We study the effects of electrostatic gating on the lateral distribution of charge carriers in two dimensional devices, in a non-linear dielectric environment. We compute the charge distribution using the Thomas-Fermi approximation to model the electrostatics of the system. The electric field lines generated by the gate are focused at the edges of the device, causing an increased depletion near the edges, compared to the center of the device. This effect strongly depends on the dimensions of the device, and the non-linear dielectric constant of the substrate. We experimentally demonstrate this effect using scanning superconducting interference device (SQUID) microscopy images of current distributions in gated LaAlO$_3$/SrTiO$_3$ heterostructures.
The electrostatics of two-dimensional (2D) lateral pn homojunctions considering the impact of electrostatic doping by means of two split bottom-gates are studied here. Analytical expressions are obtained from the solution of the 2D Poisson equation considering a depletion approximation. Straightforward analytical models for the electrostatic potential and the depletion width within both the dielectric and the 2D semiconductor are obtained for both the symmetrical and asymmetrical cases. In contrast to the case of devices with chemical doping, the obtained depletion width model of devices with …
The increasing technological control of two-dimensional materials has allowed the demonstration of 2D lateral junctions, which display unique properties that might serve as the basis for a new generation of 2D electronic and optoelectronic devices. Notably, the chemically doped MoS$_2$ homojunction, the WSe$_2$-MoS$_2$ monolayer and MoS$_2$ monolayer/multilayer heterojunctions, have been demonstrated. Here we report the investigation of 2D lateral junction electrostatics, which differs from the bulk case because of the weaker screening, producing a much longer transition region between the spa…
We study transport of indirect excitons in GaAs/AlGaAs coupled quantum wells in linear lattices created by laterally modulated gate voltage. The localization-delocalization transition (LDT) for transport across the lattice was observed with reducing lattice amplitude or increasing exciton density. The exciton interaction energy at the transition is close to the lattice amplitude. These results are consistent with the model, which attributes the LDT to the interaction-induced percolation of the exciton gas through the external potential. We also discuss applications of the lattice potentials fo…
The screened Coulomb potential plays a crucial role in the binding energies of excitons in a thin dielectric slab. The asymptotic behavior of this potential is studied when the thickness of the slab is very small as compared to the exciton Bohr radius. A regularized expression is given and the exact effective 2D potential is derived. These expressions may be useful for the computation of the exciton binding energy in 2D or quasi-2D materials.
We study the electrostatic responses (i.e. retardation effects due to the propagation of electromagnetic waves are ignored) of a linear homogeneous and anisotropic (LHA) dielectric film to an arbitrary external electrostatic potential, which may be generated by charges located either inside or outside it. A formalism is developed to calculate the polarization charges induced in the film. In our derivation, the idea is exploited that a physical boundary can be looked upon as a region of rapid variation in polarization rather than a simple geometric separation. With this no boundary conditions a…
For electrons above a superfluid helium film suspended on a specially designed dielectric substrate, $z=h(y)$, we obtain that both the transverse, along $z$, and the lateral, along $y$, quantizations are strongly enhanced due to a strong mutual coupling. The self-consistent quantum wires (QWs) with non-degenerated one-dimensional electron systems (1DESs) are obtained over a superfluid liquid helium (LH) suspended self-consistently on different dielectric substrates with a nanoscale modulation. A gap $\gtrsim 10$meV ($\gtrsim 1$meV) is obtained between the lowest two electron levels due to main…
In a recent paper, it was shown that, under the action of the lateral van der Waals (vdW) force due to a perfectly conducting corrugated surface, a neutral anisotropic polarizable particle in vacuum can be attracted not only to the nearest corrugation peak, but also to a valley, or an intermediate point between a peak and a valley, with such behaviors called peak, valley and intermediate regimes, respectively. In the present paper, we investigate how these regimes are affected by the consideration of two non-dispersive semi-infinite dielectrics $ε_{1}$ and $ε_{2}$, separated by a corrugated in…
Buckling at the micro and nanoscale generates distant bistable states which can be beneficial for sensing, shape-reconfiguration and mechanical computation applications. Although different approaches have been developed to access buckling at small scales, such as the use heating or pre-stressing beams, very little attention has been paid so far to dynamically and precisely control all the critical bifurcation parameters, the compressive stress and the lateral force on the beam. Precise and on-demand generation of compressive stress on individually addressable microstructures is especially crit…
We consider in-plane electrostatic traps for indirect excitons in coupled quantum wells, where the traps are formed by a laterally modulated gate voltage. An intrinsic obstacle for exciton confinement in electrostatic traps is an in-plane electric field that can lead to exciton dissociation. We propose a design to suppress the in-plane electric field and, at the same time, to effectively confine excitons in the electrostatic traps. We present calculations for various classes of electrostatic traps and experimental proof of principle for trapping of indirect excitons in electrostatic traps.
This paper builds on two previous works, Lindgren et al. J. Comp. Phys. 371, 712-731 (2018) and Quan et al. arXiv:1807.05384 (2018), to devise a new method to solve the problem of calculating electrostatic interactions in a system composed by many dielectric particles, embedded in a homogeneous dielectric medium, which in turn can also be permeated by charge carriers. The system is defined by the charge, size, position and dielectric constant of each particle, as well as the dielectric constant and Debye length of the medium. The effects of taking into account the dielectric nature of the part…
Creation of sharp lateral p-n junctions in graphene devices, with transition widths well below the Fermi wavelength of graphene charge carriers, is vital to study and exploit these electronic systems for electron-optical applications. The achievement of such junctions is, however, not trivial due to the presence of a considerable out-of-plane electric field in lateral p-n junctions, resulting in large widths. Metal-graphene interfaces represent a novel, promising and easy to implement technique to engineer such sharp lateral p-n junctions in graphene field-effect devices, in clear contrast to …
We propose and demonstrate a relaxed-SiGe/strained-Si (SiGe/s-Si) enhancement-mode gate stack for quantum dots. The enhancement-mode SiGe/s-Si structure is pursued because it spaces the quantum dot away from charge and spin defect rich dielectric interfaces and minimizes background dopants. A mobility of 1.6\times10^5 cm^2/Vs at 5.8\times10^{11}/cm^2 is measured in Hall bars that witness the same device process flow as the quantum dot. Periodic Coulomb blockade (CB) is measured in a double-top-gated lateral quantum dot nanostructure. The CB terminates with open diamonds up to \pm 10 mV of DC v…
We present fully quantum-mechanical magnetotransport calculations for short-period lateral superlattices with one-dimensional electrostatic modulation. A non-perturbative treatment of both magnetic field and modulation potential proves to be necessary to reproduce novel quantum oscillations in the magnetoresistance found in recent experiments in the resistance component parallel to the modulation potential. In addition, we predict oscillations of opposite phase in the component perpendicular to the modulation not yet observed experimentally. We show that the new oscillations originate from the…
The electrostatics arising in ferroelectric/dielectric two-dimensional heterostructures and superlatitices is revisited here within a simplest Kittel model, in order to define a clear paradigmatic reference for domain formation. The screening of the depolarizing field in isolated ferroelectric or polar thin films via the formation of 180$^{\circ}$ domains is well understood, whereby the width of the domains $w$ grows as the square-root of the film thickness $d$, following Kittel's law, for thick enough films ($w\ll d$). This behavior is qualitatively unaltered when the film is deposited on a d…
We describe how the out-of-plane dielectric polarizability of monolayer graphene influences the electrostatics of bilayer graphene -- both Bernal (BLG) and twisted (tBLG). We compare the polarizability value computed using density functional theory with the output from previously published experimental data on the electrostatically controlled interlayer asymmetry potential in BLG and data on the on-layer density distribution in tBLG. We show that monolayers in tBLG are described well by polarizability $α_{exp} = 10.8 \unicode{x212B}^3$ and effective out-of-plane dielectric susceptibility $ε_z …
The potential profile across a biased molecular junction is calculated within the framework of a simple Thomas-Fermi type screening model. In particular, the relationship between this profile and the lateral molecular cross section is examined. We find that a transition from a linear potential profile to a potential that drops mainly near the molecule-metal contacts occurs with increasing cross section width, in agreement with numerical quantum calculations.
The normal and the lateral Casimir interactions between corrugated ideal metallic plates in the presence of an amplifying or an absorptive dielectric slab has been studied by the path-integral quantization technique. The effect of the amplifying slab, which is located between corrugated conductors, is to increase the normal and lateral Casimir interactions, while the presence of the absorptive slab diminishes the interactions. These effects are more pronounced if the thickness of the slab increases, and also if the slab comes closer to one of the bounding conductors. When both bounding ideal c…
We have measured activation gaps for odd-integer quantum Hall states in a unidirectional lateral superlattice (ULSL) -- a two-dimensional electron gas (2DEG) subjected to a unidirectional periodic modulation of the electrostatic potential. By comparing the activation gaps with those simultaneously measured in the adjacent section of the same 2DEG sample without modulation, we find that the gaps are reduced in the ULSL by an amount corresponding to the width acquired by the Landau levels through the introduction of the modulation. The decrement of the activation gap varies with the magnetic fie…
In quantum wires, such as metallic nanotubes, the optical absorption of the transverse polarization is controlled by the depolarization effect which stems from the redistribution of conduction electrons around the circumference of the system. The traditional electrostatics treatment of the depolarization effect relies on approximating the system by a cylinder with some effective dielectric permittivity. We demonstrate that this simple intuitive picture does not adequately describe optical absorption near its threshold, as the depolarization effect becomes dominated by many-body correlations wh…
We develop a fundamental theory of the long-range electrostatic interactions in two-dimensional crystals by performing a rigorous study of the nonanalyticities of the Coulomb kernel. We find that the dielectric functions are best represented by $2\times 2$ matrices, with nonuniform macroscopic potentials that are two-component hyperbolic functions of the out-of-plane coordinate, $z$. We demonstrate our arguments by deriving the long-range interatomic forces in the adiabatic regime, where we identify a formerly overlooked dipolar coupling involving the out-of-plane components of the dynamical c…
We show that graphene-dielectric multilayers give rise to an unusual tunability of the Casimir-Lifshitz forces, and allow to easily realize completely different regimes within the same structure. Concerning thermal effects, graphene-dielectric multilayers take advantage from the anomalous features predicted for isolated suspended graphene sheets, even though they are considerably affected by the presence of the dielectric substrate. They can also archive the anomalous non-monotonic thermal metallic behavior by increasing the graphene sheets density and their Fermi energy. In addition to a stro…
Exciton dissociation at heterojunctions in photovoltaic devices is not completely understood despite being fundamentally necessary to generate electrical current. One of the fundamental issues for ab initio calculations is that hybrid interfaces combining materials with Wannier-Mott excitons and those with Frenkel excitons can easily require thousands of atoms to encompass the exciton-wave function. The problem is further exacerbated by a large permittivity difference at the interface, which requires meso-scale boundary conditions to accurately predict electrostatic potentials. For these reaso…
We demonstrate a tunnel field effect transistor based on a lateral heterostructure patterned from an $\mathrm{LaAlO_3/SrTiO_3}$ electron gas. Charge is injected by tunneling from the $\mathrm{LaAlO_3}$/$\mathrm{SrTiO_3}$ contacts and the current through a narrow channel of insulating $\mathrm{SrTiO_3}$ is controlled via an electrostatic side gate. Drain-source I/V-curves have been measured at low and elevated temperatures. The transistor shows strong electric-field and temperature-dependent behaviour with a steep sub-threshold slope %of up to as small as $10\:\mathrm{mV/decade}$ and a transcon…
We report low-temperature transport measurements performed on a planar Nb-InGaAs-Nb proximity Josephson junction hosting a gate-defined lateral quantum dot in the weak-link. We first study quasiparticle and Josephson transport through the open junction, when all gates are grounded. When the quantum dot is defined in the normal region by electrostatic depletion, cotunneling spectroscopy allows us to directly probe the energy gap induced in the two dimensional electron gas. Our data show good qualitative agreement with a model describing resonant tunneling through an Anderson impurity connected …
We propose and investigate the intrinsically thinnest transistor concept: a monolayer ballistic heterojunction bipolar transistor based on a lateral heterostructure of transition metal dichalcogenides. The device is intrinsically thinner than a Field Effect Transistor because it does not need a top or bottom gate, since transport is controlled by the electrochemical potential of the base electrode. As typical of bipolar transistors, the collector current undergoes a tenfold increase for each 60 mV increase of the base voltage over several orders of magnitude at room temperature, without sophis…
We present a simulation method to study electrolyte solutions in a dielectric slab geometry using a modified 3D Ewald summation. The method is fast and easy to implement, allowing us to rapidly resum an infinite series of image charges. In the weak coupling limit, we also develop a mean-field theory which allows us to predict the ionic distribution between the dielectric charged plates. The agreement between both approaches, theoretical and simulational, is very good, validating both methods. Examples of ionic density profiles in the strong electrostatic coupling limit are also presented. Fina…
