Two-dimensional Hole Systems Research Articles

Hot luminescence of two-dimensional electron hole systems in modulation-doped silicon

Modulation doping of silicon has great potential for miniaturization, surface passivation, and third generation photovoltaics (PV). At a modulation-doped silicon surface, we observe the formation of a 2D hole layer at the silicon surface at low temperatures by means of photoluminescence (PL) measurements. A line shape analysis of band–band and hot luminescence reveals the hole density (which is equal to the modulation-doped acceptor density). A high excitation intensity leads to a Fermi edge singularity of the band–band and hot PL emission. While the 2D layer can be characterized by the observed luminescence, the spectral region of twice the bandgap is fully dominated by emission from this surface layer, impeding the measurement of bulk hot luminescence, e.g., from Auger electrons or from nonthermalized carriers in a hot carrier PV device.

Fractional Quantum Hall State at Filling Factor ν=1/4 in Ultra-High-Quality GaAs Two-Dimensional Hole Systems.

Single-component fractional quantum Hall states (FQHSs) at even-denominator filling factors may host non-Abelian quasiparticles that are considered to be building blocks of topological quantum computers. Such states, however, are rarely observed in the lowest-energy Landau level, namely at filling factors ν<1. Here, we report evidence for an even-denominator FQHS at ν=1/4 in ultra-high-quality two-dimensional hole systems confined to modulation-doped GaAs quantum wells. We observe a deep minimum in the longitudinal resistance at ν=1/4, superimposed on a highly insulating background, suggesting a close competition between the ν=1/4 FQHS and the magnetic-field-induced, pinned Wigner solid states. Our experimental observations are consistent with the very recent theoretical calculations that predict that substantial Landau level mixing, caused by the large hole effective mass, can induce composite fermion pairing and lead to a non-Abelian FQHS at ν=1/4. Our results demonstrate that Landau level mixing can provide a very potent means for tuning the interaction between composite fermions and creating new non-Abelian FQHSs.

Highly Anisotropic Even-Denominator Fractional Quantum Hall State in an Orbitally Coupled Half-Filled Landau Level.

The even-denominator fractional quantum Hall states (FQHSs) in half-filled Landau levels are generally believed to host non-Abelian quasiparticles and be of potential use in topological quantum computing. Of particular interest is the competition and interplay between the even-denominator FQHSs and other ground states, such as anisotropic phases and composite fermion Fermi seas. Here, we report the observation of an even-denominator fractional quantum Hall state with highly anisotropic in-plane transport coefficients at Landau level filling factor ν=3/2. We observe this state in an ultra-high-quality GaAs two-dimensional hole system when a large in-plane magnetic field is applied. By increasing the in-plane field, we observe a sharp transition from an isotropic composite fermion Fermi sea to an anisotropic even-denominator FQHS. Our data and calculations suggest that a unique feature of two-dimensional holes, namely the coupling between heavy-hole and light-hole states, combines different orbital components in the wave function of one Landau level, and leads to the emergence of a highly anisotropic even-denominator fractional quantum Hall state. Our results demonstrate that the GaAs two-dimensional hole system is a unique platform for the exploration of exotic, many-body ground states.

Anomalous High-Temperature Magnetoresistance in a Dilute 2D Hole System.

We report an unusual magnetoresistance that strengthens with the temperature in a dilute two-dimensional (2D) hole system in GaAs/AlGaAs quantum wells with densities p=1.98-0.99×10^{10}/cm^{2} where r_{s}, the ratio between Coulomb energy and Fermi energy, is as large as 20-30. We show that, while the system exhibits a negative parabolic magnetoresistance at low temperatures (≲0.4 K) characteristic of an interacting Fermi liquid, a positive magnetoresistance emerges unexpectedly at higher temperatures, and grows with increasing temperature even in the regime T∼E_{F}, close to the Fermi energy. This unusual positive magnetoresistance at high temperatures can be attributed to the viscous transport of 2D hole fluid in the hydrodynamic regime where holes scatter frequently with each other. These findings give insight into the collective transport of strongly interacting carriers in the r_{s}≫1 regime and new routes toward magnetoresistance at high temperatures.

Gate-defined two-dimensional hole and electron systems in an undoped InSb quantum well

Quantum transport measurements are performed in gate-defined, high-quality, two-dimensional hole and electron systems in an undoped InSb quantum well. For both polarities, the carrier systems show tunable spin-orbit interaction as extracted from weak antilocalization measurements. The effective mass of InSb holes strongly increases with carrier density as determined from the temperature dependence of Shubnikov--de Haas oscillations. Coincidence measurements in a tilted magnetic field are performed to estimate the spin susceptibility of the InSb two-dimensional hole system. The $g$ factor of the two-dimensional hole system decreases rapidly with increasing carrier density.

Coexistence of two hole phases in high-quality p−GaAs/AlGaAs in the vicinity of Landau-level filling factors ν=1 and ν=(1/3)

We focused on the transverse AC magnetoconductance of a high-mobility $p$-GaAs/AlGaAs quantum well $(p=1.2\ifmmode\times\else\texttimes\fi{}{10}^{11}{\mathrm{cm}}^{\ensuremath{-}2})$ in the vicinity of two values of the Landau-level filling factor $\ensuremath{\nu}$: $\ensuremath{\nu}=1$ (integer quantum Hall effect) and $\ensuremath{\nu}=1/3$ (fractional quantum Hall effect). The complex transverse AC conductance ${\ensuremath{\sigma}}_{xx}^{\mathrm{AC}}(\ensuremath{\omega})$ was found from simultaneous measurements of attenuation and velocity of surface acoustic waves propagating along the interface between a piezoelectric crystal and the two-dimensional hole system under investigation. We analyzed both the real and imaginary parts of the hole conductance and compared the similarities and differences between the results for filling factor 1 and filling factor 1/3. Both to the left and to the right of these values maxima of a specific shape, ``wings,'' arose in the $\ensuremath{\sigma}(\ensuremath{\nu})$ dependences at those two $\ensuremath{\nu}$. Analysis of the results of our acoustic measurements at different temperatures and surface acoustic wave frequencies allowed us to attribute these wings to the formation of collective localized states, namely, the domains of a pinned Wigner crystal, i.e., a Wigner solid. While the Wigner solid has been observed in 2D hole systems previously, we were able to detect it at the highest hole density and, therefore, the lowest hole-hole interaction reported.

Spin polarization and spin-dependent scattering of holes observed in transverse magnetic focusing

In two-dimensional hole systems, the Rashba spin-orbit interaction leads to a spin dependent momentum. A perpendicular magnetic field spatially separates holes with different spins, creating a mass spectrometer for spin. Spin-resolved magnetic focussing has been used to measure spin polarization from the amplitude of magnetic focussing peaks. In this work, the authors show that the ${k}^{3}$ form of the Rashba spin-orbit interaction term for semiconductor holes changes the scattering rate, which has an exponential effect on the focussing peak amplitude. This result further demonstrates the impact of the Rashba spin-orbit interaction in the field of semiconductor hole spin physics.

Robust Quantum Hall Ferromagnetism near a Gate-Tuned ν=1 Landau Level Crossing.

In a low-disorder two-dimensional electron system, when two Landau levels of opposite spin or pseudospin cross at the Fermi level, the dominance of the exchange energy can lead to a ferromagnetic, quantum Hall ground state whose gap is determined by the exchange energy and has skyrmions as its excitations. This is normally achieved via applying either hydrostatic pressure or uniaxial strain. We study here a very high-quality, low-density, two-dimensional hole system, confined to a 30-nm-wide (001) GaAs quantum well, in which the two lowest-energy Landau levels can be gate tuned to cross at and near filling factor ν=1. As we tune the field position of the crossing from one side of ν=1 to the other by changing the hole density, the energy gap for the quantum Hall state at ν=1 remains exceptionally large, and only shows a small dip near the crossing. The gap overall follows a sqrt[B] dependence, expected for the exchange energy. Our data are consistent with a robust quantum Hall ferromagnet as the ground state.

Record-quality GaAs two-dimensional hole systems

The complex band structure, large spin-orbit induced band splitting, and heavy effective mass of two-dimensional (2D) hole systems hosted in GaAs quantum wells render them rich platforms to study many-body physics and ballistic transport phenomena. Here we report ultra-high-quality (001) GaAs 2D hole systems, fabricated using molecular beam epitaxy and modulation doping, with mobility values as high as $5.8\times10^6$ cm$^2$/Vs at a hole density of $p=1.3\times10^{11}$ /cm$^2$, implying a mean-free path of $\simeq27$ $\mu$m. In the low-temperature magnetoresistance trace of this sample, we observe high-order fractional quantum Hall states up to the Landau level filling $\nu=12/25$ near $\nu=1/2$. Furthermore, we see a deep minimum develop at $\nu=1/5$ in the magnetoresistance of a sample with a much lower hole density of $p=4.0\times10^{10}$ /cm$^2$ where we measure a mobility of $3.6\times10^6$ cm$^2$/Vs. These improvements in sample quality were achieved by reduction of residual impurities both in the GaAs channel and the AlGaAs barrier material, as well as optimization in design of the sample structure.

Exciton–polarons in two-dimensional semiconductors and the Tavis–Cummings model

The elementary optical excitations of a two-dimensional electron or hole system have been identified as exciton-Fermi-polarons. Nevertheless, the connection between the bound state of an exciton and an electron, termed trion, and exciton–polarons is subject of ongoing debate. Here, we use an analogy to the Tavis–Cummings model of quantum optics to show that an exciton–polaron can be understood as a hybrid quasiparticle—a coherent superposition of a bare exciton in an unperturbed Fermi sea and a bright collective excitation of many trions. The analogy is valid to the extent that the Chevy Ansatz provides a good description of dynamical screening of excitons and provided the Fermi energy is much smaller than the trion binding energy. We anticipate our results to bring new insight that could help to explain the striking differences between absorption and emission spectra of two-dimensional semiconductors.

Metal-insulator transitions in bilayer electron-hole systems in transition metal dichalcogenides

We investigated metal-insulator transitions for double layer two-dimensional electron hole systems in transition metal dicalcogenides (TMDC) stacked on opposite sides of thin layers of boron nitride (BN). The interparticle interaction is calculated by including the screening due to the polarization charges at different interfaces, including that at the encapsultion and the substrate of experimental structures. We compute and compare the energies of the metallic electron-hole plasma and the newly proposed insulating exciton solid with fixed-node diffusion Monte Carlo simulation including the high valley degeneracy of the electron bands. We found that for some examples of current experimental structures, the transition electron/hole density is in an accessible range of g x 10^12 /cm*2 with g between 4.1 and 14.5 for spacer thicknesses between 2.5 and 7.5 nm. Our result raise the possibility of exploiting this effect for logic device applications.

A crossover from Efros–Shklovskii hopping to activated transport in a GaAs two-dimensional hole system at low temperatures

In this paper, we discuss low-temperature hopping-conductivity behavior in the insulating phase, in the absence of a magnetic field. We conduct a theoretical study of the crossover from hopping to activated transport in a GaAs two-dimensional hole system at low temperatures, finding that a crossover takes place from the Efros-Shklovskii variable-range hopping (VRH) regime to an activated regime in this system. This conductivity behavior in p-GaAs quantum wells is qualitatively consistent with the laws laid down in theories of localized electron interactions. Given sufficiently strong interactions, the holes in the localized states are able to hop collectively.

Discontinuity in the transport of strongly correlated two-dimensional hole systems in zero magnetic field

Adopting undoped ultraclean two-dimensional hole systems, we approach a strongly correlated limit by reducing the carrier density down to $1\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. The temperature dependence of the resistivity as a function of the carrier density reveals a characteristic energy scale displaying a benchmark critical behavior near a critical density of ${p}_{c}\ensuremath{\sim}4\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. The insulating state below ${p}_{c}$ exhibits a sharp resistance discontinuity in response to heating across a critical temperature ${T}_{c1}\ensuremath{\sim}30\phantom{\rule{0.16em}{0ex}}\mathrm{mK}$, consistent with a first-order transition. The dc response also identifies a second critical temperature ${T}_{c2}$ where linear IV behavior is recovered. Similar effects are also demonstrated by varying an external electric field. The results support a complex quantum phase transition with intermediate phases.

Thermoelectric transport of the half-filled lowest Landau level in a p -type Ge/SiGe heterostructure

We investigate the thermoelectric transport properties of the half-filled lowest Landau level $v=1/2$ in a gated two-dimensional hole system in a strained Ge/SiGe heterostructure. The electron-diffusion dominated regime is achieved below 600 mK, where the diffusion thermopower ${{S}_{xx}}^{d}$ at $v=1/2$ shows a linear temperature dependence. In contrast, the diffusion-dominated Nernst signal ${{S}_{xy}}^{d}$ of $v=1/2$ is found to approach zero, which is independent of the measurement configuration (sweeping magnetic field at a fixed hole density or sweeping the density by a gate at a fixed magnetic field).

Orientation of hole quantum Hall nematic phases in an out-of-plane electric field

We present observations of an anisotropic resistance state at Landau level filling factor $\nu=5/2$ in a two-dimensional hole system (2DHS), which occurs for certain values of hole density $p$ and average out-of-plane electric field $E_\perp$. The 2DHS is induced by electric field effect in an undoped GaAs/AlGaAs quantum well, where front and back gates allow independent tuning of $p$ and $E_\perp$, and hence the symmetry of the confining potential. For $p\approx2\times10^{11}$~cm$^{-2}$ and $E_\perp \approx -2 \times10^{5}$~V/m, the magnetoresistance along $\langle01\bar1\rangle$ greatly exceeds that along $\langle011\rangle$, suggesting the formation of a quantum Hall nematic or `stripe' phase. Reversing the sign of $E_\perp$ rotates the stripes by $90^{\circ}$. We suggest this behavior may arise from the mixing of the hole Landau levels and a combination of the Rashba and Dresselhaus spin-orbit coupling effects.

Strong Spin-Orbit Contribution to the Hall Coefficient of Two-Dimensional Hole Systems.

Classical charge transport, such as longitudinal and Hall currents in weak magnetic fields, is usually not affected by quantum phenomena. Yet relativistic quantum mechanics is at the heart of the spin-orbit interaction, which has been at the forefront of efforts to realize spin-based electronics, new phases of matter, and topological quantum computing. In this work we demonstrate that quantum spin dynamics induced by the spin-orbit interaction is directly observable in classical charge transport. We determine the Hall coefficient R_{H} of two-dimensional hole systems at low magnetic fields and show that it has a sizable spin-orbit contribution, which depends on the density p, is independent of temperature, is a strong function of the top gate electric field, and can reach ∼20% of the total. We provide a general method for extracting the spin-orbit parameter from magnetotransport data, applicable even at higher temperatures where Shubnikov-de Haas oscillations and weak antilocalization are difficult to observe. Our work will enable experimentalists to measure spin-orbit parameters without requiring large magnetic fields, ultralow temperatures, or optical setups.

Electrical Control of the Zeeman Spin Splitting in Two-Dimensional Hole Systems.

Semiconductor holes with strong spin-orbit coupling allow all-electrical spin control, with broad applications ranging from spintronics to quantum computation. Using a two-dimensional hole system in a gallium arsenide quantum well, we demonstrate a new mechanism of electrically controlling the Zeeman splitting, which is achieved through altering the hole wave vector k. We find a threefold enhancement of the in-plane g-factor g_{∥}(k). We introduce a new method for quantifying the Zeeman splitting from magnetoresistance measurements, since the conventional tilted field approach fails for two-dimensional systems with strong spin-orbit coupling. Finally, we show that the Rashba spin-orbit interaction suppresses the in-plane Zeeman interaction at low magnetic fields. The ability to control the Zeeman splitting with electric fields opens up new possibilities for future quantum spin-based devices, manipulating non-Abelian geometric phases, and realizing Majorana systems in p-type superconductor systems.

Asymmetric g Tensor in Low-Symmetry Two-Dimensional Hole Systems

The complex structure of the valence band in many semiconductors leads to multifaceted and unusual properties for spin-3/2 hole systems compared to typical spin-1/2 electron systems. In particular, two-dimensional hole systems show a highly anisotropic Zeeman spin splitting. We have investigated this anisotropy in GaAs/AlAs quantum well structures both experimentally and theoretically. By performing time-resolved Kerr rotation measurements, we found a non-diagonal tensor $g$ that manifests itself in unusual precessional motion as well as distinct dependencies of hole spin dynamics on the direction of the magnetic field $\vec{B}$. We quantify the individual components of the tensor $g$ for [113]-, [111]- and [110]-grown samples. We complement the experiments by a comprehensive theoretical study of Zeeman splitting in in-plane and out-of-plane fields $\vec{B}$. To this end, we develop a detailed multiband theory for the tensor $g$. Using perturbation theory, we derive transparent analytical expressions for the components of the tensor $g$ that we complement with accurate numerical calculations based on our theoretical framework. We obtain very good agreement between experiment and theory. Our study demonstrates that the tensor $g$ is neither symmetric nor antisymmetric. Opposite off-diagonal components can differ in size by up to an order of magnitude.

Ambipolar quantum transport in few-layer black phosphorus

We have investigated the quantum transport properties of high-mobility electrons and holes in atomically thin black phosphorus ambipolar devices. The two-dimensional hole system exhibits unambiguously the quantum Hall effect in a magnetic field up to 30 T, while the electron system shows clearly developing Hall plateaus at integer Landau level filling factors accompanied by ${R}_{xx}$ oscillations, signaling the onset of the quantum Hall effect. By bringing the spin-resolved Landau levels of the electron system to a coincidence, we determine an electron spin susceptibility to be ${\ensuremath{\chi}}_{se}={m}^{*}{g}^{*}=1.1\ifmmode\pm\else\textpm\fi{}0.03$, which, combined with the electron mass ${m}^{*}=0.39\phantom{\rule{0.16em}{0ex}}{m}_{0}$, yields a Land\'e $g$ factor ${g}^{*}=2.8\ifmmode\pm\else\textpm\fi{}0.2$. The enhancement of spin susceptibility in the black phosphorus two-dimensional electron system is around 50% compared with band susceptibility, which agrees well with various two-dimensional charge-carrier systems with weak spin-orbit coupling, suggesting the important role played by the exchange interaction.

Density-controlled quantum Hall ferromagnetic transition in a two-dimensional hole system

Quantum Hall ferromagnetic transitions are typically achieved by increasing the Zeeman energy through in-situ sample rotation, while transitions in systems with pseudo-spin indices can be induced by gate control. We report here a gate-controlled quantum Hall ferromagnetic transition between two real spin states in a conventional two-dimensional system without any in-plane magnetic field. We show that the ratio of the Zeeman splitting to the cyclotron gap in a Ge two-dimensional hole system increases with decreasing density owing to inter-carrier interactions. Below a critical density of ~2.4 × 1010 cm−2, this ratio grows greater than 1, resulting in a ferromagnetic ground state at filling factor ν = 2. At the critical density, a resistance peak due to the formation of microscopic domains of opposite spin orientations is observed. Such gate-controlled spin-polarizations in the quantum Hall regime opens the door to realizing Majorana modes using two-dimensional systems in conventional, low-spin-orbit-coupling semiconductors.