Recursive Green Function Method Research Articles

Electronic transport in ultranarrow zigzag graphene nanoribbons with edge disorders

We investigate the transport properties of ultranarrow zigzag graphene nanoribbons (ZGNRs) with edge vacancies by using recursive Green's function method. Transport gaps are observed when the vacancies are distributed uniformly on both sides. In addition, ZGNRs with symmetrical structure have much larger transport gaps than the asymmetrical ones. This phenomenon results from the different band structures between them. We also calculate the conductance of ZGNRs with edge vacancies distributed randomly. It shows that transport gaps decrease exponentially with the increasing of ZGNRs width because the symmetry of structure is broken by the random edge vacancies. Localization analysis reveals that the electronic transport channels around Fermi energy are blockaded so that they are not responsible for electron transmission.

Robustness of topological surface states against strong disorder observed inBi2Te3nanotubes

Three-dimensional topological insulators are characterized by Dirac-like conducting surface states, the existence of which has been confirmed in relatively clean metallic samples by angle-resolved photoemission spectroscopy, as well as by anomalous Aharonov-Bohm oscillations in the magnetoresistance of nanoribbons. However, a fundamental aspect of these surface states, namely, their robustness to time-reversal-invariant disorder, has remained relatively untested. In this work, we have synthesized thin nanotubes of $\mathrm{B}{\mathrm{i}}_{2}\mathrm{T}{\mathrm{e}}_{3}$ with extremely insulating bulk at low temperatures due to disorder. Nonetheless, the magnetoresistance exhibits quantum oscillations as a function of the magnetic field along the axis of the nanotubes, with a period determined by the cross-sectional area of the outer surface. Detailed numerical simulations based on a recursive Green function method support that the resistance oscillations are arising from the topological surface states which have substantially longer localization length than that of other nontopological states. This observation demonstrates coherent transport at the surface even for highly disordered samples, thus providing a direct confirmation of the inherently topological character of surface states. The result also demonstrates a viable route for revealing the properties of topological states by suppressing the bulk conduction using disorder.

Transport in selectively magnetically doped topological insulator wires

We study the electronic and transport properties of a topological insulator nanowire including selective magnetic doping of its surfaces. We use a model which is appropriate to describe materials like Bi$_2$Se$_3$ within a k.p approximation and consider nanowires with a rectangular geometry. Within this model the magnetic doping at the (111) surfaces induces a Zeeman field which opens a gap at the Dirac cones corresponding to the surface states. For obtaining the transport properties in a two terminal configuration we use a recursive Green function method based on a tight-binding model which is obtained by discretizing the original continuous model. For the case of uniform magnetization of two opposite nanowire (111) surfaces we show that the conductance can switch from a quantized value of $e^2/h$ (when the magnetizations are equal) to a very small value (when they are opposite). We also analyze the case of non-uniform magnetizations in which the Zeeman field on the two opposite surfaces change sign at the middle of the wire. For this case we find that conduction by resonant tunneling through a chiral state bound at the middle of the wire is possible. The resonant level position can be tuned by imposing an Aharonov-Bohm flux through the nanowire cross section.

Electronic transport across linear defects in graphene

We investigate the low-energy electronic transport across grain boundaries in graphene ribbons and infinite flakes. Using the recursive Green's function method, we calculate the electronic transmission across different types of grain boundaries in graphene ribbons. We show results for the charge density distribution and the current flow along the ribbon. We study linear defects at various angles with the ribbon direction, as well as overlaps of two monolayer ribbon domains forming a bilayer region. For a class of extended defect lines with periodicity 3, an analytic approach is developed to study transport in infinite flakes. This class of extended grain boundaries is particularly interesting, since the $K$ and $K'$ Dirac points are superposed.

Transmission Through Gate-Induced Magnetic Islands on Graphene Nanoribbons

We study the spin-dependent transmission through a potential barrier in a zigzag graphene nanoribbon. In particular, we consider the effect of the magnetic order of the ribbon induced by the modulation of the local density introduced by the barrier. We model the system using an Anderson–Hubbard model that we treat in the mean field approximation. We solve this problem self-consistently and calculate the transmission coefficient using the recursive Green function method. We find that Fano-like interference dips appear on one of the spin channels as the result of the presence of spin polarized edge states in the barrier.

Microscopic Theory of Tunneling Spectroscopy in Sr2RuO4

We study the surface Andreev bound state (ABS) of superconducting Sr$_2$RuO$_4$, which is a candidate material for the realization of the chiral $p$-wave superconducting state. In order to clarify the role of chiral edge modes as ABSs, the surface density of states and the tunneling conductance is calculated in the normal metal/Sr$_2$RuO$_4$ junction within the framework of recursive Green's function method, while taking into account the orbital degrees of freedom (including Spin-Orbit interactions) with realistic material parameters. In Sr$_2$RuO$_4$, there are two bands $\alpha$ and $\beta$ originating from quasi-one-dimensional orbitals $d_{yz}$ and $d_{zx}$ and a two-dimensional band $\gamma$ originating from $d_{xy}$ orbital. We discuss about the contributions of various electronic bands to LDOS and the influence of atomic spin-orbit interaction (SOI). In the light of our calculations, quasi-one-dimensional model with dominant pair potentials in $\alpha$ and $\beta$ bands is consistent with conductance measurements in Au/Sr$_{2}$RuO$_{4}$ junctions.

Probing Majorana Bound States in T-Shaped Junctions

We investigate the transport properties of a pair of Majorana bound states in a T-shaped junction, where two normal leads are coupled with an identical Majorana bound state. Both the scattering matrix and the recursive Green function method show that the peak value of the differential conductance (Gpeak) in units of e2/h and the shot noise Fano factor in the zero bias limit (F0), which are measured at the same lead and zero temperature, satisfy a linear relation as F0 = 1 + Gpeak/2, independent of the magnitude or symmetry of the coupling strengths to the leads. Therefore, combined measurements of the differential conductance and shot noise in the T-shaped geometry can serve as a characteristic signature in probing Majorana bound states.

Obtaining localization properties efficiently using the Kubo-Greenwood formalism

We establish, through numerical calculations and comparisons with a recursive Green's-function based implementation of the Landauer-B\"uttiker formalism, an efficient method for studying Anderson localization in quasi-one-dimensional and two-dimensional systems using the Kubo-Greenwood formalism. Although the recursive Green's-function method can be used to obtain the localization length of a mesoscopic conductor, it is numerically very expensive for systems that contain a large number of atoms transverse to the transport direction. On the other hand, linear scaling has been achieved with the Kubo-Greenwood method, enabling the study of effectively two-dimensional systems. While the propagating length of the charge carriers will eventually saturate to a finite value in the localized regime, the conductances given by the Kubo-Greenwood method and the recursive Green's-function method agree before the saturation. The converged value of the propagating length is found to be directly proportional to the localization length obtained from the exponential decay of the conductance.

Quantum corrections to thermopower and conductivity in graphene

The quantum corrections to the conductivity and thermopower in monolayer graphene are studied. We use the recursive Green's-function method to calculate numerically the conductivity and thermopower of graphene. We then analyze these weak-localization corrections by fitting with the analytical theory as a function of the impurity parameters and gate potential. As a result of the quantum corrections to the thermopower, we find large magnetothermopower, which is shown to provide a very sensitive measure of the size and strength of the impurities. We compare these analytical and numerical results with existing experimental measurements of magnetoconductance of single-layer graphene and find that the average size and strength of the impurities in these samples can thereby be determined. We suggest favorable parameter ranges for future measurements of the magnetothermopower.

Emergent Percolation Length and Localization in Random Elastic Networks

We study, theoretically and numerically, a minimal model for phonons in a disordered system. For sufficient disorder, the vibrational modes of this classical system can become Anderson localized, yet this problem has received significantly less attention than its electronic counterpart. We find rich behavior in the localization properties of the phonons as a function of the density, frequency and the spatial dimension. We use a percolation analysis to argue for a Debye spectrum at low frequencies for dimensions higher than one, and for a localization/delocalization transition (at a critical frequency) above two dimensions. We show that in contrast to the behavior in electronic systems, the transition exists for arbitrarily large disorder, albeit with an exponentially small critical frequency. The structure of the modes reflects a divergent percolation length that arises from the disorder in the springs without being explicitly present in the definition of our model. Within the percolation approach we calculate the speed-of-sound of the delocalized modes (phonons), which we corroborate with numerics. We find the critical frequency of the localization transition at a given density, and find good agreement of these predictions with numerical results using a recursive Green function method adapted for this problem. The connection of our results to recent experiments on amorphous solids are discussed.

The recursive Green’s function method for graphene

We describe how to apply the recursive Green's function method to the computation of electronic transport properties of graphene sheets and nanoribbons in the linear response regime. This method allows for an amenable inclusion of several disorder mechanisms at the microscopic level, as well as inhomogeneous gating, finite temperature, and, to some extend, dephasing. We present algorithms for computing the conductance, density of states, and current densities for armchair and zigzag atomic edge alignments. Several numerical results are presented to illustrate the usefulness of the method.

SPIN-DEPENDENT ELECTRON TRANSPORT THROUGH A THREE-TERMINAL MESOSCOPIC SPIN-ORBIT COUPLED SYSTEMS

We studied theoretically the spin-dependent electron transport properties of a three-terminal nanostructure proposed by Xiao and Chen [J. Appl. Phys.1, 108 (2010)]. The spin-resolved recursive Green's function method is used to calculate the three-terminal spin-polarization. We focus on the influence both of the structural parameters and Rashba spin–orbit coupling (SOC) strength in the investigated system. It is shown that the spin-polarization is still a reasonable value for being observable in experiment with small Rashba SOC strength and longer length of the wide region in the investigated system. The underlying physics is revealed to originate from the effect of SOC-induced effective magnetic field at the structure-induced Fano resonance. This length of the middle wide region in three-terminal nanostructure can be more easily fabricated experimentally.

ANALYSIS OF QUANTUM CORRECTIONS TO CONDUCTIVITY AND THERMOPOWER IN GRAPHENE — NUMERICAL AND ANALYTICAL APPROACHES

We present numerical and analytical studies of the crossover between weak antilocalization and weak localization in monolayer graphene and their influence on thermopower. By the use of the recursive Green's function method, we find that these quantum corrections result in an enhancement of thermopower, which can be observed in the resulting magnetic field dependence. This magneto thermopower strongly depends on the size and strength of the impurities as well as on the back gate voltage of the system and the impurity concentration. We show in detail the crossover of these localization effects with these parameters. Using the disorder parameters of the numerical calculation, we find quantitative agreement with the analytical calculations.

Transport properties of mesoscopic graphene rings

Based on a recursive Green's function method, we investigate the conductance of mesoscopic graphene rings in the presence of disorder, in the limit of phase coherent transport. Two models of disorder are considered: edge disorder and surface disorder. Our simulations show that the conductance decreases exponentially with the edge disorder and the surface disorder. In the presence of flux, a clear Aharonov–Bohm conductance oscillation with the period Φ 0 ( Φ 0= h/ e) is observed. The edge disorder and the surface disorder have no effect on the period of AB oscillation. The amplitudes of AB oscillations vary with gate voltage and flux, which is consistent with the previous results. Additionally, ballistic rectification and negative differential resistance are observed in I– V curves, with on/off characteristic.

Algorithm for efficient elastic transport calculations for arbitrary device geometries

With the growth in interest in graphene, controlled nanoscale device geometries with complex form factors are now being studied and characterized. There is a growing need to understand new techniques to handle efficient electronic transport calculations for these systems. We present an algorithm that dramatically reduces the computational time required to find the local density of states and transmission matrix for open systems regardless of their topology or boundary conditions. We argue that the algorithm, which generalizes the recursive Green's function method by incorporating the reverse Cuthill-McKee algorithm for connected graphs, is ideal for calculating transmission through devices with multiple leads of unknown orientation and becomes a computational necessity when the input and output leads overlap in real space. This last scenario takes the Landauer-Buttiker formalism to general scattering theory in a computational framework that makes it tractable to perform full-spectrum calculations of the quantum scattering matrix in mesoscopic systems. We demonstrate the efficacy of these approaches on graphene stadiums, a system of recent scientific interest, and contribute to a physical understanding of Fano resonances which appear in these systems.

Reproduced Giant Localization Length of Two-Side Surface Disordered Nanowires with Long-Range Correlation

We numerically investigate the normalized localization length of two-side rough nanowires as functions of energy, magnetic field and correlation strength by using modular recursive Green's function method. It is found that in the absence of correlation, while in the presence of magnetic field, the localization length increases linearly for two-side roughness, which is different to diverging exponentially for one-side roughness. Moreover, the localization of electrons is suppressed in the low energy region, but enhanced in the high energy region. In the presence of correlation, especially, an exponential enhancement in the localization length resumes in high energy region, in contrast to that in low energy region, the long-range correlations abnormally enhance the localization of electrons. A competitive mechanism is proposed to explain this behavior.

Transport in four-terminal semiconductor nanostructures with Rashba spin–orbit interaction

We studied spin transport in a four-terminal system with Rashba spin–orbit coupling. Using discretization, we convert the non-equilibrium Green's function equations into matrix equations, which are then solved using the recursive Green's function method. The calculations show that having round edges in the scattering region leads to a more regular spin polarization, indicating that the shape of the scattering region can be used as an additional control for spintronics applications.

Theory of quantum transport in Josephson junctions with a ferromagnetic insulator

We investigate Josephson transport through ferromagnetic insulators (FIs) taking the band structure of the FIs explicitly into account. Using a recursive Green function method, we find that a π-junction is formed in this type of system. Moreover, an atomic-scale 0–π oscillation is induced by increasing the thickness of an FI and its oscillation period is universal, exactly equal to a single atomic layer. Based on these results, we show that a stable π-state can be realized in junctions based on high-Tc superconductors with a La2BaCuO5 barrier. Such FI-based Josephson junctions may become an element in the architecture of future quantum computers.

Pseudospin valve in bilayer graphene nanoribbons

We study the pseudospin valve effect in bilayer graphene nanoribbons using the recursive Green's function method. The pseudospin degree of freedom is associated with the electron density in two layers and can be controlled by external gate electrodes. We find that the conductance of nanoribbons shows different behavior compared to infinite systems due to the appearance of edge states and quantum confinement. Remarkably, a large on-off ratio can be achieved in nanoribbons with zigzag edges, even when the Fermi energy lies in the bulk energy gap. The influence of possible edge vacancies and interface conditions is also discussed.

Open quantum dots in graphene: Scaling relativistic pointer states

Open quantum dots provide a window into the connection between quantum and classical physics, particularly through the decoherence theory, in which an important set of quantum states are not "washed out" through interaction with the environment–the pointer states provide connection to trapped classical orbits which remain stable in the dots. Graphene is a recently discovered material with highly unusual properties. This single layer, one atom thick, sheet of carbon has a unique bandstructure, governed by the Dirac equation, in which charge carriers imitate relativistic particles with zero rest mass. Here, an atomic orbital-based recursive Green's function method is used for studying the quantum transport. We study quantum fluctuations in graphene and bilayer graphene quantum dots with this recursive Green's function method. Finally, we examine the scaling of the domiant fluctuation frequency with dot size.