Two-dimensional Electron Layers Research Articles

Bilayer WSe2 as a natural platform for interlayer exciton condensates in the strong coupling limit.

Exciton condensates (ECs) are macroscopic coherent states arising from condensation of electron-hole pairs1. Bilayer heterostructures, consisting of two-dimensional electron and hole layers separated by a tunnel barrier, provide a versatile platform to realize and study ECs2-4. The tunnel barrier suppresses recombination, yielding long-lived excitons5-10. However, this separation also reduces interlayer Coulomb interactions, limiting the exciton binding strength. Here, we report the observation of ECs in naturally occurring 2H-stacked bilayer WSe2. In this system, the intrinsic spin-valley structure suppresses interlayer tunnelling even when the separation is reduced to the atomic limit, providing access to a previously unattainable regime of strong interlayer coupling. Using capacitance spectroscopy, we investigate magneto-ECs, formed when partially filled Landau levels couple between the layers. We find that the strong-coupling ECs show dramatically different behaviour compared with previous reports, including an unanticipated variation of EC robustness with the orbital number, and find evidence for a transition between two types of low-energy charged excitations. Our results provide a demonstration of tuning EC properties by varying the constituent single-particle wavefunctions.

Critical filling factor for the formation of a quantum Wigner crystal screened by a nearby layer

One of the most fascinating ground states of an interacting electron system is the so-called Wigner crystal where the electrons, in order to minimize their repulsive Coulomb energy, form an ordered array. Here we report measurements of the critical filling factor ($\nu_{C}$) below which a magnetic-field-induced, quantum Wigner crystal forms in a dilute, two-dimensional electron layer when a second, high-density electron layer is present in close proximity. The data reveal that the Wigner crystal forms at a significantly smaller $\nu_{C}$ compared to the $\nu_{C}$ ($\simeq 0.20$) in single-layer two-dimensional electron systems. The measured $\nu_{C}$ exhibits a strong dependence on the interlayer distance, reflecting the interaction and screening from the adjacent, high-density layer.

Double thermoelectric power factor of a 2D electron system

Two-dimensional electron systems have attracted attention as thermoelectric materials, which can directly convert waste heat into electricity. It has been theoretically predicted that thermoelectric power factor can be largely enhanced when the two-dimensional electron layer is far narrower than the de Broglie wavelength. Although many studies have been made, the effectiveness has not been experimentally clarified thus far. Here we experimentally clarify that an enhanced two-dimensionality is efficient to enhance thermoelectric power factor. We fabricated superlattices of [N unit cell SrTi1−xNbxO3|11 unit cell SrTiO3]10—there are two different de Broglie wavelength in the SrTi1−xNbxO3 system. The maximum power factor of the superlattice composed of the longer de Broglie wavelength SrTi1−xNbxO3 exceeded ∼5 mW m−1 K−2, which doubles the value of optimized bulk SrTi1−xNbxO3. The present approach—use of longer de Broglie wavelength—is epoch-making and is fruitful to design good thermoelectric materials showing high power factor.

Terahertz spectroscopy of an electron-hole bilayer system in AlN/GaN/AlN quantum wells

We report studies on the nanoscale transport dynamics of carriers in strained AlN/GaN/AlN quantum wells: an electron-hole bilayer charge system with a large difference in transport properties between charge layers. From electronic band diagram analysis, the presence of spatially separated two-dimensional electron and hole charge layers is predicted at opposite interfaces. Since these charge layers exhibit distinct spectral signatures at terahertz frequencies, a combination of terahertz and far-infrared spectroscopy enables us to extract (a) individual contributions to the total conductivity and (b) effective scattering rates for charge-carriers in each layer. Furthermore, by comparing direct-current and THz-extracted conductivity levels, we are able to determine the extent to which structural defects affect charge transport. Our results evidence that (i) a non-unity Hall-factor and (ii) the considerable contribution of holes to the overall conductivity lead to a lower apparent mobility in Hall-effect measurements. Overall, our work demonstrates that terahertz spectroscopy is a suitable technique for studying bilayer charge systems with large differences in transport properties between layers such as quantum wells in III-nitride semiconductors.

From coupled Rashba electron- and hole-gas layers to three-dimensional topological insulators

We introduce a system of stacked two-dimensional electron and hole gas layers with Rashba spin orbit interaction and show that the tunnel coupling between the layers induces a strong three- dimensional (3D) topological insulator phase. At each of the two-dimensional bulk boundaries we find the spectrum consisting of a single anistropic Dirac cone, which we show by analytical and numerical calculations. Our setup has a unit-cell consisting of four tunnel coupled Rashba layers and presents a synthetic strong 3D topological insulator and is distinguished by its rather high experimental feasibility.

Quantum Hall effect in a system with an electron reservoir

Precise measurements of the magnetic-field and gate-voltage dependences of the capacitance of a field-effect transistor with an electron system in a wide GaAs quantum well have been carried out. It has been found that the capacitance minima caused by the gaps in the Landau spectrum of the electron system become anomalously wide when two size-quantization subbands are occupied. The effect is explained by retention of the chemical potential in the gap between the Landau levels of one of the subbands owing to redistribution of electrons between the subbands under a change in the magnetic field. The calculation taking into account this redistribution has been performed in a model of the electron system formed by two two-dimensional electron layers. The calculation results describe both the wide capacitance features and the observed disappearance of certain quantum Hall effect states.

Conduction-electron spin resonance in two-dimensional structures

The influence of the conduction-electron spin magnetization density, induced in a two-dimensional electron layer by a microwave electromagnetic field, on the reflection and transmission of the field is considered. Because of the induced magnetization and electric current, both the electric and magnetic components of the field should have jumps on the layer. A way to match the waves on two sides of the layer, valid when the quasi-two-dimensional electron gas is in the one-mode state, is proposed. By following this way, the amplitudes of transmitted and reflected waves as well as the absorption coefficient are evaluated.

Circularly polarized near-field optical mapping of spin-resolved quantum Hall chiral edge states.

We have successfully developed a circularly polarized near-field scanning optical microscope (NSOM) that enables us to irradiate circularly polarized light with spatial resolution below the diffraction limit. As a demonstration, we perform real-space mapping of the quantum Hall chiral edge states near the edge of a Hall-bar structure by injecting spin polarized electrons optically at low temperature. The obtained real-space mappings show that spin-polarized electrons are injected optically to the two-dimensional electron layer. Our general method to locally inject spins using a circularly polarized NSOM should be broadly applicable to characterize a variety of nanomaterials and nanostructures.

Spontaneous breaking of time-reversal symmetry in strongly interacting two-dimensional electron layers in silicon and germanium.

We report experimental evidence of a remarkable spontaneous time-reversal symmetry breaking in two-dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P delta layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, providing a microscopic mechanism for spontaneous lifting of the time-reversal symmetry. Our experiments suggest the emergence of a new many-body quantum state when two-dimensional electrons are confined to narrow half-filled impurity bands.

Scanning SQUID susceptometry of a paramagnetic superconductor

Scanning SQUID susceptometry images the local magnetization and susceptibility of a sample. By accurately modeling the SQUID signal we can determine physical properties such as the penetration depth and permeability of superconducting samples. We calculate the scanning SQUID susceptometry signal for a superconducting slab of arbitrary thickness with isotropic London penetration depth $\ensuremath{\lambda}$ on a nonsuperconducting substrate, where both slab and substrate can have a paramagnetic response that is linear in the applied field. We derive analytical approximations to our general expression in a number of limits. Using our results, we fit experimental susceptibility data as a function of the sample-sensor spacing for three samples: (1) $\ensuremath{\delta}$-doped SrTiO${}_{3}$, which has a predominantly diamagnetic response, (2) a thin film of LaNiO${}_{3}$, which has a predominantly paramagnetic response, and (3) the two-dimensional electron layer at a SrTiO${}_{3}$/LaAlO${}_{3}$ interface, which exhibits both types of response. These formulas will allow the determination of the concentrations of paramagnetic spins and superconducting carriers from fits to scanning SQUID susceptibility measurements.

Influence of surface treatment and interface layers on electrical spin injection efficiency and transport in InAs

Spin-valve, weak localization/antilocalization, and scanned probe microscopy measurements are used to investigate the influence of sulfur-based surface treatments and electrically insulating barrier layers on spin injection into, and spin transport within, the two-dimensional electron layer at the surface of p-type InAs at 4.2 K. An electrically insulating barrier layer is found to be required to achieve nonzero spin injection efficiency, with a 3 nm Al2O3 electrically insulating barrier providing a spin injection efficiency of 5±2%. Conductive atomic force microscopy suggests that localized leakage through the InAs native oxide is sufficient to suppress spin-polarized current injection in the absence of a more highly insulating barrier layer. Spin scattering lengths are determined experimentally from both weak localization/antilocalization and spin-valve measurements. Spin and elastic scattering lengths of 230±20 and 85±5 nm, respectively, are measured, with a sulfur-based surface treatment increasing the spin scattering length to 250±20 nm and decreasing the elastic scattering length to 65±5 nm.

Thermoelectric Properties of SrTiO3: Bulks, Superlattices, and Transistors

Here I review the thermoelectric properties of electron doped SrTiO3. Since density of states effective mass of electron carrier in SrTiO3 crystal is rather large, heavily electron doped SrTiO3 crystal exhibits rather large Seebeck coefficient (S). The reliable thermoelectric figure of merit, ZT is ∼0.08 at room temperature and ∼0.3 at 1,000 K, which is highest among metallic oxides. Recently, we found that high-density (∼1021 cm-3) two-dimensional (2D) electron layers in SrTiO3 crystal exhibits giant S, which is ∼5 times larger than that of simple bulk, when the layer thickness is as thin as one unit cell (0.3905 nm). The 2D electron layer is realized by superlattices of SrTiO3/SrTi0.8Nb0.2O3 or TiO2/SrTiO3 heterointerface. Very recently, we fabricated high performance field effect transistors (FETs) on SrTiO3 single crystal to modulate the Seebeck coefficient by applying the gate voltage.

Spin-dependent tunneling conductance in two-dimensional structures at zero magnetic field

The influence of the spin-orbit interaction on the tunneling between two-dimensional electron layers is considered. A general expression for the tunneling current is obtained with the Rashba and Dresselhaus effects and also elastic scattering of charge carriers on impurities taken into account. It is shown that the particular form of the tunneling conductance as a function of the voltage between layers is extremely sensitive to the relationship between the Rashba and Dresselhaus parameters. This makes it possible to determine the parameters of the spin-orbit interaction and the quantum scattering time directly from measurements of the tunneling conductance in the absence of magnetic field.

Low-field quantum Hall transport in an electron Fabry-Perot interferometer: Dependence of constriction filling on front-gate voltage

We report systematic quantum Hall transport experiments on Fabry-Perot electron interferometers at ultralow temperatures. The GaAs/AlGaAs heterostructure devices consist of two constrictions defined by etch trenches in the two-dimensional electron layer, enclosing an approximately circular island. Front gates deposited in etch trenches allow one to change the constriction filling, relative to the bulk. A systematic variation of the front-gate voltage affects the constriction and the island electron density, while the bulk density remains unaffected. This results in quantized plateaus in longitudinal resistance, while the Hall resistance is dominated by the low-density, low-filling constriction. At lower fields, when the quantum Hall plateaus fail to develop, we observe bulk Shubnikov-de Haas oscillations in series corresponding to an integer filling of the magnetoelectric subbands in the constrictions. This shows that the whole interferometer region is still quantum coherent at these lower fields at 10 mK. Analyzing the data within a Fock-Darwin model, we obtain the constriction electron density as a function of the front-gate bias and, extrapolating to the zero field, the number of electric subbands (conductance channels) resulting from the electron confinement in the constrictions.

Negative Interlayer Magnetoresistance and Zero-Mode Landau Level in Multilayer Dirac Electron Systems

The interlayer magnetotransport has been considered in multilayer Dirac electron systems, in which two-dimensional electron layers with Dirac-cone dispersion stack with weak interlayer coupling. Under magnetic fields, one Landau level (zero-mode) always appears at the contact point of Dirac cones, and tunneling between the zero-modes on neighboring layers dominates interlayer transport in multilayer systems. The increase of zero-mode degeneracy causes strong negative magnetoresistance. Spin splitting of the zero-mode could change the negative magnetoresistance to the positive one in high magnetic fields and low temperatures. The magnetotransport features observed in an organic conductor α-(BEDT-TTF) 2 I 3 are discussed based on the present model.

Approaching ballistic transport in suspended graphene

The discovery of graphene raises the prospect of a new class of nanoelectronic devices based on the extraordinary physical properties of this one-atom-thick layer of carbon. Unlike two-dimensional electron layers in semiconductors, where the charge carriers become immobile at low densities, the carrier mobility in graphene can remain high, even when their density vanishes at the Dirac point. However, when the graphene sample is supported on an insulating substrate, potential fluctuations induce charge puddles that obscure the Dirac point physics. Here we show that the fluctuations are significantly reduced in suspended graphene samples and we report low-temperature mobility approaching 200,000 cm2 V-1 s-1 for carrier densities below 5 x 109 cm-2. Such values cannot be attained in semiconductors or non-suspended graphene. Moreover, unlike graphene samples supported by a substrate, the conductivity of suspended graphene at the Dirac point is strongly dependent on temperature and approaches ballistic values at liquid helium temperatures. At higher temperatures, above 100 K, we observe the onset of thermally induced long-range scattering.

Manifestation of spin-orbit interaction in tunneling between two-dimensional electron layers

An influence of spin-orbit interaction on the tunneling between two two-dimensional electron layers is considered. Particular attention is addressed to the relation between the contribution of Rashba and Dresselhaus types. It is shown that without scattering of the electrons, the tunneling conductance can either exhibit resonances at certain voltage values or be substantially suppressed over the whole voltage range. The dependence of the conductance on voltage turns out to be very sensitive to the relation between Rashba and Dresselhaus contributions even in the absence of magnetic field. The elastic scattering broadens the resonances in the first case and restores the conductance to a larger magnitude in the latter one. These effects open the possibility to determine the parameters of spin-orbit interaction and electron scattering time in tunneling experiments with no necessity of external magnetic field.

Current instability and single-mode THz generation in ungated two-dimensional electron gas

We analyze the current instability of the steady state with a direct current for an ungated two-dimensional(2D) electron layer for arbitrary current and the carrier scattering strength. We demonstrate the possibility of single-mode generator operating in terahertz frequency range.

Quantum transport in electron Fabry-Perot interferometers

We report experiments on Fabry-Perot electron interferometers in the integer quantum Hall regime. The $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ heterostructure devices consist of two constrictions defined by etch trenches in two-dimensional electron layer, enclosing an approximately circular island. The interferometer is formed by counterpropagating chiral edge channels coupled by tunneling in the two constrictions. Interference fringes are observed as conductance oscillations, similar to the Aharonov-Bohm effect. Front gates deposited in etch trenches allow us to fine tune the device and to change the constriction filling $f$ relative to the bulk filling. Quantum-coherent conductance oscillations are observed on the $f=1--4$ plateaus. On plateau $f$, we observe $f$ conductance oscillations per fundamental flux period $h∕e$. This is attributed to the dominance of the electron-electron Coulomb interaction, effectively mixing Landau level occupation. On the other hand, the back-gate charge period is the same (one electron) on all plateaus, independent of filling. This is attributed to the self-consistent electrostatics in the large electron island. We also report dependence of the oscillation period on front-gate voltage for $f=1$, 2, and 4 for three devices. We find a linear dependence, with the slope inversely proportional to $f$ for $f=1$ and 2.

Pronounced metal–insulator transition according to dipole trap model for two-dimensional Si-MOS structures

Originally the dipole trap scattering model was treated with several approximations and limitations in order to obtain an analytical solution for the temperature and density dependence of the resistivity of high-mobility Si-MOS structures. In contrast, we perform numerical calculations within this model and are thus able to drop several of the earlier restrictions. We include the charge of the trap states in the effective potential run between the metallic gate and the two-dimensional electron layer. In addition, a spatial distribution of the trap density and an energetic broadening of the trap states is taken into account in our calculations. We are thus able to get a distinct metal-to-insulator transition within the dipole trap model for realistic assumptions.