Magnetoquantum Oscillations in a Lateral Superlattice

Weiss, Dieter

doi:10.1007/978-1-4684-7412-1_8

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…1.2 Weiss oscillations and the ν = 1/2 state Here, we study theoretically commensurability oscillations in the magnetoresistance near ν = 1/2, focusing on those oscillations that result from the presence of a periodic onedimensional static potential [9]. These commensurability oscillations are commonly known as Weiss oscillations [25][26][27][28]. For a free two-dimensional Fermi gas, the locations of the Weiss oscillation minima, say, as a function of the transverse magnetic field b, satisfy…”

Section: Motivationmentioning

confidence: 99%

Fluctuations and magnetoresistance oscillations near the half-filled Landau level

Mitra

Mulligan

2019

Phys. Rev. B

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We study theoretically the magnetoresistance oscillations near a half-filled lowest Landau level (ν = 1/2) that result from the presence of a periodic one-dimensional electrostatic potential. We use the Dirac composite fermion theory of Son [Phys. Rev. X 5 031027 (2015)], where the ν = 1/2 state is described by a (2+1)-dimensional theory of quantum electrodynamics. We extend previous work that studied these oscillations in the mean-field limit by considering the effects of gauge field fluctuations within a large flavor approximation. A self-consistent analysis of the resulting Schwinger-Dyson equations suggests that fluctuations dynamically generate a Chern-Simons term for the gauge field and a magnetic field-dependent mass for the Dirac composite fermions away from ν = 1/2. We show how this mass results in a shift of the locations of the oscillation minima that improves the comparison with experiment [Kamburov et. al., Phys. Rev. Lett. 113, 196801 (2014)]. The temperature-dependent amplitude of these oscillations may enable an alternative way to measure this mass. This amplitude may also help distinguish the Dirac and Halperin, Lee, and Read composite fermion theories of the half-filled Landau level.

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Section: Motivationmentioning

confidence: 99%

Fluctuations and magnetoresistance oscillations near the half-filled Landau level

Mitra

Mulligan

2019

Phys. Rev. B

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“…Weiss oscillations [3][4][5] are quantum oscillations that occur because of the presence of a periodic scalar or vector potential. The length scale provided by the period of the imposed potential allows additional oscillations to occur when the cyclotron radius is (approximately) commensurate with the period [6]. These oscillations occur at magnetic field values B(p) satisfying ℓ 2 B(p) = d 2k F p − φ , p = 1, 2, 3, .…”

Section: Introductionmentioning

confidence: 99%

Weiss oscillations and particle-hole symmetry at the half-filled Landau level

Cheung

Mulligan

2017

Phys. Rev. B

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Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal ±e 2 /2h at half-filling. We study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half-filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field, the oscillations occur symmetrically as the electron density is varied about half-filling. We find an approximate "sum rule" obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long wavelength physics.

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The Role of Impurity Scattering in the Quantum Waveguide

Mao

Huang

Zhou

1993

Physica Status Solidi (b)

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The effect of elastic scattering due to impurities in the quantum waveguide is investigated with an exact calculation. It is treated as a one-dimensional scattering problem and any width effect is neglected.The method is applied to the quantum modulated transistor and the Aharonov-Bohm ring. The overall transmission of the structure is found to be distorted owing to the scattering, the extent of the distortion being not only dependent on the impurity potential strength, but also on the impurity positions. The cutoff frequency of the transistor affected by the scattering is also discussed.

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Magnetoquantum Oscillations in a Lateral Superlattice

Cited by 3 publications

References 19 publications

Fluctuations and magnetoresistance oscillations near the half-filled Landau level

Fluctuations and magnetoresistance oscillations near the half-filled Landau level

Weiss oscillations and particle-hole symmetry at the half-filled Landau level

The Role of Impurity Scattering in the Quantum Waveguide

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