We present exact analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions fully confined within a smooth one-dimensional potential $V(x)=\ensuremath{-}\ensuremath{\alpha}/\text{cosh}(\ensuremath{\beta}x)$, which provides good fit profiles existing top-gated graphene structures. show that there is threshold value characteristic strength $\ensuremath{\alpha}/\ensuremath{\beta}$ first mode appears, in striking contrast to nonrelativistic case. A simple...

We demonstrate theoretically that quasi-metallic carbon nanotubes emit terahertz radiation induced by an applied voltage. It is shown in the ballistic transport regime their spontaneous emission spectra have a universal frequency and bias voltage dependence, which raises possibility of utilizing this effect for high-frequency nanoelectronic devices.

We present exact analytical zero-energy solutions for a class of smooth-decaying potentials, showing that the full confinement charge carriers in electrostatic potentials graphene quantum dots and rings is indeed possible without recourse to magnetic fields. These allow us draw conclusions on general requirements potential support fully confined states, including critical value strength spatial extent.

We analyze bound modes of two-dimensional massless Dirac fermions confined within a hyperbolic secant potential, which provides good fit for potential profiles existing top-gated graphene structures. show that states both positive and negative energies exist in the energy spectrum there is threshold value characteristic strength first mode appears. Analytical solutions are presented several limited cases supercriticality discussed.

We investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. obtain exact solution shifted and truncated problems, wave functions expressed in terms special (namely, Whittaker functions), while energy spectrum must be determined via solutions transcendental equations. Most notably, there are critical band gaps below which certain low-lying quantum states missing manifestation...

Searching for new states of matter and unusual quasiparticles in emerging materials especially low-dimensional systems is one the major trends contemporary condensed physics. Dirac materials, which host are described by ultrarelativistic Dirac-like equations, a significant current interest from both fundamental applied physics perspective. Here we show that pair two-dimensional massless Dirac-Weyl fermions can form bound state independently sign inter-particle interaction potential, as long...

We study electronic and optical properties of single layer phosphorene quantum dots with various shapes, sizes, edge types (including disordered edges) subjected to an external electric field normal the structure plane. Compared graphene dots, in clusters similar shape size there is a set states energies dispersed at around Fermi level. These make majority metallic enrich absorption gap low-energy peaks tunable by field. The presence level characteristic feature that independent morphology roughness.

We present an analytical tight-binding theory of the optical properties graphene nanoribbons with zigzag edges. Applying transfer matrix technique to nearest-neighbor Hamiltonian, we derive expressions for electron wave functions and transition elements incident light polarized along structure axis. It follows from obtained results that selection rules result function parity factor ${(\ensuremath{-}1)}^{J}$, where $J$ is band number. These are $\mathrm{\ensuremath{\Delta}}J$ odd transitions...

We show how it is possible to trap two-dimensional massless Dirac fermions in spatially inhomogeneous magnetic fields, as long the formed quantum dot (or ring) of a slowly decaying nature. It found that modulation depth leads successive confinement-deconfinement transitions vortexlike states with certain angular momentum, until regime reached where only one sign momentum are supported. illustrate these characteristics both exact solutions and hitherto unknown quasi-exactly solvable model...

The interband optical absorption of linearly polarized light by two-dimensional (2D) semimetals hosting tilted and anisotropic Dirac cones in the band structure is analysed theoretically. Supercritically (type-II) are characterized an that highly dependent on incident photon polarization frequency tunable changing Fermi level with a back-gate voltage. Type-II exhibit open surfaces large regions Brillouin zone where valence conduction bands sit either above or below level. As consequence,...

The bound state energy eigenvalues for the two-dimensional Kepler problem are found to be degenerate. This "accidental" degeneracy is due existence of a analogue quantum-mechanical Runge-Lenz vector. Reformulating in momentum space leads an integral form Schroedinger equation. equation solved by projecting onto surface three-dimensional sphere. eigenfunctions then expanded terms spherical harmonics, and this relation special functions which has not previously been tabulated. dynamical...

Electron motion in a (n,1) carbon nanotube is shown to correspond de Broglie wave propagating along helical line on the wall. This leads periodicity of electron potential energy presence an electric field normal axis. The period this proportional radius and greater than interatomic distance nanotube. As result, behavior subject transverse similar that semiconductor superlattice. In particular, Bragg scattering electrons from long-range periodic results opening gaps spectrum Modification...

We propose and justify two schemes utilizing the unique electronic properties of carbon nanotubes for novel THz applications including tunable generation by hot electrons in quasi-metallic radiation detection armchair strong magnetic fields.

We investigated several proposals utilizing the unique electronic properties of carbon nanotubes (CNTs) for a broad range applications to THz optoelectronics, including generation by Cerenkov-type emitters based on and hot electrons in quasimetallic nanotubes, frequency multiplication chiral-nanotube-based superlattices controlled transverse electric field, radiation detection emission armchair strong magnetic field. Dispersion equations electron beam instability threshold conditions...

We study analytically the optical properties of a simple model for an electron-hole pair on ring subjected to perpendicular magnetic flux and in-plane electric field. show how tune this excitonic system from optically active dark as function these external fields. Our results offer mechanism exciton storage readout.

We calculate the exciton binding energy in single-walled carbon nanotubes with narrow band gaps, accounting for quasirelativistic dispersion of electrons and holes. Exact analytical solutions quantum relativistic two-body problem are obtained several limiting cases. show that scales gap, conclude on basis data available semiconductor there is no transition to an excitonic insulator quasimetallic their THz applications feasible.

Using the variable phase method, we reformulate Dirac equation governing charge carriers in graphene into a nonlinear first-order differential from which can treat both confined-state problems electron waveguides and above-barrier scattering for arbitrary-shaped potential barriers wells, decaying at large distances. We show that this method agrees with known analytic result hyperbolic secant go on to investigate nature of more experimentally realizable waveguides, showing when Fermi energy...

We show that strong light–matter coupling can be used to overcome a long-standing problem has prevented efficient optical emission from carbon nanotubes. The luminescence the nominally bright exciton state of nanotubes is quenched due fast nonradiative scattering dark having lower energy. present theoretical analysis by placing in an microcavity excitonic may split into two hybrid exciton–polariton states, while remains unaltered. For sufficiently between and cavity, we energy polariton...

Magneto-oscillations of the electric dipole moment are predicted and analyzed for a single-electron nanoscale ring pierced by magnetic flux (an Aharonov-Bohm ring) subjected to an field in ring's plane. These oscillations accompanied periodic changes selection rules interlevel optical transitions allowing control polarization properties associated terahertz radiation.

The electrons found in Dirac materials are notorious for being difficult to manipulate due the Klein phenomenon and absence of backscattering. Here we investigate how spatial modulations Fermi velocity two-dimensional can give rise localization effects, with either full (zero-dimensional) confinement or partial (one-dimensional) possible depending on geometry modulation. We present several exactly solvable models illustrating nature bound states which arise, revealing gradient is crucial...

We obtain exact solutions to the two-dimensional (2D) Dirac equation for one-dimensional Pöschl-Teller potential which contains an asymmetry term. The eigenfunctions are expressed in terms of Heun confluent functions, while eigenvalues determined via a simple transcendental equation. For symmetric case, supercritical states as spheroidal wave and approximate analytical expressions obtained corresponding eigenvalues. A universal condition any square integrable is minimum strength required...

We consider the motion of electrons confined to a two dimensional plane with an externally applied perpendicular inhomogeneous magnetic field, both and without Coulomb potential. find that as long field is slowly-decaying, bound states in quantum dots are indeed possible. Several example cases such considered which one can eigenvalues eigenfunctions closed form, including hitherto unknown quasi-exactly solvable models treated confluent biconfluent Heun polynomials. It shown how modulation...

We studied monatomic linear carbon chains stabilized by gold nanoparticles attached to their ends and deposited on a solid substrate. observe spectral features of straight containing from 8 24 atoms. Low-temperature PL spectra reveal characteristic triplet fine structures that repeat themselves for different lengths. The is invariably composed sharp intense peak accompanied two broader satellites situated 15 40 meV below the main peak. interpret these resonances as an edge-state neutral...