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Register a new userSpatial Mapping of Local Density Variations in Two-dimensional Electron Systems Using Scanning Photoluminescence
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Added by
Edwin Yoonjang Chung
Publication date
2019
fields
Physics
and research's language is
English
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We have developed a scanning photoluminescence technique that can directly map out the local two-dimensional electron density with a relative accuracy of $sim2.2times10^8$ cm$^{-2}$. The validity of this approach is confirmed by the observation of the expected density gradient in a high-quality GaAs quantum well sample that was not rotated during the molecular beam epitaxy of its spacer layer. In addition to this global variation in electron density, we observe local density fluctuations across the sample. These random density fluctuations are also seen in samples that were continuously rotated during growth, and we attribute them to residual space charges at the substrate-epitaxy interface. This is corroborated by the fact that the average magnitude of density fluctuations is increased to $sim9times10^{9}$ cm$^{-2}$ from $sim1.2times10^9$ cm$^{-2}$ when the buffer layer between the substrate and the quantum well is decreased by a factor of seven. Our data provide direct evidence for local density inhomogeneities even in very high-quality two-dimensional carrier systems.
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In a previous paper we suggested that a macroscopic force field applied across a two-dimensional electron gas channel could induce a microscopic charge density wave as soon as the proper compressibility becomes negative, which happens at densities much higher than the critical density for the Wigner crystal transition. The suggestion was based on a calculation of the ground state energy in the local density approximation. In this paper we refine our calculation of the energy by including a self-consistent gradient correction to the kinetic energy. Due to the increased energy cost of rapid density variations, we find a much lower critical density for the onset of the charge density wave. This critical density coincides with the result of a linear stability analysis of the uniform ground state in the absence of the electric field.
We demonstrate tunable transverse rectification in a density-modulated two-dimensional electron gas (2DEG). The density modulation is induced by two surface gates, running in parallel along a narrow stripe of 2DEG. A transverse voltage in the direction of the density modulation is observed, i.e. perpendicular to the applied source-drain voltage. The polarity of the transverse voltage is independent of the polarity of the source-drain voltage, demonstrating rectification in the device. We find that the transverse voltage $U_{y}$ depends quadratically on the applied source-drain voltage and non-monotonically on the density modulation. The experimental results are discussed in the framework of a diffusion thermopower model.
Spectroscopic methods involving the sudden injection or ejection of electrons in materials are a powerful probe of electronic structure and interactions. These techniques, such as photoemission and tunneling, yield measurements of the single particle density of states (SPDOS) spectrum of a system. The SPDOS is proportional to the probability of successfully injecting or ejecting an electron in these experiments. It is equal to the number of electronic states in the system able to accept an injected electron as a function of its energy and is among the most fundamental and directly calculable quantities in theories of highly interacting systems. However, the two-dimensional electron system (2DES), host to remarkable correlated electron states such as the fractional quantum Hall effect, has proven difficult to probe spectroscopically. Here we present an improved version of time domain capacitance spectroscopy (TDCS) that now allows us to measure the SPDOS of a 2DES with unprecedented fidelity and resolution. Using TDCS, we perform measurements of a cold 2DES, providing the first direct measurements of the single-particle exchange-enhanced spin gap and single particle lifetimes in the quantum Hall system, as well as the first observations of exchange splitting of Landau levels not at the Fermi surface. The measurements reveal the difficult to reach and beautiful structure present in this highly correlated system far from the Fermi surface.
Two-dimensional electrons confined to GaAs quantum wells are hallmark platforms for probing electron-electron interaction. Many key observations have been made in these systems as sample quality improved over the years. Here, we present a breakthrough in sample quality via source-material purification and innovation in GaAs molecular beam epitaxy vacuum chamber design. Our samples display an ultra-high mobility of $44times10^6$ cm$^2$/Vs at an electron density of $2.0times10^{11}$ /cm$^2$. These results imply only 1 residual impurity for every $10^{10}$ Ga/As atoms. The impact of such low impurity concentration is manifold. Robust stripe/bubble phases are observed, and several new fractional quantum Hall states emerge. Furthermore, the activation gap of the $ u=5/2$ state, which is widely believed to be non-Abelian and of potential use for topological quantum computing, reaches $Deltasimeq820$ mK. We expect that our results will stimulate further research on interaction-driven physics in a two-dimensional setting and significantly advance the field.
We report electrical conductivity $sigma$ measurements on a range of two-dimensional electron gases (2DEGs) of varying linear extent. Intriguingly, at low temperatures ($T$) and low carrier density ($n_{mathrm{s}}$) we find the behavior to be consistent with $sigma sim L^{alpha}$, where $L$ is the length of the 2DEG along the direction of transport. Importantly, such scale-dependent behavior is precisely in accordance with the scaling hypothesis of localization~[Abrahams~textit{et al.}, Phys. Rev. Lett. textbf{42}, 673 (1979)] which dictates that in systems where the electronic wave function $xi$ is localized, $sigma$ is not a material-specific parameter, but depends on the system dimensions. From our data we are able to construct the $beta$-function $equiv (h/e^2) d ln sigma / d ln L$ and show this to be strongly consistent with theoretically predicted limiting values. These results suggest, remarkably, that the electrons in the studied 2DEGs preserve phase coherence over lengths $sim~10~mu$m. This suggests the utility of the 2DEGs studied towards applications in quantum information as well as towards fundamental investigations into many-body localized phases.
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