Dilute Two-dimensional Electron System Research Articles

Composite fermion liquid to Wigner solid transition in the lowest Landau level of zinc oxide

Interactions between the constituents of a condensed matter system can drive it through a plethora of different phases due to many-body effects. A prominent platform for it is a dilute two-dimensional electron system in a magnetic field, which evolves intricately through various gaseous, liquid and solid phases governed by Coulomb interaction. Here we report on the experimental observation of a phase transition between the composite fermion liquid and adjacent magnetic field induced phase with a character of Wigner solid. The experiments are performed in the lowest Landau level of a MgZnO/ZnO two-dimensional electron system with attributes of both a liquid and a solid. An in-plane magnetic field component applied on top of the perpendicular magnetic field extends the Wigner-like phase further into the composite fermion liquid phase region. Our observations indicate the direct competition between a composite fermion liquid and a Wigner solid formed either by electrons or composite fermions.

Strongly correlated two-dimensional plasma explored from entropy measurements.

Charged plasma and Fermi liquid are two distinct states of electronic matter intrinsic to dilute two-dimensional electron systems at elevated and low temperatures, respectively. Probing their thermodynamics represents challenge because of lack of an adequate technique. Here, we report a thermodynamic method to measure the entropy per electron in gated structures. Our technique appears to be three orders of magnitude superior in sensitivity to a.c. calorimetry, allowing entropy measurements with only 10(8) electrons. This enables us to investigate the correlated plasma regime, previously inaccessible experimentally in two-dimensional electron systems in semiconductors. In experiments with clean two-dimensional electron system in silicon-based structures, we traced entropy evolution from the plasma to Fermi liquid regime by varying electron density. We reveal that the correlated plasma regime can be mapped onto the ordinary non-degenerate Fermi gas with an interaction-enhanced temperature-dependent effective mass. Our method opens up new horizons in studies of low-dimensional electron systems.

Metallic state of low-mobility silicon at high carrier density induced by an ionic liquid

High mobility and dilute two-dimensional electron systems exhibit metallic behavior down to the lowest experimental temperatures. In studies of ionic liquid gated insulating silicon, we have observed transitions to a metallic state in low mobility samples at much higher areal carrier densities than found for samples of high mobility. We have also observed a mobility peak in metallic samples as the carrier density was increased beyond $10^{13} \text{cm}^{-2}$.

Scanning tunneling spectroscopy of a dilute two-dimensional electron system exhibiting Rashba spin splitting

Using scanning tunneling spectroscopy (STS) at 5 K in $B$ fields up to 7 T, we investigate the local density of states of a two-dimensional electron system (2DES) created by Cs adsorption on $p$-type InSb(110). The 2DES, which in contrast to previous STS studies exhibits a 2D Fermi level, shows standing waves at $B=0\text{ }\text{T}$ with corrugations decreasing with energy and with wave numbers in accordance with theory. In magnetic field percolating drift states are observed within the disorder broadened Landau levels. Due to the large electric field perpendicular to the surface, a beating pattern of the Landau levels is found and explained quantitatively by Rashba spin splitting within the lowest 2DES subband. The Rashba splitting does not contribute significantly to the standing wave patterns in accordance with theory.

EFFECTS OF ELECTRON-ELECTRON INTERACTIONS IN TWO DIMENSIONS

Strong electron-electron interactions in dilute two-dimensional electron systems in silicon lead to Pauli spin susceptibility growing critically at low electron densities. This effect originates from renormalization of the effective mass rather than the g-factor. The relative mass enhancement is system- and disorder-independent, which suggests that it is determined by electron-electron interactions only.

Spin susceptibility and polarization field in a dilute two-dimensional electron system in (111) silicon

We find that the polarization field, B_chi, obtained by scaling the weak-parallel-field magnetoresistance at different electron densities in a dilute two-dimensional electron system in (111) silicon, corresponds to the spin susceptibility that grows strongly at low densities. The polarization field, B_sat, determined by resistance saturation, turns out to deviate to lower values than B_chi with increasing electron density, which can be explained by filling of the upper electron subbands in the fully spin-polarized regime.

Effects of interactions in two dimensions

Strong electron–electron interactions in dilute two-dimensional electron systems in silicon lead to Pauli spin susceptibility growing critically at low electron densities. This effect originates from renormalization of the effective mass rather than the g-factor. The relative mass enhancement is system and disorder independent, which suggests that it is determined by electron–electron interactions only.

Strongly enhanced effective mass in dilute two-dimensional electron systems: System-independent origin

We measure the effective mass in a dilute two-dimensional electron system in (111) silicon by analyzing the temperature dependence of the Shubnikov--de Haas oscillations in the low-temperature limit. A strong enhancement of the effective mass with decreasing electron density is observed. The mass renormalization as a function of the interaction parameter ${r}_{s}$ is in good agreement with that reported for (100) silicon, which shows that the relative mass enhancement is system and disorder independent, being determined by electron-electron interactions only.

Charged Excitons in the Quantum Hall Regime

We review our recent optical experiments on two-dimensional electron systems at temperatures below 1 K and under high magnetic fields. The two-dimensional electron systems are realized in modulation-doped GaAs-AlGaAs single quantum wells. Via gate electrodes the carrier density of the two-dimensional electron systems can be tuned in a quite broad range between about 1×10^{10} cm^{-2} and 2×10^{11} cm^{-2}. In dilute two-dimensional electron systems, at very low electron densities, we observe the formation of negatively charged excitons in photoluminescence experiments. In this contribution we report about the observation of a dark triplet exciton, which is observable at temperatures below 1 K and for electron filling factors <1/3, i.e., in the fractional quantum Hall regime only. In experiments where we have increased the density of the two-dimensional electron systems so that a uniform two-dimensional electron system starts to form, we have found a strong energy anomaly of the charged excitons in the vicinity of filling factor 1/3. This anomaly was found to exist in a very narrow parameter range of the density and temperature, only. We propose a model where we assume that localized charged excitons and a uniform Laughlin liquid coexist. The localized charged exciton in close proximity to the Laughlin liquid leads to the creation of a fractionally-charged quasihole in the liquid, which can account for the experimentally observed anomaly.

Sharply increasing spin susceptibility near the metal–insulator transition in a two-dimensional electron system

Abstract We have measured the effective mass and Lande g factor in very dilute two-dimensional electron systems in silicon and found a sharp increase of the effective mass near the metal–insulator transition, while the g factor remains nearly constant and close to its value in bulk silicon. Using tilted magnetic fields, we have found that the enhanced effective mass is independent of the degree of spin polarization, which points to a spin-independent origin of the mass enhancement and is in contradiction with existing theories.

Sharply increasing effective mass: a precursor of a spontaneous spin polarization in a dilute two-dimensional electron system

We have measured the effective mass, m, and Lande g-factor in very dilute two-dimensional electron systems in silicon. Two independent methods have been used: (i) measurements of the magnetic field required to fully polarize the electrons' spins and (ii) analysis of the Shubnikov-de Haas oscillations. We have observed a sharp increase of the effective mass with decreasing electron density while the g-factor remains nearly constant and close to its value in bulk silicon. The corresponding strong rise of the spin susceptibility may be a precursor of a spontaneous spin polarization; unlike in the Stoner scenario, it originates from the enhancement of the effective mass rather than the increase of g-factor. Furthermore, using tilted magnetic fields, we have found that the enhanced effective mass is independent of the degree of spin polarization and, therefore, its increase is not related to spin exchange effects, in contradiction with existing theories. Our results show that the dilute 2D electron system in silicon behaves well beyond a weakly interacting Fermi liquid.

Spin-independent origin of the strongly enhanced effective mass in a dilute 2D electron system.

We accurately measure the effective mass in a dilute two-dimensional electron system in silicon by analyzing the temperature dependence of the Shubnikov-de Haas oscillations in the low-temperature limit. A sharp increase of the effective mass with decreasing electron density is observed. We find that the enhanced effective mass is independent of the degree of spin polarization, which points to a spin-independent origin of the mass enhancement and is in contradiction with existing theories.

Anomalous dispersion of charged excitons in dilute two-dimensional electron systems at low temperatures

We report the observation of a strong anomaly in the magnetic-field dispersion of negatively charged excitons in dilute two-dimensional electron systems. The anomaly exists in an intermediate density range around $1\ifmmode\times\else\texttimes\fi{}{10}^{11} {\mathrm{cm}}^{\ensuremath{-}2},$ and at temperatures $T&lt;1 \mathrm{K},$ only. The strength of the anomaly at $T=0.1 \mathrm{K}$ is about 2.5 meV, and the most striking feature is that it can be completely destroyed by a small thermal energy of about 0.2 meV (2 K). Furthermore, the anomaly is observed both in photoluminescence and direct absorption measurements, which gives a strong indication that it is of intrinsic origin.

Effects of a Parallel Magnetic Field on the Metal-Insulator Transition in a Dilute Two-Dimensional Electron System

The temperature dependence of conductivity sigma(T) of a two-dimensional electron system in silicon has been studied in parallel magnetic fields B. At B = 0, the system displays a metal-insulator transition at a critical electron density n(c)(0), and dsigma/dT>0 in the metallic phase. At low fields ( B < or approximately equal to 2 T), n(c) increases as n(c)(B)-n(c)(0) proportional, variant Bbeta ( beta approximately 1), and the zero-temperature conductivity scales as sigma(n(s),B,T = 0)/sigma(n(s),0,0) = f(B(beta)/delta(n)), where delta(n) = [n(s)-n(c)(0)]/n(c)(0) and n(s) is electron density, as expected for a quantum phase transition. The metallic phase persists in fields of up to 18 T, consistent with the saturation of n(c) at high fields.

Oscillator strengths of dark charged excitons at low electron filling factors

By direct absorption spectroscopy and comparison to photoluminescence (PL), we investigate negatively charged excitons in dilute two-dimensional electron systems at temperatures down to $T=40 \mathrm{mK}$ in the regime of the fractional quantum Hall effect. At very low temperatures, for filling factor $\ensuremath{\nu}&lt;1/3,$ an additional excitation appears in the PL spectrum, between the well-known singlet and triplet excitons. The observation of a similar excitation by PL was reported very recently [G. Yusa et al., Phys. Rev. Lett. 87, 216402 (2001)], and the excitation was assigned, in spite of the PL intensity similar to that of the neutral exciton, to be due to a dark triplet exciton. By comparing PL and direct absorption spectra in optically thin samples at $T&lt;100 \mathrm{mK},$ we can identify the new excitation indeed as a ``dark'' mode, since we find that the oscillator strength is much smaller than those of the ``bright'' modes.

Effects of a Parallel Magnetic Field on the Metal-Insulator Transition in a Dilute Two-Dimensional Electron System

Effects of a Parallel Magnetic Field on the Metal-Insulator Transition in a Dilute Two-Dimensional Electron System

Plasmon dispersion in dilute two-dimensional electron systems: Quantum-classical and Wigner crystal–electron liquid crossover

We theoretically calculate the finite-wave-vector plasmon dispersion in a low-density two-dimensional (2D) electron layer taking into account finite temperature, finite layer width, and local-field corrections. We compare our theoretical results with recent Raman-scattering spectroscopic experimental 2D plasmon dispersion data in GaAs quantum wells at very low carrier densities ${(r}_{s}&gt;10)$ and large wave vectors $(q&gt;~{k}_{F}).$ We find good agreement with the experimental data, providing an explanation for why the experimentally measured dispersion seems to obey the simple classical long-wavelength 2D plasmon dispersion formula. We also provide a critical discussion on the observable manifestations of the quantum-classical and the Wigner crystal--electron liquid crossover behavior in the 2D plasmon properties as a function of electron density and temperature in GaAs quantum-well systems.

Indication of the ferromagnetic instability in a dilute two-dimensional electron system.

The magnetic field B(c), in which the electrons become fully spin polarized, is found to be proportional to the deviation of the electron density from the zero-field metal-insulator transition in a two-dimensional electron system in silicon. The tendency of B(c) to vanish at a finite electron density suggests a ferromagnetic instability in this strongly correlated electron system.

Hall coefficient of a dilute two-dimensional electron system in a parallel magnetic field

Measurements in magnetic fields applied at a small angle with respect to the 2D plane of the electrons of a low-density silicon MOSFET indicate that the Hall coefficient is independent of parallel field from H=0 to $H>H_{sat}$, the field above which the longitudinal resistance saturates and the electrons have reached full spin-polarization. This implies that the mobilities of the spin-up and spin-down electrons remain comparable at all magnetic fields, and suggests there is strong mixing of spin-up and spin-down electron states.

Metallic behavior and related phenomena in two dimensions

For about twenty years, it has been the prevailing view that there can be no metallic state or metal-insulator transition in two dimensions in zero magnetic field. In the last several years, however, unusual behavior suggestive of such a transition has been reported in a variety of dilute two-dimensional electron and hole systems. The physics behind these observations is presently not understood. We review and discuss the main experimental findings and suggested theoretical models.