compared to the standard Lifshitz-Kosevich theory ͑⍀ is the cyclotron frequency͒. At low fields, zz displays Shubnikov-de Haas ͑SdH͒ oscillations which in the limit ⍀ ӷ 1 transforms into sharp peaks. The peaks reach their maximum values zz ϰ ប⍀ T when LLs cross the chemical potential . When falls into the tails between the LLs, the zz displays first a thermal activation behavior zz ϰ exp͓−͑ប⍀ − ͒ / T͔ and, then at lower temperatures T, crosses over into a variable-range-hopping regime with zz ϰ exp͑− ͱ T 0 / T͒, where T 0 ϰ ͉B − B 0 ͉ ␥ . Above B 0 , the in-plane electrons are in the quantum-Hallinsulator regime and the background interlayer magnetoresistance R b has an insulatorlike temperature dependence. Below B 0 , the in-plane electrons are in the conventional SdH oscillation regime and R b has a metal-like temperature dependence. On the insulating side, R b displays a universal dependence on the scaling variable ͑B − B 0 ͒ / T . Scaling is destroyed in tilted magnetic fields at angles corresponding to the spin zeros. All the above features in the zz have been observed in the ␤Љ-͑BEDT-TTF͒ 2 SF 5 CH 2 CF 2 SO 3 , in which the critical exponent is equal to =1/ ␥ = 0.65. The IQHE regime at high fields in this quasi-two-dimensional organic conductor is favored by the fixed value of the chemical potential. It is shown that at low temperatures ͑T Ӷប/ ͒, oscillations of the conductivity and magnetization are related by the condition zz ϰ B 2 ‫ץ‬M / ‫ץ‬B, in agreement with observations in ␤Љ-͑BEDT-TTF͒ 2 SF 5 CH 2 CF 2 SO 3 . The analysis shows that the above features in the conductivity cannot be explained within the model with a narrow-band dispersive electron transport across the layers because the model is incompatible with the incoherence condition t Ӷប/ . Moreover, in the self-consistent Born approximation, this model yields a nonphysical negative conductivity zz Ͻ 0.

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Magnetoresistance oscillations in a periodically modulated two-dimensional electron gas: The magnetic-breakdown approach

Cited by 9 publications

References 31 publications

From laterally modulated two-dimensional electron gas towards artificial graphene

From laterally modulated two-dimensional electron gas towards artificial graphene

Exact Parent Hamiltonian for the Quantum Hall States in a Lattice

Incoherence, metal-to-insulator transition, and magnetic quantum oscillations of interlayer resistance in an organic conductor

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