2D Hole Density Research Articles

Thermal and Quantum Melting Phase Diagrams for a Magnetic-Field-Induced Wigner Solid.

A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting two-dimensional (2D) system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array in order to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at low temperatures and very small Landau level filling factors (ν≃1/5). In dilute GaAs 2D hole systems, on the other hand, thanks to the larger hole effective mass and the ensuing Landau level mixing, the WS forms at relatively higher fillings (ν≃1/3). Here we report our measurements of the fundamental temperature vs filling phase diagram for the 2D holes' WS-liquid thermal melting. Moreover, via changing the 2D hole density, we also probe their Landau level mixing vs filling WS-liquid quantum melting phase diagram. We find our data to be in good agreement with the results of very recent calculations, although intriguing subtleties remain.

Theory of operating characteristics of a semiconductor quantum well laser: Inclusion of global electroneutrality in the structure

A model for calculating the operating characteristics of semiconductor quantum well (QW) lasers is presented. The model exploits the condition of global electroneutrality, which includes the charge carriers both in the two-dimensional (2D) active region (QW) and bulk waveguide region (optical confinement layer - OCL). The charge of each sign in the OCL is shown to be significantly larger than that in the QW. As a result of this, (i) the global electroneutrality condition reduces to the condition of electroneutrality in the OCL and (ii) the local electroneutrality in the QW can be strongly violated, i.e., the 2D electron and hole densities in the QW can significantly differ from each other.

Magnetotransport study on as-grown and annealed n- and p-type modulation-doped GaInNAs/GaAs strained quantum well structures

We report the observation of thermal annealing- and nitrogen-induced effects on electronic transport properties of as-grown and annealed n- and p-type modulation-doped Ga1 - xInxNyAs1 - y (x = 0.32, y = 0, 0.009, and 0.012) strained quantum well (QW) structures using magnetotransport measurements. Strong and well-resolved Shubnikov de Haas (SdH) oscillations are observed at magnetic fields as low as 3 T and persist to temperatures as high as 20 K, which are used to determine effective mass, 2D carrier density, and Fermi energy. The analysis of temperature dependence of SdH oscillations revealed that the electron mass enhances with increasing nitrogen content. Furthermore, even the current theory of dilute nitrides does not predict a change in hole effective mass; nitrogen dependency of hole effective mass is found and attributed to both strain- and confinement-induced effects on the valence band. Both electron and hole effective masses are changed after thermal annealing process. Although all samples were doped with the same density, the presence of nitrogen in n-type material gives rise to an enhancement in the 2D electron density compared to the 2D hole density as a result of enhanced effective mass due to the effect of nitrogen on conduction band. Our results reveal that effective mass and 2D carrier density can be tailored by nitrogen composition and thermal annealing-induced effects.PACS72.00.00; 72.15.Gd; 72.80.Ey

Connecting the Reentrant Insulating Phase and the Zero-Field Metal-Insulator Transition in a 2D Hole System

We present the transport and capacitance measurements of 10 nm wide GaAs quantum wells with hole densities around the critical point of the 2D metal-insulator transition (critical density p(c) down to 0.8 × 10(10)/cm2, r(s) ∼ 36). For metallic hole density p(c) < p < p(c) + 0.15 × 10(10)/cm2, a reentrant insulating phase (RIP) is observed between the ν = 1 quantum Hall state and the zero-field metallic state and it is attributed to the formation of pinned Wigner crystal. Through studying the evolution of the RIP versus 2D hole density, we show that the RIP is incompressible and continuously connected to the zero-field insulator, suggesting a similar origin for these two phases.

Hole-density dependence of the cyclotron mass of 2D holes in a GaAs(001) quantum well

The dependence of the heavy-hole cyclotron mass in GaAs(001) quantum wells on the 2D-hole density has been measured by the optical detection method for resonance microwave by-absorption. A significant increase (almost doubling) has been observed in the cyclotron mass of heavy holes with an increase in the charge carrier density from 1.2 × 1010 cm−2 to 1.3 × 1011 cm−2.

Hole subbands and Landau levels in p-type single Al xGa 1− xAs/GaAs heterostructures

We studied the energy band structure of two-dimensional holes in p-type single Al x Ga 1− x As/GaAs heterojunctions under a strong magnetic field up to 14 T . The electric field present in investigated structures near the interfaces produces a mixing of heavy and light hole states. This results in a strong nonparabolicity and anisotropy of energy levels and their non-linear behavior under an external magnetic field. We calculated energies and wave functions of hole subbands as a function of magnetic field in a Faraday configuration employing a realistic model of potential distribution and using new numerical method described in Kubisa et al., Phys. Rev. B 67 (2003) 035305. The theoretical results were compared with results of low-temperature photoluminescence measurements for samples with different 2D hole densities and a very good agreement was obtained.

Confinement symmetry, mobility anisotropy, and metallic behavior in(311)AGaAs two-dimensional holes

We study two dimensional hole systems confined to GaAs quantum wells grown on the (311)A surface of GaAs substrates. Such samples exhibit an in-plane mobility anisotropy. At constant 2D hole density, we vary the symmetry of the quantum well potential and measure the temperature dependence of the resistivity along two different current directions, in a regime where the samples exhibit metallic behavior. The symmetry has a significant and non-trivial effect on the metallic behavior. Moreover, differences between the temperature-dependence of the resistivity along the two mobility directions point to specific scattering mechanisms being important in the expression of the metallic behavior.

Spin-splitting in GaAs two-dimensional holes

We present quantitative measurements and calculations of the spin-orbit-induced zero-magnetic-field spin splitting in two-dimensional (2D) hole systems in modulation-doped GaAs (3 1 1) A quantum wells. The results show that the splitting is large and tunable. In particular, via a combination of back- and front-gate biases, we can tune the splitting while keeping the 2D hole density constant. The data also reveal a surprising result regarding the magnetoresistance (Shubnikov–de Haas) oscillations in a 2D system with spin-split energy bands: the frequencies of the oscillations are not simply related to the population of the spin-subbands. Next we concentrate on the metallic-like behavior observed in these 2D holes and its relation to spin-splitting. The data indicate that the metallic behavior is more pronounced when two spin-subbands with unequal populations are occupied. Our measurements of the magnetoresistance of these 2D hole systems with an in-plane magnetic field corroborate this conclusion: while the system is metallic at zero magnetic field, it turns insulating when one of the spin subbands is depopulated at high magnetic field.

Rashba spin splitting in two-dimensional electron and hole systems

In two-dimensional (2D) hole systems the inversion asymmetry induced spin splitting differs remarkably from its familiar counterpart in the conduction band. While the so-called Rashba spin splitting of electron states increases linearly with in-plane wave vector k_|| the spin splitting of heavy hole states can be of third order in k_|| so that spin splitting becomes negligible in the limit of small 2D hole densities. We discuss consequences of this behavior in the context of recent arguments on the origin of the metal-insulator transition observed in 2D systems.

Nonmonotonic Temperature-Dependent Resistance in Low Density 2D Hole Gases

The low temperature longitudinal resistance-per-square Rxx(T) in ungated GaAs/AlGaAs quantum wells of high peak hole mobility 1.7x10^6 cm^2/Vs is metallic for 2D hole density p as low as 3.8x10^9 cm-2. The electronic contribution to the resistance, R_{el}(T), is a nonmonotonic function of T, exhibiting thermal activation, R_{el}(T) ~ exp{-E_a/kT}, for kT<<E_F and a heretofore unnoted decay R_{el}(T) ~ 1/T for k_T>EF. The form of R_{el}(T) is independent of density, indicating a fundamental relationship between the low and high T scattering mechanisms in the metallic state.

Exciton-assisted tunneling transport in heterojunction microstructures

Longitudinal tunneling transport in the low-dimensional heterojunction structures induced by the excitonic Coulomb interaction has been formulated and discussed in the framework of Fermi's golden rule. We have investigated the tunneling transition of free carriers to quantum-well Wannier–Mott excitons incorporated in the sequential tunneling Hamiltonian. The modeling is evaluated by a set of coupled rate equations involving subband states of electron, hole and exciton. The exciton-assisted tunneling (EAT) phenomenon has its characteristic fingerprint causing tunneling current prior to the resonance electric fields, and a significant modulation of the I–V characteristics. It is also found that the bias offset and the FWHM of the EAT current spectrum can be comparable to that of resonant tunneling (RT) current, depending both on the 2D hole density of the confined subband and the excitonic properties in the active region. The EAT effect has a different I–V spectral line shape, compared to that of the RT or its replica, tailing off in the resonance regime induced by the exciton binding energy.

Cyclotron mass of two-dimensional holes in strained-layer GaAs/In0.20Ga0.80As/GaAs quantum well structures

We report a systematic study of the effective mass of two-dimensional (2D) holes in a series of ten p-type GaAs/In0.20Ga0.80As/GaAs quantum well structure samples. The 2D hole density and its effective mass (m*)are independently determined from Shubnikov–de Haas and cyclotron resonance measurements at 4.2 K. We find the m* increases from (0.123±0.005) me to (0.191±0.015) me as the 2D hole density is varied from 0.54×1011/cm2to 8.5×1011/cm2. The experimental data are described quantitatively in terms of a two-band tight binding model using the valence band edge mass and strain-induced valence band splitting as parameters.

Electronic Raman scattering in p-doped GaAs/Ga1-xAlxAs quantum-well structures: Scattering mechanisms and many-particle interactions.

By means of resonance Raman spectroscopy we have investigated intersubband transitions of quasi-two-dimensional (2D) hole gases in p-type modulation-doped GaAs/${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum-well structures. The observed excitations have an essentially single-particle character due to Landau damping of collective excitations and due to single-particle scattering by energy-density fluctuations under conditions of extreme resonance. In samples with well widths of typically 100\char21{}200 \AA{} and 2D hole densities \ensuremath{\rho}\ensuremath{\sim}${10}^{11}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, we observe a characteristic variation of intersubband-transition energies with laser frequency in depolarized and in polarized scattering configurations. This variation is caused by the nonparabolic subband dispersion of the 2D single-particle hole subbands. Experiments under variation of p, by illuminating the sample with photons that have energies above the band gap of the ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As barriers, allow an estimate of the relative strengths of direct and exchange Coulomb interactions. From these experiments a greater relative strength of the exchange interaction, in comparison to that found for 2D electron gases, can be deduced.

Cyclotron resonance of high-mobility GaAs/AlGaAs (311) 2DHGs

Cyclotron resonance of high-mobility (up to 300000 cm2 V-1 s-1 at 100 mK) GaAs/AlGaAs two-dimensional hole gases (2DHGs) grown on (311)A oriented substrates has been measured in magnetic fields up to 17 T and at temperatures down to 350 mK. The 2D hole density is in the range (1.0-2.0)*1011 cm-2. Two resonances are in general observed; at low magnetic fields the lower-field resonance dominates but a progressive transfer of oscillator strength takes place as the field increases. A self-consistent calculation of the Landau fan diagram for the higher-symmetry (100) direction is used to interpret the data and identify the observed transitions.

Cyclotron resonance studies of two-dimensional holes in strained Si1−xGex/Si quantum wells

Far-infrared magnetotransmission spectroscopy has been employed to study p-type modulation-doped strained Si1−xGex/Si quantum wells grown by atmospheric pressure chemical vapor deposition at magnetic fields up to 23 T. The cyclotron resonance (CR) mass of the two-dimensional hole gas (2DHG) in a strained 7.5 nm Si0.63Ge0.37 quantum well was determined to be (0.29±0.02)m0 for a 2D hole density of 2.3×1012/cm2 at 3 K. The CR mass of 2DHGs in strained Si1−xGex is comparable to previous measurements of the CR mass of 2DHGs in strained InyGa1−yAs with similar 2D hole densities.

Cyclotron resonance of two-dimensional holes in strained-layer quantum well structure of (100)In0.20Ga0.80As/GaAs

Cyclotron resonance of the two-dimensional hole gas (2DHG) in the strained-layer quantum well structure of In0.20Ga0.80As/GaAs is observed in far-infrared transmission measurements made at 4.2 K. The cyclotron mass of the 2DHG in the In0.20Ga0.80As channel is (0.191±0.008)me for a 2D hole density p2D =8.5×1011/cm2.