Recursive Greenʼs function method for multi-terminal nanostructures

Thorgilsson, Gunnar; Viktorsson, G.; Erlingsson, Sigurdur I.

doi:10.1016/j.jcp.2013.12.054

Cited by 35 publications

(42 citation statements)

References 17 publications

(22 reference statements)

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“…From this GF both transport and local properties can be obtained. However, for most purposes we do not require every element of the GF matrix element in the device region, and so to avoid a timeconsuming, full-matrix inversion, various recursive or other decomposition methods are often applied [9,14,20,[25][26][27][28][29][30][31][32].…”

Section: Adaptive Recursion For Device Regionmentioning

confidence: 99%

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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: Adaptive Recursion For Device Regionmentioning

confidence: 99%

“…Hence, we use an approach similar to the ones in Refs. [25][26][27] and employ an adaptive partitioning of the Hamiltonian matrix in order to bring it into the desired tridiagonal form suitable for recursive methods.…”

Section: Adaptive Recursion For Device Regionmentioning

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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“…To calculate these quantities we use conventional recursive Green's function techniques (see, e.g., Refs. [37][38][39]). …”

Section: Conductancementioning

confidence: 99%

Transport in selectively magnetically doped topological insulator wires

2015

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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's 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 nonuniform 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.

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“…Like the surface approach, our surface-bulk recursive Green's function can be generalized to other systems and geometries [44,47]. We believe this material will be also useful for researchers unfamiliar with the Green's function method, interested in the new challenges of nanosciences and their implementations.…”

Section: Discussionmentioning

confidence: 99%

“…(102). The surface RGF is widely used in transport simulation with several applications [44][45][46] with sophistications [47]. In the next section we will present an alternative version, capable to access the Green's functions of the edge and bulk at once, possibly finding usefullness in topological insulators.…”

Section: Surface Green's Functions Decimationmentioning

confidence: 99%

Pedagogical introduction to equilibrium Green's functions: condensed-matter examples with numerical implementations

Odashima

Prado

Vernek

2016

Rev. Bras. Ensino Fís.

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The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible to extract information from the system under study, such as the density of states, relaxation times and response functions. Despite its power and versatility, it is known as a laborious and sometimes cumbersome method. Here we introduce the equilibrium Green's functions and the equation-of-motion technique, exemplifying the method in discrete lattices of non-interacting electrons. We start with simple models, such as the two-site molecule, the infinite and semi-infinite one-dimensional chains, and the two-dimensional ladder. Numerical implementations are developed via the recursive Green's function, implemented in Julia, an open-source, efficient and easy-to-learn scientific language. We also present a new variation of the surface recursive Green's function method, which can be of interest when simulating simultaneously the properties of surface and bulk.

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Recursive Greenʼs function method for multi-terminal nanostructures

Cited by 35 publications

References 17 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

Transport in selectively magnetically doped topological insulator wires

Pedagogical introduction to equilibrium Green's functions: condensed-matter examples with numerical implementations

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