Periodic Electrostatic Potential Research Articles

Parent Berry Curvature and the Ideal Anomalous Hall Crystal

We study a model of electrons moving in a parent band of uniform Berry curvature. At sufficiently high parent Berry curvature, we show that strong repulsive interactions generically lead to the formation of an anomalous Hall crystal: a topological state with spontaneously broken continuous translation symmetry. Our results are established via a mapping to a problem of Wigner crystallization in a regular 2D electron gas. Interestingly, we find that a periodic electrostatic potential induces a competing state with opposite Chern number. Our theory offers a unified perspective for understanding several aspects of the recently observed integer and fractional quantum anomalous Hall effects in rhombohedral multilayer graphene and provides a recipe for engineering new topological states. Published by the American Physical Society 2024

Coupled exciton internal and center-of-mass motions in two-dimensional semiconductors by a periodic electrostatic potential

Coupled exciton internal and center-of-mass motions in two-dimensional semiconductors by a periodic electrostatic potential

Numerical simulations unveil superradiant coherence in a lattice of charged quantum oscillators

A system of Nosc charged oscillators interacting with the electromagnetic field, spatially confined in a 3D lattice of sub-wavelength dimension, can condense into a superradiant coherent state if appropriate density and frequency conditions are met. In this state, the common frequency ω of the oscillators and the plasma frequency ωp of the charges are combined into a frequency ω′=ω2+ωp2 that is off-shell with respect to the wavelength of the photon modes involved, preventing them from propagating outside the material. Unlike other atomic cavity systems, the frequency ω in this case is not determined by the cavity itself but is defined by the periodic electrostatic potential that confines the charged particles in the lattice. Additionally, the electromagnetic modes involved have wave vectors distributed in all spatial directions, resulting in a significant increase in coupling. The analytical study of this system can be carried out in the limit of large Nosc by searching for an approximation of the ground state via suitable coherent trial states. Alternatively, numerical simulations can be employed for smaller Nosc. In the numerical approach, it is possible to go beyond the Rotating Wave Approximation (RWA) and introduce a dissipation term for the photon modes. This dissipation term can account for the ohmic quench in a metal and also consider photon losses at the boundary of the material. By utilizing numerical solutions and Monte Carlo simulations, the presence of condensation has been confirmed, and an energy gap of a few electron volts (eV) per particle has been observed in typical metal crystals with protons bound to tetrahedral or octahedral sites.

Formation of Artificial Fermi Surfaces with a Triangular Superlattice on a Conventional Two-Dimensional Electron Gas.

Imposing an external periodic electrostatic potential to the electrons confined in a quantum well makes it possible to engineer synthetic two-dimensional band structures, with electronic properties different from those in the host semiconductor. Here we report the fabrication and study of a tunable triangular artificial lattice on a GaAs/AlGaAs heterostructure where it is possible to transform from the original GaAs band structure and a circular Fermi surface to a new band structure with multiple artificial Fermi surfaces simply by altering a gate bias. For weak electrostatic modulation magnetotransport measurements reveal multiple quantum oscillations and commensurability oscillations due to the electron scattering from the artificial lattice. Increasing the strength of the modulation reveals new commensurability oscillations of the electrons from the artificial Fermi surface scattering from the triangular artificial lattice. These results show that low disorder gate-tunable lateral superlattices can be used to form artificial two-dimensional crystals with designer electronic properties.

Surface Doping of Organic Single-Crystal Semiconductors to Produce Strain-Sensitive Conductive Nanosheets.

A highly periodic electrostatic potential, even though established in van der Waals bonded organic crystals, is essential for the realization of a coherent band electron system. While impurity doping is an effective chemical operation that can precisely tune the energy of an electronic system, it always faces an unavoidable difficulty in molecular crystals because the introduction of a relatively high density of dopants inevitably destroys the highly ordered molecular framework. In striking contrast, a versatile strategy is presented to create coherent 2D electronic carriers at the surface of organic semiconductor crystals with their precise molecular structures preserved perfectly. The formation of an assembly of redox‐active molecular dopants via a simple one‐shot solution process on a molecularly flat crystalline surface allows efficient chemical doping and results in a relatively high carrier density of 1013 cm−2 at room temperature. Structural and magnetotransport analyses comprehensively reveal that excellent carrier transport and piezoresistive effects can be obtained that are similar to those in bulk crystals.

Fluctuations and magnetoresistance oscillations near the half-filled Landau level

We study theoretically the magnetoresistance oscillations near a half-filled lowest Landau level ($\nu = 1/2$) that result from the presence of a periodic one-dimensional electrostatic potential. We use the Dirac composite fermion theory of Son [Phys. Rev. X 5 031027 (2015)], where the $\nu=1/2$ state is described by a $(2+1)$-dimensional theory of quantum electrodynamics. We extend previous work that studied these oscillations in the mean-field limit by considering the effects of gauge field fluctuations within a large flavor approximation. A self-consistent analysis of the resulting Schwinger--Dyson equations suggests that fluctuations dynamically generate a Chern-Simons term for the gauge field and a magnetic field-dependent mass for the Dirac composite fermions away from $\nu=1/2$. We show how this mass results in a shift of the locations of the oscillation minima that improves the comparison with experiment [Kamburov et. al., Phys. Rev. Lett. 113, 196801 (2014)]. The temperature-dependent amplitude of these oscillations may enable an alternative way to measure this mass. This amplitude may also help distinguish the Dirac and Halperin, Lee, and Read composite fermion theories of the half-filled Landau level.

Twisted graphene nanoribbons as nonlinear nanoelectronic devices

We argue that twisted graphene nanoribbons subjected to a transverse electric field can operate as a variety of nonlinear nanoelectronic devices with tunable current-voltage characteristics controlled by the transverse field. Using the density-functional tight-binding method to address the effects of mechanical strain induced by the twisting, we show that the electronic transport properties remain almost unaffected by the strain in relevant cases and propose an efficient simplified tight-binding model which gives reliable results. The transverse electric field creates a periodic electrostatic potential along the nanoribbon, resulting in a formation of a superlattice-like energy band structure and giving rise to different remarkable electronic properties. We demonstrate that if the nanoribbon geometry and operating point are selected appropriately, the system can function as a field-effect transistor or a device with nonlinear current-voltage characteristic manifesting one or several regions of negative differential resistance. The latter opens possibilities for applications such as an active element of amplifiers, generators, and new class of nanoscale devices with multiple logic states.

The electrostatically forced Faraday instability: theory and experiments

The onset of interfacial instability in two-fluid systems using a viscous, leaky dielectric model is studied. The instability arises as a result of resonance between the parametric frequency of an imposed electric field and the system’s natural frequency. In addition to a rigorous model that uses Floquet instability analysis, where both viscous and charge effects are considered, this study also provides convincing validating experiments. In other results, it is shown that (a) the imposition of a periodic electrostatic potential acts to counter gravity and this countering effect becomes more effective if a DC voltage is also added, (b) a critical DC voltage exists at which the interface becomes unstable such that no parametric frequency is required to completely destabilize the interface and (c) the leaky dielectric model approaches a model for a perfect dielectric/perfect conductor pair as the conductivity ratio becomes large. It is also shown via experiments that parametric resonant instability using electrostatic forcing may be reliably used to estimate interfacial tension to sufficient accuracy.

Embedded Cluster Model for Al2O3 and AlPO4 Surfaces Using Point Charges and Periodic Electrostatic Potential

An embedded cluster model with either a large number of point charges (PCs) or periodic electrostatic (PE) potential was proposed to incorporate the electrostatic effects by the bulk surface and applied to non-transition-metal oxide supports such as Al2O3 and AlPO4. A large number of PCs are placed on several layers of surface. The PC values were taken to be the same as the Bader charges obtained from periodic DFT calculation of slab model. The PE potential was derived so as to consider the infinite three-dimensional PC distribution obtained by the calculation of slab model. One electron integral of the PE potential in the Gaussian basis function was evaluated using Poisson’s equation, Fourier transformation within a supercell approach, and the Ewald summation method. These embedded cluster models were applied to Rh2-adsorbed Al2O3 and AlPO4. A bare cluster model with neither PC nor the PE potential presented very poor computational results for the interaction energies of Rh2 with Al2O3 and AlPO4 surfaces...

Weiss oscillations and particle-hole symmetry at the half-filled Landau level

Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal $\pm e^2/2h$ at half-filling. We study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half-filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field, the oscillations occur symmetrically as the electron density is varied about half-filling. We find an approximate "sum rule" obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long wavelength physics.

Measurement of exciton correlations using electrostatic lattices

We present a method for determining correlations in a gas of indirect excitons in a semiconductor quantum well structure. The method involves subjecting the excitons to a periodic electrostatic potential that causes modulations of the exciton density and photoluminescence (PL). Experimentally measured amplitudes of energy and intensity modulations of exciton PL serve as an input to a theoretical estimate of the exciton correlation parameter and temperature. We also present a proof-of-principle demonstration of the method for determining the correlation parameter and discuss how its accuracy can be improved.

Revealing Hofstadter spectrum for graphene in a periodic potential

We calculate the energy bands for graphene monolayers when electrons move through a periodic electrostatic potential in the presence of a uniform perpendicular magnetic field. We clearly demonstrate the quantum fractal nature of the energy bands at reasonably low magnetic fields. We present results for the energy bands as functions of both wave number and magnetic flux through the unit cells of the resulting moir\'e superlattice. The effects due to pseudospin coupling and Landau orbit mixing by a strong scattering potential have been exhibited. At low magnetic fields when the Landau orbits are much larger than the period of the modulation, the Landau levels are only slightly broadened. This feature is also observed at extremely high magnetic fields. The density of states has been calculated and shows a remarkable self-similarity like the energy bands. We estimate that for modulation period of 10 nm the region where the Hofstadter butterfly is revealed is $B\ensuremath{\le}2$ T.

Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices

Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum, consisting of highly degenerate Landau energy levels. When subject to both a magnetic field and a periodic electrostatic potential, two-dimensional systems of electrons exhibit a self-similar recursive energy spectrum. Known as Hofstadter's butterfly, this complex spectrum results from an interplay between the characteristic lengths associated with the two quantizing fields, and is one of the first quantum fractals discovered in physics. In the decades since its prediction, experimental attempts to study this effect have been limited by difficulties in reconciling the two length scales. Typical atomic lattices (with periodicities of less than one nanometre) require unfeasibly large magnetic fields to reach the commensurability condition, and in artificially engineered structures (with periodicities greater than about 100 nanometres) the corresponding fields are too small to overcome disorder completely. Here we demonstrate that moiré superlattices arising in bilayer graphene coupled to hexagonal boron nitride provide a periodic modulation with ideal length scales of the order of ten nanometres, enabling unprecedented experimental access to the fractal spectrum. We confirm that quantum Hall features associated with the fractal gaps are described by two integer topological quantum numbers, and report evidence of their recursive structure. Observation of a Hofstadter spectrum in bilayer graphene means that it is possible to investigate emergent behaviour within a fractal energy landscape in a system with tunable internal degrees of freedom.

Dirac-Kronig-Penney model for strain-engineered graphene

Motivated by recent proposals on strain-engineering of graphene electronic circuits we calculate conductivity, shot-noise and the density of states in periodically deformed graphene. We provide the solution to the Dirac-Kronig-Penney model, which describes the phase-coherent transport in clean monolayer samples with an one-dimensional modulation of the strain and the electrostatic potentials. We compare the exact results to a qualitative band-structure analysis. We find that periodic strains induce large pseudo-gaps and suppress charge transport in the direction of strain modulation. The strain-induced minima in the gate-voltage dependence of the conductivity characterize the quality of graphene superstructures. The effect is especially strong if the variation of inter-atomic distance exceeds the value a^2/l, where a is the lattice spacing of free graphene and l is the period of the superlattice. A similar effect induced by a periodic electrostatic potential is weakened due to Klein tunnelling.

Manipulation of photons at the surface of three-dimensional photonic crystals

In three-dimensional (3D) photonic crystals, refractive-index variations with a periodicity comparable to the wavelength of the light passing through the crystal give rise to so-called photonic bandgaps, which are analogous to electronic bandgaps for electrons moving in the periodic electrostatic potential of a material's crystal structure. Such 3D photonic bandgap crystals are envisioned to become fundamental building blocks for the control and manipulation of photons in optical circuits. So far, such schemes have been pursued by embedding artificial defects and light emitters inside the crystals, making use of 3D bandgap directional effects. Here we show experimentally that photons can be controlled and manipulated even at the 'surface' of 3D photonic crystals, where 3D periodicity is terminated, establishing a new and versatile route for photon manipulation. By making use of an evanescent-mode coupling technique, we demonstrate that 3D photonic crystals possess two-dimensional surface states, and we map their band structure. We show that photons can be confined and propagate through these two-dimensional surface states, and we realize their localization at arbitrary surface points by designing artificial surface-defect structures through the formation of a surface-mode gap. Surprisingly, the quality factors of the surface-defect mode are the largest reported for 3D photonic crystal nanocavities (Q up to approximately 9,000). In addition to providing a new approach for photon manipulation by photonic crystals, our findings are relevant for the generation and control of plasmon-polaritons in metals and the related surface photon physics. The absorption-free nature of the 3D photonic crystal surface may enable new sensing applications and provide routes for the realization of efficient light-matter interactions.

Comparing the image potentials for intercalated graphene with a two-dimensional electron gas with and without a gated grating

We calculate the surface response function and the image potential of a system of layered two-dimensional (2D) electron gas structures. A point charge is placed at a distance away from the surface which lies in the $xy$- plane. These 2D layers are coupled through the Coulomb interaction and there is no interlayer electron hopping. The separation between adjacent layers can be adjusted to investigate the roles which the layer separation and the number of layers play on both the surface response function and the image potential. Specifically, we consider the system composed of graphene layers or the layered 2D electron gas (EG) formed at the interface of a semiconductor heterostructure such as GaAs/AlGaAs. We show that the image potential for graphene is qualitatively the same as for the 2DEG. We examine the way in which the image potential is modified by applying a one-dimensional periodic electrostatic potential (through a gated grating for modulation). The results indicate that the charge screening for graphene is not much different from the 2DEG.

Effect of a periodic electrostatic potential on magnetized particle transport

A classical trajectory Monte Carlo study is reported regarding the motion of a charged particle that is caused to drift across a magnetic field toward an artificially structured boundary, which produces a spatially periodic electrostatic potential. It is found that, for the system studied, the drift toward the boundary is inhibited if the particle’s speed associated with motion parallel to the magnetic field is much larger than the particle’s speed associated with cyclotron motion. The results are not dependent on the particle’s sign of charge. Possible implications for magnetic confinement of beams or plasmas are discussed.

Modelling of Lévy walk kinetics of charged particles in edge electrostatic turbulence in tokamaks

We model and discuss the possible types of motion that charged particles may undergo in a stationary and spatially periodic electrostatic potential and a homogeneous magnetic field. The model is considered to be the simplest approximation of more complex phenomena of plasma edge turbulence in tokamaks. Therein, low frequency turbulence appears in the plasma edge, resulting in a fluctuation of the electron density, and also in the generation of a turbulent electrostatic field. Typical parameters of this turbulent electrostatic field are an electrical potential amplitude of 10–100 V and wave numbers k≈103 m-1. In our model, we consider these regimes, together with a homogeneous magnetic field with a magnitude of 1 T. We investigate the dynamics of singly-ionized carbon ions – a typical plasma impurity – with kinetic energies on the order of 10 eV. Besides the obvious Larmor and drift motions, a motion of random-walk and of Levy walk character appear therein. All of these types of motion can play an important role in the modelling of the anomalous diffusion of particles from the plasma edge turbulence region. The dynamics mentioned will cause an inevitable escape of energetic particles and thus of power loss from the thermonuclear reactor. Moreover, Levy walk kinetics represents a very interesting kind of kinetics, currently of great interest, which was previously not so often discussed.

Electronically modulated two-dimensional plasmons coupled to surface plasmon modes

We present a calculation for a two-dimensional (2D) electron gas layer interacting with a slab of conductive material. We treat the plasmons in the slab in the local limit and obtain the frequency of the coupled mode corresponding to the extended 2D plasmon interacting with the background plasmons in the presence of a conducting surface. The dispersion equation of a double quantum well is obtained and we show how the split symmetric and antisymmetric modes are formed and modified by the localized surface plasmon. For a single layer, we show that when a one-dimensional (1D) periodic electrostatic potential is applied to the surface, each of the symmetric and antisymmetric modes will be further split by the interaction with the 1D modulation, leading to folding of plasmon dispersion curves for different modes. For double layers, we show that the coupled 2D and surface plasmons may result in radiated energy. Our analysis is based on a calculation of the surface response function obtained using a transfer-matrix method.

Spin-orbit lateral superlattices: Energy bands and spin polarization in 2DEG

The Bloch spinors, energy spectrum, and spin density in energy bands are studied for a two-dimensional electron gas (2DEG) with Rashba spin-orbit (SO) interaction subject to the one-dimensional (1D) periodic electrostatic potential of a lateral superlattice. The space symmetry of the Bloch spinors with spin parity is studied. It is shown that the Bloch spinors at fixed quasi-momentum describe the standing spin waves with the wavelength equal to the superlattice period. The spin projections in these states have components both parallel and transverse to the 2DEG plane. The anticrossing of the energy dispersion curves due to the interplay between the SO and periodic terms is observed, thus, leading to the spin flip. The relation between the spin parity and the interband optical selection rules is discussed, and the effect of magnetization of the SO superlattice in the presence of an external electric field is predicted.