We show that a difference in time scales of vertical and lateral dynamics permits one to analyze the problem of interacting electrons confined in an axially symmetric three-dimensional potential with a lateral oscillator confinement by means of the effective two-dimensional Hamiltonian with a screened Coulomb interaction. Using an adiabatic approximation based on action-angle variables, we present solutions for the effective charge of the Coulomb interaction (screening) for a vertical confinement potential simulated by parabolic, square, and triangular wells. While for the parabolic potential the solution for the effective charge is given in a closed anlytical form, for the other cases similar solutions can be easily calculated numerically.
The use of a nearby metallic ground-plane to limit the range of the Coulomb interactions between carriers is a useful approach in studying the physics of two-dimensional (2D) systems. This approach has been used to study Wigner crystallization of electrons on the surface of liquid helium, and most recently, the insulating and metallic states of semiconductor-based two-dimensional systems. In this paper, we perform calculations of the screening effect of one 2D system on another and show that a 2D system is at least as effective as a metal in screening Coulomb interactions. We also show that th…
We have investigated the Coulomb screening properties and plasmon spectrum in a bilayer graphene under a perpendicular electric bias. The bias voltage applied between the two graphene layers opens a gap in the single particle energy spectrum and modifies the many-body correlations and collective excitations. The energy gap can soften the plasmon modes and lead to a crossover of the plasmons from a Landau damped mode to being undamped. Plasmon modes of long lifetime may be observable in experiments and may have potentials for device applications.
We examine within the self-consistent Thomas-Fermi-Poisson approach the low-temperature screening properties of a two-dimensional electron gas (2DEG) subjected to strong perpendicular magnetic fields. Numerical results for the unconfined 2DEG are compared with those for a simplified Hall bar geometry realized by two different confinement models. It is shown that in the strongly non-linear screening limit of zero temperature the total variation of the screened potential is related by simple analytical expressions to the amplitude of an applied harmonic modulation potential and to the strength o…
We recently introduced a method based on density functional theory (DFT) and non-equilibrium Green's function techniques (NEGF) for calculating the addition energies of single molecule nano-junctions in the Coulomb blockade (CB) regime. Here we apply this approach to benzene molecules lying parallel and at various distances from two aluminum fcc (111) surfaces, and discuss the distance dependence in our calculations in terms of electrostatic screening effects. The addition energies near the surface are reduced by about a factor of two, which is comparable to previously reported calculations em…
We have developed a technique utilizing a double quantum well heterostructure that allows us to study the effect of a nearby ground-plane on the metallic behavior in a GaAs two-dimensional hole system (2DHS) in a single sample and measurement cool-down, thereby maintaining a constant disorder potential. In contrast to recent measurements of the effect of ground-plane screening of the long-range Coulomb interaction in the insulating regime, we find surprisingly little effect on the metallic behavior when we change the distance between the 2DHS and the nearby ground-plane.
We describe a practical procedure to calculate the Coulomb matrix elements of 2D spatially separated and confined charge carriers, which are needed for detailed theoretical descriptions of important condensed matter finite systems. We derive an analytical expression, for arbitrary separations, in terms of a single infinite series and apply a u-type Levin transform in order to accelerate the resulting infinite series. This procedure has proven to be efficient and accurate. Direct consequences concerning the functional dependence of the matrix elements on the separation distance, transition ampl…
We have investigated the Coulomb screening properties and collective excitations in a graphene bilayer. The static screening effect is anisotropic and is much stronger in the undoped graphene bilayer than in a monolayer graphene [1]. The dynamic screening shows the properties of a Dirac gas in the low frequency and that of a Fermi gas in the high frequency. The transition from the Dirac to the Fermi gas is also observed in the plasmon spectrum. Finally, we find that an electron gas in a doped graphene bilayer has quite similar properties as those of a Fermi gas in materials containing two ener…
In this work we implement the self-consistent Thomas-Fermi approach and a local conductivity model to an electron-electron bilayer system. The presence of an incompressible strip, originating from screening calculations at the top (or bottom) layer is considered as a source of an external potential fluctuation to the bottom (or top) layer. This essentially yields modifications to both screening properties and the magneto-transport quantities. The effect of the temperature, inter-layer distance and density mismatch on the density and the potential fluctuations are investigated. It is observed t…
We present a quasiparticle interference study of clean and Mn surface-doped TaAs, a prototypical Weyl semimetal, to test the screening properties as well as the stability of Fermi arcs against Coulomb and magnetic scattering. Contrary to topological insulators, the impurities are effectively screened in Weyl semimetals. The adatoms significantly enhance the strength of the signal such that theoretical predictions on the potential impact of Fermi arcs can be unambiguously scrutinized. Our analysis reveals the existence of three extremely short, previously unknown scattering vectors. Comparison …
Coulomb interaction and its screening play an important role in many physical phenomena of materials ranging from optical properties to many-body effects including superconductivity. Here, we report on a systematic study of dielectric screening in few-layer black phosphorus (BP), a two-dimensional material with promising electronic and optical characteristics. We use a combination of a tight-binding model and rigorously determined bare Coulomb interactions, which allows us to consider relevant microscopic effects beyond the long-wavelength limit. We calculate the dielectric function of few-lay…
Excitonic resonance and binding energies can be altered by controlling the environmental screening of the attractive Coulomb potential. Although this screening response is often assumed to be static, the time evolution of the excitonic quasiparticles manifests a frequency-dependence in its Coulomb screening efficacy. In this letter, we investigate a ground (1s) and first excited exciton state (2s) in a multi-layered transition metal dichalcogenide (MoS$_2$) upon ultrafast photo-excitation. We explore the dynamic screening effects on the latter and show its resonance frequency is the relevant f…
A residual disorder in the gate system is the main problem on the way to create artificial graphene based on two-dimensional electron gas. The disorder can be significantly screened/reduced due to the many-body effects. To analyse the screening/disorder problem we consider AlGaAs/GaAs/AlGaAs heterostructure with two metallic gates. We demonstrate that the design least susceptible to the disorder corresponds to the weak coupling regime (opposite to tight binding) which is realised via system of quantum anti-dots. The most relevant type of disorder is the area disorder which is a random variatio…
We study acoustic-phonon-induced relaxation of charge excitations in single and tunnel-coupled quantum dots containing few confined interacting electrons. The Full Configuration Interaction approach is used to account for the electron-electron repulsion. Electron-phonon interaction is accounted for through both deformation potential and piezoelectric field mechanisms. We show that electronic correlations generally reduce intradot and interdot transition rates with respect to corresponding single-electron transitions, but this effect is lessened by external magnetic fields. On the other hand, p…
The screening of Coulomb interaction controls many-body physics in carbon nanotubes, as it tunes the range and strength of the force that acts on charge carriers and binds electron-hole pairs into excitons. In doped tubes, the effective Coulomb interaction drives the competition between Luttinger liquid and Wigner crystal, whereas in undoped narrow-gap tubes it dictates the Mott or excitonic nature of the correlated insulator observed at low temperature. Here, by computing the dielectric function of selected narrow- and zero-gap tubes from first principles, we show that the standard effective-…
The ability to control the strength of interaction is essential for studying quantum phenomena emerging from a system of correlated fermions. For example, the isotope effect illustrates the effect of electron-phonon coupling on superconductivity, providing an important experimental support for the BCS theory. In this work, we report a new device geometry where the magic-angle twisted bilayer graphene (tBLG) is placed in close proximity to a Bernal bilayer graphene (BLG) separated by a 3 nm thick barrier. Using charge screening from the Bernal bilayer, the strength of electron-electron Coulomb …
The static dielectric function in AA-stacked bilayer graphene (BLG), subjected to an electric field applied perpendicular to layers, is calculated analytically within the random phase approximation (RPA). This result is used to calculate the screened Coulomb interaction and the electrical conductivity. The screened Coulomb interaction, which here can be tuned by the perpendicular electric field, shows a power-law decay as $1/(γ^{2}+V^2)$ at long-distance limit where $V$ and $γ$ are the electrical potential and the inter-layer hopping energy respectively, indicating that the Coulomb interaction…
The frequency dependence of shot noise in mesoscopic diffusive contacts is calculated with account taken of long-range Coulomb interaction and external screening. While the low-frequency noise is 1/3 of noise of classical Poisson process independently of the contact shape, the high-frequency noise tends to the full classical value for long and narrow contacts because of strong screening by the surrounding medium. In this case, the current fluctuations at opposite ends of the contact are completely independent.
Coulomb screening, together with degeneracy, is characteristic of the metallic electron gas. While there is little trace of its effects in transport and noise in the bulk, at mesoscopic scales the electronic fluctuations start to show appreciable Coulomb correlations. Within a strictly standard Boltzmann and Fermi-liquid framework, we analyze these phenomena and their relation to the mesoscopic fluctuation-dissipation theorem, which we prove. We identify two distinct screening mechanisms for mesoscopic fluctuations. One is the self-consistent response of the contact potential in a non-uniform …
We suggest a simple model of disorder in graphene assuming that there are randomly distributed positive and negative centers with equal concentration $N/2$ in the bulk of silicon oxide substrate. We show that at zero gate voltage such disorder creates two-dimensional concentration $n_0 \sim N^{2/3}$ of electrons and holes in graphene. Electrons and holes reside in alternating in space puddles of the size $R_0 \sim N^{-1/3}$. A typical puddle has only one or two carriers in agreement with recent scanning single electron transistor experiment.
Renormalization of Landau level energies in graphene in strong magnetic field due to Coulomb interaction is studied theoretically, and calculations are compared with two experiments on carrier-density dependent scanning tunneling spectroscopy. An approximate preservation of the square-root dependence of the energies of Landau levels on their numbers and magnetic field in the presence of the interaction is examined. Many-body calculations of the renormalized Fermi velocity with the statically screened interaction taken in the random-phase approximation show good agreement with both experiments.…
In this paper we systematically analyze the electronic structures of polar and nonpolar wurtzite-InN/GaN quantum dots and their modification due to the quantum-confined Stark effect caused by intrinsic fields. This is achieved by combining continuum elasticity theory with an empirical tight binding model to describe the elastic and single-particle electronic properties in these nitride systems. Based on these results, a many-body treatment is used to determine optical absorption spectra. The efficiency of optical transitions depends on the interplay between the Coulomb interaction and the quan…
For high-speed optoelectronic applications relying on fast relaxation or energy transfer mechanisms, understanding of carrier relaxation and recombination dynamics is critical. Here, we compare the differences in photoexcited carrier dynamics in 2D and quasi-3D colloidal methylammonium lead iodide perovskite nanoplatelets via differential transmission spectroscopy. We find that the cooling of excited electron-hole pairs by phonon emission progresses much faster and is intensity-independent in the 2D-case. This is due to the low dielectric surrounding of the thin perovskite layers, for which th…
The screening effect due to a scanning tunneling microscope tip which is placed in the vicinity of an interacting quantum wire is considered. With the help of a bosonization procedure, we are able to determine non perturbatively the Green's functions of the quantum wire in the presence of both electrostatic screening by the tip and Coulomb interactions in the wire. In our approach we justify that the working Hamiltonian of the whole system is quadratic when $K_c>1/2$ and can be solved by integration over the degrees of freedom of the tip. Once the Green's functions are known, we calculate the …
This paper considers the self-consistent Coulomb interaction within arrays of self-assembled InAs quantum dots (QDs) which are embedded in a pn structure. Strong emphasis is being put on the statistical occupation of the electronic QD states which has to be solved self-consistently with the actual three-dimensional potential distribution. A model which is based on a Green's function formalism including screening effects is used to calculate the interaction of QD carriers within an array of QDs, where screening due to the inhomogeneous bulk charge distribution is taken into acount. We apply our…
A quantitative description of Coulomb interactions is developed for two-dimensional superconducting materials, enabling us to compare intrinsic with external screening effects, such as those due to substrates. Using the example of a doped monolayer of MoS2 embedded in a tunable dielectric environment, we demonstrate that the influence of external screening is limited to a length scale, bounded from below by the effective thickness of the quasi-two-dimensional material and from above by its intrinsic screening length. As a consequence, it is found that unconventional Coulomb-driven superconduct…
We investigate the instabilities that may lead to the breakdown of the Luttinger liquid in the small-diameter (5,0) nanotubes, paying attention to the competition between the effective interaction mediated by phonon-exchange and the Coulomb interaction. We use bosonization methods to achieve an exact treatment of the Coulomb interaction at small momentum-transfer, and apply next renormalization group methods to analyze the low-energy behavior of the electron system. This allows us to discern the growth of several response functions for charge-density-wave modulations and for superconducting in…
We calculate exactly the vacuum polarization charge density in the field of a subcritical Coulomb impurity, $Z|e|/r$, in graphene. Our analysis is based on the exact electron Green's function, obtained by using the operator method, and leads to results that are exact in the parameter $Zα$, where $α$ is the "fine structure constant" of graphene. Taking into account also electron-electron interactions in the Hartree approximation, we solve the problem self-consistently in the subcritical regime, where the impurity has an effective charge $Z_{eff}$, determined by the localized induced charge. We …
Coulomb screening of superconductivity in magic-angle twisted bilayer graphene
School of Physics & Astronomy, University of Manchester（曼彻斯特大学物理与天文学学院）；National Graphene Institute, University of Manchester（曼彻斯特大学国家石墨烯研究所）；Department of Physics, Washington University in St. Louis（华盛顿大学圣路易斯分校物理系）；Department of Physics and Astronomy, University of Pennsylvania（宾夕法尼亚大学物理与天文学系）；Department of Physics, University of Antwerp（安特卫普大学物理系）；Henry Royce Institute for Advanced Materials, The University of Manchester（曼彻斯特大学亨利·罗伊斯先进材料研究所）；National Institute for Materials Science（国立材料研究所）；Department of Materials Science and Engineering, National University of Singapore（新加坡国立大学材料科学与工程系）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
We analyze the screening of an external Coulomb charge in gapless graphene cone, which is taken as a prototype of a topological defect. In the subcritical regime, the induced charge is calculated using both the Green's function and the Friedel sum rule. The dependence of the polarization charge on the Coulomb strength obtained from the Green's function clearly shows the effect of the conical defect and indicates that the critical charge itself depends on the sample topology. Similar analysis using the Friedel sum rule indicates that the two results agree for low values of the Coulomb charge bu…
This article develops a consistent theory of free carrier screening of a two-dimensional electron gas in the silicon inversion layer in the presence of stacked layers of dielectric environment-commonly knows as gate stack in context of field-effect transistors. It is shown that the finite thickness and of dielectric stacks alters the free carrier screening, a crucial quantity, which determines screened coulomb interaction in the inversion layer, and ubiquitously appears in carrier transport theory in semiconductors. Results are analytical and can be used to accurate prediction Coulomb-interact…
We calculate the temperature dependent conductivity of graphene in the presence of randomly distributed Coulomb impurity charges arising from the temperature dependent screening of the Coulomb disorder without any phonons. The purely electronic temperature dependence of our theory arises from two independent mechanisms: the explicit temperature dependence of the finite temperature dielectric function $ε(q,T)$ and the finite temperature energy averaging of the transport scattering time. We find that the calculated temperature dependent conductivity is non-monotonic, decreasing with temperature …
In low-dimensional structures with strong Rashba spin-orbit interaction (SOI), the Coulomb fields between moving electrons produce a SOI component of the pair interaction that competes with the potential Coulomb repulsion. If the Rashba SOI constant of the material is sufficiently high, the total electron-electron interaction becomes attractive, which leads to the formation of the two-electron bound states. We show that because of the dielectric screening in a thin film the binding energy is significantly higher as compared to the case of the bulk screening.
Charge screening effect in metallic carbon nanotubes is investigated in a model including the one-dimensional long-range Coulomb interaction. It is pointed out that an external charge which is being fixed spatially is screened by internal electrons so that the resulting object becomes electrically neutral. We found that the screening length is given by about the diameter of a nanotube.
A fully selfconsistent treatment for gap generation and Coulomb screening in excitonic insulators is presented. The method is based on the equations of motion for the relevant dynamical variables combined with a variational approach. Applying the theory for a model system of bilayer graphene, an excitonic groundstate with a gap exceeding 10 meV is predicted.
We show that by combining high-k dielectric substrate and high density of charge carriers, Coulomb impurity can be effectively screened, leading to an unprecedented room-temperature mobility of ~150cm2/Vs in monolayer MoS2. The high sample quality enables us to quantitatively extract the mobility components limited by Coulomb impurities, intrinsic and surface optical phonons, and study their scaling with temperature, carrier density and dielectric constant. The excellent agreement between our theoretical analysis and experimental data demonstrates unambiguously that room-temperature phonon-lim…
The transport of fluids at the nanoscale is fundamental to manifold biological and industrial processes, ranging from neurotransmission to ultrafiltration. Yet, it is only recently that well-controlled channels with cross-sections as small as a few molecular diameters became an experimental reality. When aqueous electrolytes are confined within such channels, the Coulomb interactions between the dissolved ions are reinforced due to dielectric contrast at the channel walls: we dub this effect `interaction confinement'. Yet, no systematic way of computing these confined interactions has been pro…
