Exciton States in Narrow-Gap Carbon Nanotubes

Quasi-exact solutions to the quantum relativistic two-body problem are obtained for a one-dimensional Woods-Saxon-like potential. The quantised positive energy spectrum is obtained in the square well potential limit in terms of a set of simple transcendental equations. This potential is used to calculate excitonic states in narrow-gap single-walled carbon nanotubes and the binding energy is shown to scale with the band gap.This work was supported by the EU H2020 RISE project CoExAN (Grant No. H2020-644076), EU FP7 ITN NOTEDEV (Grant No. FP7-607521), FP7 IRSES projects CANTOR (Grant No. FP7-612285), QOCaN (Grant No. FP7-316432), and InterNoM (Grant No. FP7-612624). R.R.H. acknowledges financial support from URCO (Grant No. 15 F U/S 1TAY13-1TAY14) and Research Links Travel Grant by the British Council Newton Fund

Trapping Charge Carriers in Low-Dimensional Dirac Materials

This is the author accepted manuscript. The final version is available from World Scientific Publishing via the DOI in this recordWe consider the problem of confining the famously elusive Dirac-like quasiparticles, as found in some recently discovered low-dimensional systems. After briefly surveying the existing theoretical proposals for creating bound states in Dirac materials, we study relativistic excitations with a position-dependent mass term. With the aid of an exactly-solvable model, we show how bound states begin to emerge after a critical condition on the size of the mass term is met. We also reveal some exotic properties of the unusual confinement discovered, including an elegant chevron structure of the bound state energies as a function of the size of the mass.Juan de la Cierva program (MINECO, Spain)EU H2020 RISE project CoExANITMO Fellowship and Professorship Progra

Magnetic quantum dots and rings in two dimensions

This is the final version of the article. Available from the publisher via the DOI in this record.We consider the motion of electrons confined to a two-dimensional plane with an externally applied perpendicular inhomogeneous magnetic field, both with and without a Coulomb potential. We find that as long as the magnetic field is slowly decaying, bound states in magnetic quantum dots are indeed possible. Several example cases of such magnetic quantum dots are considered in which one can find the eigenvalues and eigenfunctions in closed form, including two hitherto unknown quasi-exactly-solvable models treated with confluent and biconfluent Heun polynomials. It is shown how a modulation of the strength of the magnetic field can exclude magnetic vortexlike states, rotating with a certain angular momenta and possessing a definite spin orientation, from forming. This indicates one may induce localization-delocalization transitions and suggests a mechanism for spin separation

Double-Gated Nanohelix as a Novel Tunable Binary Superlattice

This is the final version. Available on open access from Springer via the DOI in this recordAvailability of data and materials: The data for the figures all stem from numerically diagonalizing the matrix described by Eq. 5 and can readily be achieved in any numerical software package. With this in mind, the datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.We theoretically investigate the problem of an electron confined to a nanohelix between two parallel gates modelled as charged wires. The double-gated nanohelix system is a binary superlattice with properties highly sensitive to the gate voltages. In particular, the band structure exhibits energy band crossings for certain combinations of gate voltages, which could lead to quasi-relativistic Dirac-like phenomena. Our analysis for optical transitions induced by linearly and circularly polarized light suggests that a double-gated nanohelix can be used for versatile optoelectronic applications.European Union Horizon 2020Engineering and Physical Sciences Research Council (EPSRC)Government of the Russian Federatio

Optical selection rules of zigzag graphene nanoribbons

PublishedThis is the final version of the article. Available from American Physical Society via the DOI in this record.We present an analytical tight-binding theory of the optical properties of graphene nanoribbons with zigzag edges. Applying the transfer matrix technique to the nearest-neighbor tight-binding Hamiltonian, we derive analytical expressions for electron wave functions and optical transition matrix elements for incident light polarized along the structure axis. It follows from the obtained results that optical selection rules result from the wave function parity factor (−1)J, where J is the band number. These selection rules are that ΔJ is odd for transitions between valence and conduction subbands and that ΔJ is even for transitions between only valence (conduction) subbands. Although these selection rules are different from those in armchair carbon nanotubes, there is a hidden correlation between absorption spectra of the two structures that should allow one to use them interchangeably in some applications. The correlation originates from the fact that van Hove singularities in the tubes are centered between those in the ribbons if the ribbon width is about a half of the tubes circumference. The analysis of the matrix elements dependence on the electron wave vector for narrow ribbons shows a smooth nonsingular behavior at the Dirac points and the points where the bulk states meet the edge states.This work was supported by the EU FP7 ITN NOTEDEV (Grant No. FP7-607521), EU H2020 RISE project CoExAN (Grant No. H2020-644076), FP7 IRSES projects CANTOR (Grant No. FP7-612285), QOCaN (Grant No. FP7-316432), InterNoM (Grant No. FP7-612624), and Graphene Flagship (Grant No. 604391). The authors are very thankful to R. Keens and C. A. Downing for a careful reading of the manuscript and to A. Shytov and K. G. Batrakov for useful advice and fruitful discussions

Optical absorption in two-dimensional materials with tilted Dirac cones

This is the final version. Available from the American Physical Society via the DOI in this recordThe interband optical absorption of linearly polarised light by two-dimensional (2D) semimetals hosting tilted and anisotropic Dirac cones in the bandstructure is analysed theoretically. Super- critically tilted (type-II) Dirac cones are characterised by an absorption that is highly dependent on the incident photon polarisation and frequency, and is tunable by changing the Fermi level with a back-gate voltage. Type-II Dirac cones exhibit open Fermi surfaces and large regions of the Brillouin zone where the valence and conduction bands sit either above or below the Fermi level. As a consequence, unlike their sub-critically tilted (type-I) counterparts, type-II Dirac cones have many states that are Pauli blocked even when the Fermi level is tuned to the level crossing point. We analyse the interplay of the tilt parameter with the Fermi velocity anisotropy, demonstrating that the optical response of a Dirac cone cannot be described by its tilt alone. As a special case of our general theory we discuss the proposed 2D type-I semimetal 8-Pmmn Borophene. Guided by our in-depth analytics we develop an optical recipe to fully characterise the tilt and Fermi velocity anisotropy of any 2D tilted Dirac cone solely from its absorption spectrum. We expect our work to encourage Dirac cone engineering as a major route to create gate-tunable thin-film polarisers.European Union Horizon 2020Engineering and Physical Sciences Research Council (EPSRC)NATORoyal Societ

Hidden correlation between absorption peaks in achiral carbon nanotubes and nanoribbons

This is the final version. Available on open access from Elsevier via the DOI in this recordIn this paper we study the effect of absorption peak correlation in finite length carbon nanotubes and graphene nanoribbons. It is shown, in the orthogonal {\pi}-orbital tight-binding model with the nearest neighbor approximation, that if the ribbon width is a half of the tube circumference the effect takes place for all achiral ribbons (zigzag, armchair and bearded), and corresponding tubes, starting from lengths of about 30 nm. This correlation should be useful in designing nanoribbon-based optoelectronics devices fully integrated into a single layer of graphene.This work was supported by the EU FP7 ITN NOTEDEV (Grant No. FP7-607521), EU H2020 RISE project CoExAN (Grant No. H2020-644076), FP7 IRSES projects CANTOR (Grant No. FP7-612285), QOCaN (Grant No. FP7-316432), InterNoM (Grant No. FP7-612624); Graphene Flagship (Grant No. 604391) and partially by the Belarus state program of scientific investigations “Convergence-2020”

Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential

This is the final version. Available from the American Physical Society via the DOI in this recordThe double-well problem for the two-dimensional Dirac equation is solved for a family of quasi-one-dimensional potentials in terms of confluent Heun functions. We demonstrate that for a double well separated by a barrier, both the energy level splitting associated with the wavefunction overlap of well states, and the gap size of the avoided crossings associated with well and barrier state repulsion, can be controlled via the parameters of the potential. The transitions between the two states comprising a doublet, as well as transitions across the pseudo-gaps are strongly allowed, highly anisotropic, and for realistic graphene devices can be tuned to fall within the highly desirable terahertz frequency range.European Union Horizon 2020URCOMinistry of Science and Higher Education of the Russian Federation, Goszadani

Quantum confinement in Dirac-like nanostructures

This is the author accepted manuscript. The final version is available from Academic Press via the DOI in this record In Westminster Abbey, in a nave near to Newton’s monument, lies a memorial stone to Paul Dirac. The inscription on the stone includes the relativistic wave equation for an electron: the Dirac equation. At the turn of the 21st century, it was discovered that this eponymous equation was not simply the preserve of particle physics. The isolation of graphene by Andre Geim and Konstantin Novoselov in Manchester led to the exploration of a novel class of materials – Dirac materials - whose electrons behave like Dirac particles. While the mobility of these quasi-relativistic electrons is attractive from the perspective of potential ultrafast devices, it also presents a distinct challenge: how to confine Dirac particles so as to avoid making inherently leaky devices? Here we discuss the unconventional quantum tunnelling of Dirac particles, we explain a strategy to create bound states electrostatically, and we briefly review some pioneering experiments seeking to trap Dirac electrons

Bipolar electron waveguides in two-dimensional materials with tilted Dirac cones

This is the author accepted manuscript. The final version is available from IOP Publishing via the DOI in this recordData availability statement: No new data were created or analysed in this study.We show that the (2+1)-dimensional massless Dirac equation, which includes a tilt term, can be reduced to the biconfluent Heun equation for a broad range of scalar confining potentials, including the well-known Morse potential. Applying these solutions, we investigate a bipolar electron waveguide in 8--$Pmmn$ borophene, formed by a well and barrier, both described by the Morse potential. We demonstrate that the ability of two-dimensional materials with tilted Dirac cones to localize electrons in both a barrier and a well can be harnessed to create pseudogaps in their electronic spectrum. These pseudogaps can be tuned through varying the applied top-gate voltage. Potential opto-valleytronic and terahertz applications are discussed.NATOEuropean Union Horizon 2020Engineering and Physical Sciences Research Council (EPSRC)URC