Mapping borophene onto graphene: Quasi-exact solutions for guiding potentials in tilted Dirac cones

Abstract

We show that if the solutions to the (2+1)-dimensional massless Dirac equation for a given 1D potential are known, then they can be used to obtain the eigenvalues and eigenfunctions for the same potential, orientated at an arbitrary angle, in a tilted anisotropic 2D Dirac material. This simple set of transformations enables all the exact and quasi-exact solutions associated with 1D quantum wells in graphene to be applied to the confinement problem in tilted Dirac materials such as borophene. We also show that smooth electron waveguides in tilted Dirac materials can be used to manipulate the degree of valley polarization of quasiparticles travelling along a particular direction of the channel. We examine the particular case of the hyperbolic secant potential to model realistic top-gated structures for valleytronic applications.

arXiv comment12 pages, 5 figures and 1 Supplementary Material

References in corpus (67)

• The electronic properties of graphene
• Spintronics: Fundamentals and applications
• Valley filter and valley valve in graphene
• Transport measurements across a tunable potential barrier in graphene
• Semimetallic Two-Dimensional Boron Allotrope with Massless Dirac Fermions
• Electronic transport and quantum Hall effect in bipolar graphene p-n-p junction
• Pressure-Induced Zero-Gap Semiconducting State in Organic Conductor $\alpha$-(BEDT-TTF)${}_2$I${}_3$ Salt
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Review of borophene and its potential applications
• Gate-controlled Guiding of Electrons in Graphene
• Quasi-exactly solvable quartic potential
• Conductance of p-n-p graphene structures with 'air-bridge' top gates
• Strain-induced pseudomagnetic field in Dirac semimetal borophene
• Smooth electron waveguides in graphene
• Fabrication of Graphene p-n-p Junctions with Contactless Top Gates
• Anisotropic carrier mobility of distorted Dirac cones: theory and application
• On a solution of the Schrodinger equation with a hyperbolic double-well potential
• Effect of electron-hole asymmetry on optical conductivity in 8-Pmmn borophene
• Quasi-exact solution to the Dirac equation for the hyperbolic secant potential
• Topological and Transport Properties of Dirac Fermions in Antiferromagnetic Metallic Phase of Iron-Based Superconductors
• Guiding of Electrons in a Few Mode Ballistic Graphene Channel
• Klein tunneling and electron optics in Dirac-Weyl fermion systems with tilted energy dispersion
• Oblique Klein tunneling in 8-Pmmn borophene p-n junctions
• The $8Pmmn$ borophene sheet: A solid-state platform for space-time engineering
• Optical properties of massive anisotropic tilted Dirac systems
• One-dimensional Coulomb problem in Dirac materials
• Signature of tilted Dirac cones in Weiss oscillations of $8-Pmmn$ borophene
• Metal-Insulator transition in 8-Pmmn Borophene under perpendicular incidence of electromagnetic radiation
• Probing quantum criticality using nonlinear Hall effect in a metallic Dirac system
• Type-II Dirac surface states in topological crystalline insulators
• Anisotropic longitudinal optical conductivities of tilted Dirac bands in 1T${}^{\prime }$-MoS${}_2$
• Tilt-induced kink in the plasmon dispersion of two-dimensional Dirac electrons
• Electric field assisted amplification of magnetic fields in tilted Dirac cone systems
• Magnetotransport properties of 8-Pmmn borophene: effects of Hall field and strain
• Two-dimensional Dirac particles in a Pöschl-Teller waveguide
• Electrically tunable valley polarization in Weyl semimetals with tilted energy dispersion
• Guiding Dirac fermions in graphene with a carbon nanotube
• Fingerprints of tilted Dirac cones on the RKKY exchange interaction in 8-Pmmn Borophene
• Bound states in a hyperbolic asymmetric double-well
• Effects of the Dirac cone tilt in two-dimensional Dirac semimetal
• Polarization tensor for tilted Dirac fermion materials: Covariance in deformed Minkowski spacetime
• Dynamical band gap tuning in Weyl semi-metals by intense elliptically polarized normal illumination and its application to $8-Pmmn$ borophene
• Anomalous caustics and Veselago focusing in 8-Pmmn borophene p-n junctions with arbitrary junction directions
• Kubo conductivity for anisotropic tilted Dirac semimetals and its application to 8-Pmmn borophene: The role of different frequency, temperature and scattering limits
• Levinson theorem for Dirac particles in one dimension
• Two-dimensional type-II Dirac fermions in a LaAlO3/LaNiO3/LaAlO3 quantum well
• Synthetic non-Abelian gauge fields and gravitomagnetic effects in tilted Dirac cone systems
• Thermoelectric transport properties of borophane
• Anomalous heat flow in 8-$Pmmn$ borophene with tilted Dirac cones
• Valley caloritronics in a photodriven hetero-junction of Dirac materials
• The Strong Levinson Theorem for the Dirac Equation
• Floquet spectrum for anisotropic and tilted Dirac materials under linearly polarized light at all field intensities
• Perpendicular Andreev reflection: Solid state signature of black hole horizon
• Velocity-determined anisotropic behaviors of RKKY interaction in 8-\textit{Pmmn} borophene
• Electrically charged Andreev modes in two-dimensional tilted Dirac cone systems
• Bipolar electron waveguides in graphene
• Pair states in one-dimensional Dirac systems
• Oblique and asymmetric Klein tunneling across smooth NP junctions or NPN junctions in 8-Pmmn borophene
• Carbon nanotube array as a van der Waals two-dimensional hyperbolic material
• Chemical-Strain Induced Tilted Dirac Nodes in (BEDT-TTF)${}_2$X${}_3$ (X = I, Cl, Br, F) Based Charge-Transfer Salts
• Nonlinear and anisotropic polarization rotation in two dimensional Dirac materials
• A new coupling mechanism between two graphene electron waveguides for ultrafast switching
• Undamped transverse electric mode in undoped two-dimensional tilted Dirac cone materials
• Spin Transport and Spin Pump in Graphene-like Materials: Effect of tilt in Dirac cones
• Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential
• Anomalous Lorenz number in massive and tilted Dirac systems
• Tunable wavevector filtering in borophane based normal metal-barrier-normal metal junctions

Cited by in corpus (4)

• Signatures of Lifshitz transition in the optical conductivity of two-dimensional tilted Dirac materials
• Optical valley separation in two-dimensional semimetals with tilted Dirac cones
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
• Designer gapped and tilted Dirac cones in lateral graphene superlattices