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The non-equilibrium steady states of a semi-infinite quasi-one-dimensional univalent binary electrolyte solution, characterised by non-vanishing electric currents, are investigated by means of Poisson-Nernst-Planck (PNP) theory. Exact…
For the structure of the thin electrical double layer~(EDL) and the property related to the EDL capacitance, we analyze boundary layer solutions (corresponding to the electrostatic potential) of a non-local elliptic equation which is a…
The electronic structure of the zig-zag bilayer strip is analyzed. The electronic spectra of the bilayer strip is computed. The dependence of the edge state band flatness on the bilayer width is found. The density of states at the Fermi…
Electronic, transport, and spin properties of grain boundaries (GBs) are investigated in electrostatically doped graphene at finite electron densities within the Hartree and Hubbard approximations. We demonstrate that depending on the…
The electronic density of states of graphene is equivalent to that of relativistic electrons. In the absence of disorder or external doping the Fermi energy lies at the Dirac point where the density of states vanishes. Although transport…
Ferroelectricity has recently been demonstrated in germanium-based inorganic halide perovskites. We use atomistic first-principles-based simulations to study ultra-thin CsGeBr$_3$ films with thicknesses of 4-18 nm and develop a theory for…
In this work, low-energy electron microscopy is employed to probe structural as well as electronic information in few-layer WSe$_2$ on epitaxial graphene on SiC. The emergence of unoccupied states in the WSe$_2$--graphene heterostructures…
We present an analytic theory of the spin-resolved pair distribution functions $g_{\sigma\sigma'}(r)$ and the ground-state energy of an electron gas with an arbitrary degree of spin polarization. We first use the Hohenberg-Kohn variational…
The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon…
We revisit the uniaxially strained graphene immersed in a uniform homogeneous magnetic field orthogonal to the layer in order to describe the time evolution of coherent states build from a semi-classical model. We consider the symmetric…
The virial theorem is applied to graphene and other Dirac Materials for systems close to the Dirac points where the dispersion relation is linear. From this, we find the exact form for the total energy given by $E = \mathcal{B}/r_s$ where…
Determining the electronic properties of nanoscopic, low-dimensional materials free of external influences is key to discovery and understanding of new physical phenomena. An example is the suspension of graphene, which has allowed access…
Graphene, the first truly two-dimensional (one atom thin) material, possesses strongly nonlinear electrodynamic and optical properties. At low (microwave, terahertz) frequencies this results from the unique electronic property of graphene -…
The polarization state of the optical electromagnetic field lying several nanometers above complex dielectric structures reveals the intricate light-matter interaction that occurs in this near-field zone. This information can only be…
Current research presents an innovative model of half-space plasmon excitations for electron gas of arbitrary degeneracy in an ambient jellium-like positive background . The linearized Schr\"{o}dinger-Poisson system is used to derive…
Two-dimensional ferroelectrics can maintain vertical polarization up to room temperature, and are, therefore, promising for next-generation nonvolatile memories. Although natural two-dimensional ferroelectrics are few, moir\'{e}…
Charge impurities in graphene can host an infinite family of Rydberg-like resonance states of massless Dirac particles. These states, appearing for supercritical charge, are described by Bohr-Sommerfeld quantization of collapsing classical…
The calculation of the polarization in ferroelectric thin films is performed using an analytical solution of the Euler-Lagrange differential equation with boundary conditions with different extrapolation lengths of positive sign on the…
We present a theory of the pair distribution function $g(z)$ and many-body effective electron-electron interaction for one dimensional (1D) electron liquid. Our approach involves the solution of a zero-energy scattering Schr\"odinger…
We study the electronic properties of 2D electron gas (2DEG) with quadratic dispersion and with relativistic dispersion as in graphene in the inhomogeneous magnetic field consisting of the Aharonov-Bohm flux and a constant background field.…