Quantum lifetime in ultrahigh quality GaAs quantum wells: Relationship to Δ5/2 and impact of density fluctuations

Abstract

We consider quantum lifetime derived from low-field Shubnikov-de Haas oscillations as a metric of quality of the two-dimensional electron gas in GaAs quantum wells that expresses large excitation gaps of the ⌫ = 5 2 fractional quantum Hall state in the N=1 Landau level. In high quality samples small density inhomogeneities dramatically impact the amplitude of Shubnikov-de Haas oscillations such that the canonical method (cf. Coleridge, Phys. Rev. B 44, 3793) for determination of quantum lifetime substantially underestimates ⌧ q unless density inhomogeneity is explicitly considered. We have developed a method which can be used to determine density inhomogeneity and extract the intrinsic ⌧ q by analyzing the Shubnikov-de Haas oscillations. However, even after accounting for inhomogeneity, ⌧ q does not correlate well with sample quality as measured by 5/2 , the excitation gap of the fractional quantum Hall state at 5/2 filling.

Hall field-induced resistance oscillations in a tunable-density GaAs quantum well

“…Since the gate is much farther away than the donor layer (d 1 /d 2 ∼ 0.1), it has a negligible impact on mobility. However, it can still limit the quantum mobility which is dominated by small-angle scattering [55]; with a random charge density of n 2 = 1 × 10 11 cm −2 , it would limit the quantum mobility of SB2 electrons to µ q2 ≈ (4ed 2 / )/ √ 2πn 2 ≈ 0.6 × 10 6 cm 2 /Vs [44]. This estimate is not unreasonable [56], considering that other scattering sources further diminish µ q2 .…”

Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures

“…29,93,118,119,[176][177][178][179] Similarly, the energy gap at ν = 5/2 did not scale with the quantum lifetime. 73,176 In fact in gated samples it was found that the quantum lifetime is approximately constant over the density range at which the energy gap at ν = 5/2 decreased from its largest value to zero. 73,119 These results are perhaps not surprising since, in contrast to the energy gap at ν = 5/2, both the mobility and the quantum lifetime are parameters measured near zero magnetic field, in a regime that may be understood within a single electron description.…”

“…Indeed, in the presence of a density variation, the magnetoresistance will be a convolution of magnetoresistances corresponding to the range of electron densities and therefore a density inhomogeneity will lead to a broadening of sharp resistive features. Density inhomogeneity in high quality GaAs/AlGaAs samples may be estimated from the widths of sharp magnetoresistance peaks, 72 from an analysis of quantum lifetime measurements, 73 and it is also accessible with the micro-photoluminescence technique on lengthscales larger than the laser spotsize. 74,75 We believe that the improved sample homogeneity results from a combination of improved sample growth and sample illumination techniques.…”

Suppression of Magneto-Intersubband Resistance Oscillations by Large-Scale Fluctuations of the Intersubband Energy Splitting

“…Modern molecular beam epitaxy makes it possible to grow selectively doped GaAs quantum wells where the two-dimensional (2D) electron gas has a low-temperature mobility of m 2 /(V s) [1][2][3][4]. However, despite the advances made in growing technology and optimizing the design of high-mobility heterostructures, they are not ideal 2D electron systems.…”