Transport of Massless Dirac Fermions in Non-topological Type Edge States

Latyshev, Yu. I.; Орлов, А. П.; Enaldiev, V. V.; Zagorodnev, I. V.; Vyvenko, O. F.; Petrov, Yu. V.; Monçeau, P.

doi:10.1038/srep07578

Cited by 21 publications

(23 citation statements)

References 42 publications

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“…Periodic arrays of antidots have been studied as a way to open a band gap in graphene [56][57][58] or to obtain waveguiding effects [59,60]. Furthermore, a single perforation in a graphene sheet has been considered as a nanopore for DNA sensing [61,62] and recent studies in magnetic fields have shown the AharonovBohm effect appearing in conducting edge states around a nanohole [63].…”

Section: Vortex Currents Near Perforationsmentioning

confidence: 99%

Patched Green's function techniques for two-dimensional systems: Electronic behavior of bubbles and perforations in graphene

et al. 2015

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We present a numerically efficient technique to evaluate the Green's function for extended two dimensional systems without relying on periodic boundary conditions. Different regions of interest, or 'patches', are connected using self energy terms which encode the information of the extended parts of the system. The calculation scheme uses a combination of analytic expressions for the Green's function of infinite pristine systems and an adaptive recursive Green's function technique for the patches. The method allows for an efficient calculation of both local electronic and transport properties, as well as the inclusion of multiple probes in arbitrary geometries embedded in extended samples. We apply the Patched Green's function method to evaluate the local densities of states and transmission properties of graphene systems with two kinds of deviations from the pristine structure: bubbles and perforations with characteristic dimensions of the order of 10-25 nm, i.e. including hundreds of thousands of atoms. The strain field induced by a bubble is treated beyond an effective Dirac model, and we demonstrate the existence of both Friedel-type oscillations arising from the edges of the bubble, as well as pseudo-Landau levels related to the pseudomagnetic field induced by the nonuniform strain. Secondly, we compute the transport properties of a large perforation with atomic positions extracted from a TEM image, and show that current vortices may form near the zigzag segments of the perforation.

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Section: Vortex Currents Near Perforationsmentioning

confidence: 99%

Patched Green's function techniques for two-dimensional systems: Electronic behavior of bubbles and perforations in graphene

et al. 2015

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“…For the indirect interband photon emission to dominate over the "normal" Drude absorption, the long-wave length Fourier components of the scattering potential should prevail. Such kind of scattering potentials can be formed also by extended surface corrugations, quantum dots on the graphene bilayer surface [35], and nanohole arrays [36,37].…”

mentioning

confidence: 99%

Negative terahertz conductivity in disordered graphene bilayers with population inversion

Svintsov

Otsuji

Mitin

et al. 2015

Applied Physics Letters

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The gapless energy band spectra make the structures based on graphene and graphene bilayers with the population inversion created by optical or injection pumping to be promising media for the interband terahertz (THz) lasing. However, a strong intraband absorption at THz frequencies still poses a challenge for efficient THz lasing. In this paper, we show that in the pumped graphene bilayer structures, the indirect interband radiative transitions accompanied by scattering of carriers caused by disorder can provide a substantial negative contribution to the THz conductivity (together with the direct interband transitions). In the graphene bilayer structures on high-κ substrates with point charged defects, these transitions almost fully compensate the losses due to the intraband (Drude) absorption. We also demonstrate that the indirect interband contribution to the THz conductivity in a graphene bilayer with the extended defects (such as the charged impurity clusters, surface corrugation, and nanoholes) can surpass by several times the fundamental limit associated with the direct interband transitions and the Drude conductivity. These predictions can affect the strategy of the graphene-based THz laser implementation.The absence of a band gap in the atomically thin carbon structures,such as graphene and graphene bilayers, enables their applications in different terahertz (THz) and infrared devices [1][2][3][4]. One of the most challenging and promising problems is the creation of the graphenebased THz lasers [5][6][7]. These lasers are expected to operate at room temperature, particularly, in the 6-10 THz range, where the operation of III-V quantum cascade lasers is hindered by the optical phonons [8]. Recent pump-probe spectroscopy experiments confirm the possibility of the coherent radiation amplification in the optically pumped graphene [9][10][11][12][13][14][15][16], enabled by a relatively long-living interband population inversion [17]. As opposed to optically pumped graphene lasers, graphenebased injection lasers are expected to operate in the continuous mode, with the interband population inversion maintained by the electron and hole injection from the n-and p-type contacts [18]. A single pumped graphene sheet as the gain medium provides the maximum radiation amplification coefficient corresponding to the quantity 4πσ Q /c = πα = 2.3%, where σ Q = e 2 /4 is the universal optical conductivity of a single graphene layer, e is the electron charge, is the Planck constant and α ≃ 1/137 is the fine-structure constant [17]. The THz

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“…It was found [16] that the spectrum of Tamm-Shockley edge states in graphene is linear with respect to momentum, which is similar to a section of the conical spectrum of SSs in TIs. Moreover, the band character of the conductivity through these states in normal conditions [17] was proved by a direct transport experiment. Let us describe a theory necessary to explain these experiments.…”

Section: Edge States In Graphenementioning

confidence: 99%

“…The wave function of edge states is exponentially localized near the boundary. A typical localization length determined from experiment [17] is 2 nm. The value of a should be determined from comparison with experiment; however, from a comparison with model microscopic calculations [66,67], one should expect that it is small: |a| ≪ 1.…”

Section: Edge States In Graphenementioning

confidence: 99%

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Surface states of a system of dirac fermions: A minimal model

Enaldiev

2016

J. Exp. Theor. Phys.

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A brief survey is given of theoretical works on surface states (SSs) in Dirac materials. Within the formalism of envelope wave functions and boundary conditions for these functions, a minimal model is formulated that analytically describes surface and edge states of various (topological and nontopological) types in several systems with Dirac fermions (DFs). The applicability conditions of this model are discussed. I. THE ENVELOPE-FUNCTION METHOD. INTRODUCTION TO THE HISTORY OF THE PROBLEMBy the middle of the 20-th century, the problem arose of explaining and predicting the electronic properties of semiconductors in external fields. Various versions of the single-band effective-mass method were developed. The Luttinger-Kohn envelope-function (EF) method 1 based on a generalization of the kp-approach turned out to be very convenient. The formalism of EFs admitted a natural multiband generalization. Such a generalization was made by Keldysh in his theory of deep impurities 2. In [2], Keldysh also noticed that, under certain conditions, EFs in a narrow-band semiconductor obey an effective Dirac equation (a system of four first-order differential equations). It is interesting that, in III-V semiconductors, this situation occurs under reversal of the sign of the strong spin-orbit splitting of the valence band. The idea of inversion of bands in crystals with strong spinorbit interaction will be addressed below in this paper. In the same year as [2], it was shown [3] that the spectrum of electrons and holes in bismuth near the L points of the Brillouin zone should be described by an anisotropic Dirac Hamiltonian.According to modern terminology, bismuth can be considered as a Dirac material, and the first Dirac material at that. These materials include graphene, bismuth-antimony alloys, lead chalcogenides, 2D and 3D topological insulators, Dirac semimetals, Weyl semimetals, and many other materials. One-particle excitations in these materials are called massless (for gapless materials) or massive Dirac fermions (DFs).The energy spectrum E(p) of free DFs in the threedimensional isotropic case is analogous to the spectrum of a relativistic electron:Here m is the electron effective mass, which is usually one or two orders of magnitude less than the mass of a free electron in vacuum, and c is the effective velocity of light. This velocity is two orders of magnitude less than the velocity of light in vacuum; therefore, real Fermi excitations are, in fact, non-relativistic. However, relativistic corrections due to spin-orbit interaction in crystals with close bands may be rather large, which contributes to the formation of DFs. A finite mass in the spectrum of relativistic particles corresponds to a finite width of the forbidden band according to the well-known formulaThe 1960s marked the emergence of the physics of 2D electron systems. Quantum size effect was started to be used to realize the 3D → 2D transition. The conventional theory of size quantization is based on the single-band effective mass approximation with zero bou...

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Transport of Massless Dirac Fermions in Non-topological Type Edge States

Cited by 21 publications

References 42 publications

Patched Green's function techniques for two-dimensional systems: Electronic behavior of bubbles and perforations in graphene

Patched Green's function techniques for two-dimensional systems: Electronic behavior of bubbles and perforations in graphene

Negative terahertz conductivity in disordered graphene bilayers with population inversion

Surface states of a system of dirac fermions: A minimal model

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