We consider states localized by electrostatic potentials in phosphorene using an atomistic tight binding approach. From the results of the tight-binding calculations of the confined states we extract effective masses for the conduction band electrons in the armchair and zigzag directions. The masses derived in this way are used for a simple single-band effective mass model which, as we find, reproduces very well the tight-binding energy spectrum in external magnetic field, the probability densities and the interaction effects. Both methods produce Wigner crystallization for the ground-state of the electron pair with the single-electron islands separated in the armchair direction already for small quantum dots.
The anisotropy in resonant tunneling transport through an electrostatic barrier in mono layer black phosphorus either in presence or in absence of an oscillating potential is studied. Non-perturbative Floquet theory is applied to solve the time dependent problem and the results obtained are discussed thoroughly. The resonance spectra in field free transmission are Lorentzian in nature although the width of the resonance for the barrier along the zigzag direction is too thinner than that for the armchair one. Resonant transmission is suppressed for both the cases by the application of oscillati…
We consider the Aharonov-Bohm (AB) effect on a confined electron ground state in a quantum ring defined electrostatically within the phosphorene monolayer. The strong anisotropy of effective masses in phosphorene quenches ground-state oscillations for a circular ring because of interrupted persistent current circulation around the ring. An elliptic deformation of the confinement potential can compensate for the anisotropy of the effective masses and produce ground-state parity transformations with the AB periodicity. Moreover, a specific ratio of the semiaxes is determined for which the spectr…
We theoretically investigate phosphorene zigzag nanorribons as a platform for constriction engineering. In the presence of a constriction at the upper edge, quantum confinement of edge protected states reveals resonant tunnelling Breit-Wigner transmission peaks, if the upper edge is uncoupled to the lower edge. Coupling between edges in thin constrictions gives rise to Fano-like and anti-resonances in the transmission spectrum of the system.
First principles density-functional theory calculations were performed to investigate quantum confinement and edge effects on the electronic properties of zigzag green phosphorene nanoribbons (ZGPNRs) with edge chemical species including H, OH, F, Cl, O, and S for the ribbons width in the range of 0.5 \~{} 3.7 nm. The ZGPNRs were obtained from the relaxed two-dimensional (2D) green phosphorene monolayer with different cutting strategies and the most energetically favorable ribbon configuration was selected for further exploration of the size and edge effects. It was found that the electronic p…
We theoretically analyze the possibility to confine electrons in single-layer graphene with the help of metallic gates, via the evaluation of the density of states of such a gate-defined quantum dot in the presence of a ring-shaped metallic contact. The possibility to electrostatically confine electrons in a gate-defined ``quantum dot'' with finite-carrier density, surrounded by an undoped graphene sheet, strongly depends on the integrability of the electron dynamics in the quantum dot. With the present calculations we can quantitatively compare confinement in dots with integrable and chaotic …
We study electrostatic quantum dot confinement for charge carriers in silicene. The confinement is formed by vertical electric field surrounding the quantum dot area. The resulting energy gap in the outside of the quantum dot traps the carriers within, and the difference of electrostatic potentials on the buckled silicene sublattices produces nonzero carrier masses outside the quantum dot. We study the electrostatic confinement defined inside a silicene flake with both the atomistic tight-binding approach as well as with the continuum approximation for a circularly symmetric electrostatic pote…
We compare the conductance of an undoped graphene sheet with a small region subject to an electrostatic gate potential for the cases that the dynamics in the gated region is regular (disc-shaped region) and classically chaotic (stadium). For the disc, we find sharp resonances that narrow upon reducing the area fraction of the gated region. We relate this observation to the existence of confined electronic states. For the stadium, the conductance looses its dependence on the gate voltage upon reducing the area fraction of the gated region, which signals the lack of confinement of Dirac quasipar…
We investigate effects of lateral confinement on spin splitting of energy levels in 2D hole gases grown on [311] GaAs. We found that lateral confinement enhances anisotropy of spin splitting relative to the 2D gas for both confining directions. Unexpectedly, the effective $g$-factor does not depend on the 1D energy level number $N$ for $B\|[0\bar{1}1]$ while it has strong $N$-dependence for $B\|[\bar{2}33]$. Apart from quantitative difference in the spin splitting of energy levels for the two orthogonal confinement directions we also report qualitative differences in the appearance of spin-spl…
Coulomb blockade is observed in a graphene nanoribbon device with a top gate. When two pn junctions are formed via the back gate and the local top gate, electrons are confined between the pn junctions which act as the barriers. When no pn junctions are induced by the gate voltages, electrons are still confined, as a result of strong disorder, but in a larger area. Measurements on five other devices with different dimensions yield consistent results.
We study Wigner crystallization of electron systems in phosphorene quantum dots with confinement of an electrostatic origin with both circular and elongated geometry. The anisotropy of the effective mass allows for the formation of Wigner molecules in the laboratory frame with a confined charge density that has lower symmetry than the confinement potential. We find that in circular quantum dots separate single-electron islands are formed for two and four confined electrons but not for three trapped carriers. The spectral signatures of the Wigner crystallization to be resolved by transport spec…
We report the electronic structure and optical absorption spectra of monolayer black phosphorus (phosphorene) nanoribbons (PNRs) via first-principles simulations. The band gap of PNRs is strongly enhanced by quantum confinement. However, differently orientated PNRs exhibit distinct scaling laws for the band gap vs the ribbon width (w). The band gaps of armchair PNRs scale as 1/(w^2), while zigzag PNRs exhibit a 1/w behavior. These distinct scaling laws reflect a significant implication of the band dispersion of phosphorene: electrons and holes behave as classical particles along the zigzag dir…
We report the fabrication and characterization of an electrostatic quantum dot in pure Germanium with an integrated charge measurement transistor. The device uses the Al2O3/Germanium interface for the confinement of carriers in the Germanium and an hybrid design with an electron quantum dot and hole transistor for the charge detection. The hole transistor, using with NiGe source and drain contacts, despite the modest low temperature carrier mobility of 450 cm2/Vs, has shown a sensitivity to the dot electric potential sufficient to detect single charges tunneling in and out of the quantum dot. …
We study spatially indirect excitons confined in a 10 $μ$m wide electrostatic trap of a GaAs double quantum well. We introduce a technique to control the amplitude of the electric field interacting with the excitons electric dipole, with nanosecond precision. Our approach relies on electronic waveforms corrected for the distorsions occurring at highest frequencies so that impedance matching is not necessary. Thus, we manipulate the confinement of cold gases without inducing sizeable perturbations down to sub-Kelvin bath temperatures.
We investigate the electrostatic confinement of charge carriers in a gapped graphene quantum dot in the presence of a magnetic flux. The circular quantum dot is defined by an electrostatic gate potential delimited in an infinite graphene sheet which is then connected to a two terminal setup. Considering different regions composing our system, we explicitly determine the solutions of the energy spectrum in terms of Hankel functions. Using the scattering matrix together with the asymptotic behavior of the Hankel functions for large arguments, we calculate the density of states and show that it h…
The electrostatic confinement of massless charge carriers is hampered by Klein tunneling. Circumventing this problem in graphene mainly relies on carving out nanostructures or applying electric displacement fields to open a band gap in bilayer graphene. So far, these approaches suffer from edge disorder or insufficiently controlled localization of electrons. Here we realize an alternative strategy in monolayer graphene, by combining a homogeneous magnetic field and electrostatic confinement. Using the tip of a scanning tunneling microscope, we induce a confining potential in the Landau gaps of…
Due to Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design mesoscopic structures in graphene by magnetic barriers, e.g. quantum dots or quantum point contacts.
We study and compare two analytic models of graphene quantum dots for calculating charge relaxation times due to electron-phonon interaction. Recently, charge relaxation processes in graphene quantum dots have been probed experimentally and here we provide a theoretical estimate of relaxations times. By comparing a model with pure edge confinement to a model with electrostatic confinement, we find that the latter features much larger relaxation times. Interestingly, relaxation times in electrostatically defined quantum dots are predicted to exceed the experimentally observed lower bound of ~10…
Due to Klein tunneling, electrostatic confinement of electrons in graphene is not possible. This hinders the use of graphene for quantum dot applications. Only through quasi-bound states with finite lifetime has one achieved to confine charge carriers. Here we propose that bilayer graphene with a local region of decoupled graphene layers is able to generate bound states under the application of an electrostatic gate. The discrete energy levels in such a quantum blister correspond to localized electron and hole states in the top and bottom layers. We find that this layer localization and the en…
For the pristine phosphorene nanoribbons (PNRs) with edge states, there exist two categories of edge bands near the Fermi energy (EF), i.e., the shuttle-shaped twofold-degenerate and the near-flat simple degenerate edge bands. However, the usual experimental measurement may not distinguish the difference between the two categories of edge bands. Here we study the varying rule for the edge bands of PNRs under an external electrostatic field. By using the KWANT code based on the tight-binding approach, we find that the twofold-degenerate edge bands can be divided into two separated shuttles unti…
We combine electrostatic and magnetic confinement to define a quantum dot in bilayer graphene. The employed geometry couples $n$-doped reservoirs to a $p$-doped dot. At magnetic field values around $B = 2~$T, Coulomb blockade is observed. This demonstrates that the coupling of the co-propagating modes at the $p$-$n$ interface is weak enough to form a tunnel barrier, facilitating transport of single charge carriers onto the dot. This result may be of use for quantum Hall interferometry experiments.
The rich and electrostatically tunable phase diagram exhibited by moiré materials has made them a suitable platform for hosting single material multi-purpose devices. To engineer such devices, understanding electronic transport and localization across electrostatically defined interfaces is of fundamental importance. Little is known, however, about how the interplay between the band structure originating from the moiré lattice and electric potential gradients affects electronic confinement. Here, we electrostatically define a cavity across a twisted double bilayer graphene sample. We observe t…
Technological advances allow for tunable lateral confinement of cold dipolar excitons in coupled quantum wells. We consider theoretically the Josephson effect between exciton condensates in two traps separated by a weak link. The flow of the exciton supercurrent is driven by the dipole energy difference between the traps. The Josephson oscillations may be observed after ensemble average of the time correlation of photons separately emitted from the two traps. The fringe visibility is controlled by the trap coupling and is robust against quantum and thermal fluctuations.
We study single and double quantum dots defined electrostatically within silicene. The spin-valley structure of the confined single- and two-electron system is determined and the effects of the intervalley scattering induced by the crystal edge and the Coulomb interaction are quantified. The states in a double quantum system are discussed in the context of the spatial symmetry of the single- and two-electron extended orbitals. We determine the charge, spin and valley transitions times induced by alternate electric fields of the microwave frequency. The valley transition times can be controlled…
We theoretically analyse the possibility to electrostatically confine electrons in circular quantum dot arrays, impressed on contacted graphene nanoribbons by top gates. Utilising exact numerical techniques, we compute the scattering efficiency of a single dot and demonstrate that for small-sized scatterers the cross-sections are dominated by quantum effects, where resonant scattering leads to a series of quasi-bound dot states. Calculating the conductance and the local density of states for quantum dot superlattices we show that the resonant carrier transport through such graphene-based nanos…
The route to reliable quantum nanoelectronic devices hinges on precise control of the electrostatic environment. For this reason, accurate methods for electrostatic simulations are essential in the design process. The most widespread methods for this purpose are the Thomas-Fermi approximation, which provides quick approximate results, and the Schrödinger-Poisson method, which better takes into account quantum mechanical effects. The mentioned methods suffer from relevant shortcomings: the Thomas-Fermi method fails to take into account quantum confinement effects that are crucial in heterostruc…
Quantum point contacts (QPC) are fundamental building blocks of nanoelectronic circuits. For their emission dynamics as well as for interaction effects such as the 0.7-anomaly the details of the electrostatic potential are important, but the precise potential shapes are usually unknown. Here, we measure the one-dimensional subband spacings of various QPCs as a function of their conductance and compare our findings with models of lateral parabolic versus hard wall confinement. We find that a gate-defined QPC near pinch-off is compatible with the parabolic saddle point scenario. However, as the …
A spatially modulated Dirac gap in a graphene sheet leads to charge confinement, thus enabling a graphene quantum dot to be formed without the application of external electric and magnetic fields [Appl. Phys. Lett. \textbf{97}, 243106 (2010)]. This can be achieved provided the Dirac gap has a local minimum in which the states become localised. In this work, the physics of such a gap-induced dot is investigated in the continuum limit by solving the Dirac equation. It is shown that gap-induced confined states couple to the states introduced by an electrostatic quantum well potential. Hence the r…
Oxide heterostructures are of great interest both for fundamental and applicative reasons. In particular the two-dimensional electron gas at the LaAlO$_3$/SrTiO$_3$ or LaTiO$_3$/SrTiO$_3$ interfaces displays many different physical properties and functionalities. However there are clear indications that the interface electronic state is strongly inhomogeneous and therefore it is crucially relevant to investigate possible intrinsic electronic mechanisms underlying this inhomogeneity. Here the electrostatic potential confining the electron gas at the interface is calculated self-consistently, fi…
Massless Dirac particles cannot be confined by an electrostatic potential. This is a problem for making graphene quantum dots but confinement can be achieved with a magnetic field and here, general conditions for confined and deconfined states are derived. There is a class of potentials for which the character of the state can be controlled at will. Then a confinement-deconfinement transition occurs which allows the Klein paradox to be probed experimentally in graphene dots.
Indium selenide, a post-transition metal chalcogenide, is a novel two-dimensional (2D) semiconductor with interesting electronic properties. Its tunable band gap and high electron mobility have already attracted considerable research interest. Here we demonstrate strong quantum confinement and manipulation of single electrons in devices made from few-layer crystals of InSe using electrostatic gating. We report on gate-controlled quantum dots in the Coulomb blockade regime as well as one-dimensional quantization in point contacts, revealing multiple plateaus. The work represents an important mi…
The recent discovery of Dirac semimetals represents a new achievement in our fundamental understanding of topological states of matter. Due to their topological surface states, high mobility, and exotic properties associated with bulk Dirac points, these new materials have attracted significant attention and are believed to hold great promise for fabricating novel topological devices. For nanoscale device applications, effects from finite size usually play an important role. In this report, we theoretically investigate the electronic properties of Dirac semimetal nanostructures. Quantum confin…
We investigate the influence of confinement on the positional order of a quasi-1D electron system trapped on the surface of liquid helium. We find evidence that the melting of the Wigner solid (WS) depends on the confinement strength, as well as electron density and temperature. A reentrant solid-liquid-solid transition is observed for increasing electron density under constant electrostatic confinement. As the electron row number $N_y$ changes, varying commensurability results in a modulation of the WS order, even when $N_y$ is large (several tens). This is confirmed by Monte Carlo simulation…
Quantum confined devices that manipulate single electrons in graphene are emerging as attractive candidates for nanoelectronics applications. Previous experiments have employed etched graphene nanostructures, but edge and substrate disorder severely limit device functionality. Here we present a technique that builds quantum confined structures in suspended bilayer graphene with tunnel barriers defined by external electric fields that break layer inversion symmetry, thereby eliminating both edge and substrate disorder. We report clean quantum dot formation in two regimes: at zero magnetic field…
We investigate the interplay between confinement and the fermion doubling problem in Dirac-like Hamiltonians. Individually, both features are well known. First, simple electrostatic gates do not confine electrons due to the Klein tunneling. Second, a typical lattice discretization of the first-order derivative $k \rightarrow -i\partial_x$ skips the central point and allow spurious low-energy, highly oscillating solutions known as fermion doublers. While a no-go theorem states that the doublers cannot be eliminated without artificially breaking a symmetry, here we show that the symmetry broken …
We study spin effects of quantum wires formed in bilayer graphene by electrostatic confinement. With a proper choice of the confinement direction, we show that in the presence of magnetic field, spin-orbit interaction induced by curvature, and intervalley scattering, bound states emerge that are helical. The localization length of these helical states can be modulated by the gate voltage which enables the control of the tunnel coupling between two parallel wires. Allowing for proximity effect via an s-wave superconductor, we show that the helical modes give rise to Majorana fermions in bilayer…
Magic angle twisted bilayer graphene has emerged as a powerful platform for studying strongly correlated electron physics, owing to its almost dispersionless low-energy bands and the ability to tune the band filling by electrostatic gating. Techniques to control the twist angle between graphene layers have led to rapid experimental progress but improving sample quality is essential for separating the delicate correlated-electron physics from disorder effects. Owing to the 2D nature of the system and the relatively low carrier density, the samples are highly susceptible to small doping inhomoge…
The realization of integrated quantum circuits requires precise on-chip control of charge carriers. Aiming at the coherent coupling of distant nanostructures at zero magnetic field, here we study the ballistic electron transport through two quantum point contacts (QPCs) in series in a three terminal configuration. We enhance the coupling between the QPCs by electrostatic focusing using a field effect lens. To study the emission and collection properties of QPCs in detail we combine the electrostatic focusing with magnetic deflection. Comparing our measurements with quantum mechanical and class…
The general theory for quantum simulation of cubic semiconductor n-MOSFETs is presented within the effective mass equation approach. The full three-dimensional transport problem is described in terms of coupled transverse subband modes which arise due to quantum confinement along the body thickness direction. Couplings among the subbands are generated for two reasons: due to spatial variations of the confinement potential along the transport direction, and due to non-alignment of the device coordinate system with the principal axes of the constant energy conduction band ellipsoids. The problem…
Quantum confinement of graphene Dirac-like electrons in artificially crafted nanometer structures is a long sought goal that would provide a strategy to selectively tune the electronic properties of graphene, including bandgap opening or quantization of energy levels However, creating confining structures with nanometer precision in shape, size and location, remains as an experimental challenge, both for top-down and bottom-up approaches. Moreover, Klein tunneling, offering an escape route to graphene electrons, limits the efficiency of electrostatic confinement. Here, a scanning tunneling mic…
In this study, the electrostatically induced quantum confinement structure, quantum point contact, has been realized in p-type trilayer tungsten diselenide-based van der Waals heterostructure with modified van der Waals contact method with degenerately doped transition metal dichalcogenide crystals. Clear quantized conductance and pinch-off state through the one-dimensional confinement were observed by dual-gating of split gate electrodes and top gate. Conductance plateaus were observed at step of 0.5 $\times$ 2e$^{2}$/h at zero and high magnetic field in addition to quarter plateaus at a fini…
An ultra-strong photovoltaic effect has recently been reported for electrons trapped on a liquid Helium surface under a microwave excitation tuned at intersubband resonance [D. Konstantinov et. al. : J. Phys. Soc. Jpn. 81, 093601 (2012) ]. In this article, we analyze theoretically the redistribution of the electron density induced by an overheating of the surface electrons under irradiation, and obtain quantitative predictions for the photocurrent dependence on the effective electron temperature and confinement voltages. We show that the photo-current can change sign as a function of the param…
We examine the impact of quantum confinement on the interaction potential between two charges in two-dimensional semiconductor nanosheets in solution. The resulting effective potential depends on two length scales, namely the thickness $d$ and an emergent length scale $d^* \equiv εd / ε_{\text{sol}}$, where $ε$ is the permittivity of the nanosheet and $ε_{\text{sol}}$ is the permittivity of the solvent. In particular, quantum confinement, and not electrostatics, is responsible for the logarithmic behavior of the effective potential for separations smaller than $d$, instead of the one-over-dist…
Electrostatic confinement of charge carriers in bilayer graphene provides a unique platform for carbon-based spin, charge or exchange qubits. By exploiting the possibility to induce a band gap with electrostatic gating, we form a versatile and widely tunable multi-quantum dot system. We demonstrate the formation of single, double and triple quantum dots that are free of any sign of disorder. In bilayer graphene we have the possibility to form tunnel barriers using different mechanisms. We can exploit the ambipolar nature of bilayer graphene where pn-junctions form natural tunnel barriers. Alte…
In quantum metrology, semiconductor single-electron pumps are used to generate accurate electric currents with the ultimate goal of implementing the emerging quantum standard of the ampere. Pumps based on electrostatically defined tunable quantum dots (QDs) have thus far shown the most promising performance in combining fast and accurate charge transfer. However, at frequencies exceeding approximately 1 GHz, the accuracy typically decreases. Recently, hybrid pumps based on QDs coupled to trap states have led to increased transfer rates due to tighter electrostatic confinement. Here, we operate…
We study the influence of a magnetic flux tube on the possibility to electrostatically confine electrons in a graphene quantum dot. Without magnetic flux tube, the graphene pseudospin is responsible for a quantization of the total angular momentum to half-integer values. On the other hand, with a flux tube containing half a flux quantum, the Aharonov-Bohm phase and Berry phase precisely cancel, and we find a state at zero angular momentum that cannot be confined electrostatically. In this case, true bound states only exist in regular geometries for which states without zero-angular-momentum co…
