Emergence of bound states in ballistic magnetotransport of graphene antidots

An experimental method for detection of bound states around an antidot formed from a hole in a graphene sheet is proposed by measuring the ballistic two terminal conductances. In particularly, we consider the effect of bound states formed by magnetic field on the two terminal conductance and show that one can observe Breit-Wigner like resonances in the conductance as a function of the Fermi level close to the energies of the bound states. In addition, we develop a new numerical method in which the computational effort is proportional to the linear dimensions, instead of the area of the scattering region beeing typical for the existing numerical recursive Green's function method.Comment: 7 pages, 6 figure

Peculiar Nature of Snake States in Graphene

We study the dynamics of the electrons in a non-uniform magnetic field applied perpendicular to a graphene sheet in the low energy limit when the excitation states can be described by a Dirac type Hamiltonian. We show that as compared to the two-dimensional electron gas (2DEG) snake states in graphene exibit peculiar properties related to the underlying dynamics of the Dirac fermions. The current carried by snake states is locally uncompensated even if the Fermi energy lies between the first non-zero energy Landau levels of the conduction and valence bands. The nature of these states is studied by calculating the current density distribution. It is shown that besides the snake states in finite samples surface states also exist.Comment: 4 pages, 5 figure

Effect of the band structure topology on the minimal conductivity for bilayer graphene with symmetry breaking

Using the Kubo formula we develop a general and simple expression for the minimal conductivity in systems described by a 2×2 Hamiltonian. As an application we derive an analytical expression for the minimal conductivity tensor of bilayer graphene as a function of a complex parameter w related to recently proposed symmetry breaking mechanisms resulting from electron-electron interaction or strain applied to the sample. The number of Dirac points changes with varying parameter w, and this directly affects the minimal conductivity. Our analytic expression is confirmed using an independent calculation based on the Landauer approach, and we find remarkably good agreement between the two methods. We demonstrate that the minimal conductivity is very sensitive to the change of the parameter w and the orientation of the electrodes with respect to the sample. Our results show that the minimal conductivity is closely related to the topology of the low-energy band structure

Electronic standing waves on the surface of the topological insulator Bi2Te3

A line defect on a metallic surface induces standing waves in the electronic local density of states (LDOS). Asymptotically far from the defect, the wave number of the LDOS oscillations at the Fermi energy is usually equal to the distance between nesting segments of the Fermi contour, and the envelope of the LDOS oscillations shows a power-law decay as moving away from the line defect. Here, we theoretically analyze the LDOS oscillations close to a line defect on the surface of the topological insulator Bi2Te3, and identify an important pre-asymptotic contribution with wave number and decay characteristics markedly different from the asymptotic contributions. Wave numbers characterizing the pre-asymptotic LDOS oscillations are in good agreement with recent data from scanning tunneling microscopy experiments [Phys. Rev. Lett. 104, 016401 (2010)].Comment: 8 pages, 5 figures; published versio

Intrinsic Spin-Orbit Interaction in Graphene

In graphene, we report the first theoretical demonstration of how the intrinsic spin orbit interaction can be deduced from the theory and how it can be controlled by tuning a uniform magnetic field, and/or by changing the strength of a long range Coulomb like impurity (adatom), as well as gap parameter. In the impurity context, we find that intrinsic spin-orbit interaction energy may be enhanced by increasing the strength of magnetic field and/or by decreasing the band gap mass term. Additionally, it may be strongly enhanced by increasing the impurity strength. Furthermore, from the proposal of Kane and Mele [Phys. Rev. Lett. 95, 226801 (2005)], it was discussed that the pristine graphene has a quantized spin Hall effect regime where the Rashba type spin orbit interaction term is smaller than that of intrinsic one. Our analysis suggest the nonexistence of such a regime in the ground state of flat graphene

Electrically tunable transverse magnetic focusing in graphene

Author's final manuscript January 9, 2013Electrons in a periodic lattice can propagate without scattering for macroscopic distances despite the presence of the non-uniform Coulomb potential due to the nuclei. Such ballistic motion of electrons allows the use of a transverse magnetic field to focus electrons. This phenomenon, known as transverse magnetic focusing (TMF), has been used to study the Fermi surface of metals and semiconductor heterostructures, as well as to investigate Andreev reflection and spin–orbit interaction, and to detect composite fermions. Here we report on the experimental observation of TMF in high-mobility mono-, bi- and tri-layer graphene devices. The ability to tune the graphene carrier density enables us to investigate TMF continuously from the hole to the electron regime and analyse the resulting focusing fan. Moreover, by applying a transverse electric field to tri-layer graphene, we use TMF as a ballistic electron spectroscopy method to investigate controlled changes in the electronic structure of a material. Finally, we demonstrate that TMF survives in graphene up to 300 K, by far the highest temperature reported for any system, opening the door to new room-temperature applications based on electron-optics.National Science Foundation (U.S.) (CAREER Award DMR-0845287)United States. Office of Naval Research. GATE MURI Projec

Landau Levels and Edge States in Graphene with Strong Spin-Orbit Coupling

We investigate the electronic properties of graphene in a magnetic and a strain-induced pseudo-magnetic field in the presence of strong spin-orbit interactions (SOI). For a homogeneous field we provide analytical results for the Landau level eigenstates for arbitrary intrinsic and Rashba SOI, including also the effect of a Zeeman field. We then study the edge states in a semi-infinite geometry in the absence of the Rashba term. We find that, for a critical value of the magnetic field, a quantum phase transition occurs, which separates two phases both with spin-filtered helical edge states but with opposite direction of the spin current. Finally,we discuss magnetic waveguides with inhomogeneous field profiles that allow for chiral snake orbits. Such waveguides are practically immune to disorder-induced backscattering, and the SOI provides non-trivial spin texture to these modes

Quantum interference and nonequilibrium josephson currents in molecular andreev interferometers

We study the quantum interference (QI) effects in three-terminal Andreev interferometers based on polyaromatic hydrocarbons (PAHs) under non-equilibrium conditions. The Andreev interferometer consists of a PAH coupled to two superconducting and one normal conducting terminals. We calculate the current measured in the normal lead as well as the current between the superconducting terminals under non-equilibrium conditions. We show that both the QI arising in the PAH cores and the bias voltage applied to a normal contact have a fundamental effect on the charge distribution associated with the Andreev Bound States (ABSs). QI can lead to a peculiar dependence of the normal current on the superconducting phase difference that was not observed in earlier studies of mesoscopic Andreev interferometers. We explain our results by an induced asymmetry in the spatial distribution of the electron-and hole-like quasiparticles. The non-equilibrium charge occupation induced in the central PAH core can result in a π transition in the current-phase relation of the supercurrent for large enough applied bias voltage on the normal lead. The asymmetry in the spatial distribution of the electron-and hole-like quasiparticles might be used to split Cooper pairs and hence to produce entangled electrons in four terminal setups. © 2020 by the authors. Licensee MDPI, Basel, Switzerland