A general algorithm for computing bound states in infinite tight-binding  systems

Istas, Mathieu; Groth, Christoph; Akhmerov, A. R.; Wimmer, Michael; Waintal, Xavier

doi:10.21468/scipostphys.4.5.026

Cited by 18 publications

(15 citation statements)

References 28 publications

(29 reference statements)

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“…Finally one mentions that Istas, Groth and Waintal have recently proposed an approach to cope with "mostly translationally invariant systems" (Istas et al, 2018), i.e., systems with weak disorder. With this method, systems of complex geometries are decomposed into two parts; one fully periodic part that is stitched with another part containing the disorder potential and electrodes.…”

Section: Landauer-b üTtiker Quantum Transport Methodologymentioning

confidence: 99%

Linear scaling quantum transport methodologies

et al. 2021

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Section: Landauer-b üTtiker Quantum Transport Methodologymentioning

confidence: 99%

Linear scaling quantum transport methodologies

et al. 2021

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“…A global solution needs to be continuous at x = 0, and it exists if there is a nonzero linear combination of the left mode vectors ψ i L that is also a linear combination of right mode vectors ψ i R . We therefore obtain the edge spectrum by numerically finding points in the (E, k) plane where W is singular [25].…”

Section: Gapless Domain Wall Modesmentioning

confidence: 99%

Amorphous topological phases protected by continuous rotation symmetry

2021

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Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous topological materials, where the Hamiltonian is invariant on average under reflection over any axis due to continuous rotation symmetry. We show that the edge remains protected from localization in the topological phase, and the local disorder caused by the amorphous structure results in critical scaling of the transport in the system. In order to classify such phases we perform a systematic search over all the possible symmetry classes in two dimensions and construct the example models realizing each of the proposed topological phases. Finally, we compute the topological invariant of these phases as an integral along a meridian of the spherical Brillouin zone of an amorphous Hamiltonian.

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“…We use the bound state algorithm developed in Ref. 20 to address this problem. Altogether, our MTIS algorithm consists of a non-trivial combination of the residue solver, the numerical Fourier transform solver, the glueing sequence solver and the bound state solver.…”

Section: B Principle Of the Techniquementioning

confidence: 99%

“…We have devoted an earlier article to this problem to which we refer for all technical details. 20 We suppose that we have computed the energy E α (k y , k z ) and the associated state ψ α (x, k y , k z ) of the semi-infinite problem. Once this is done, we numerically inverse the function E α (k y , k z ) to obtain k α =k y (E, k z ).…”

Section: The Bound State Problemmentioning

confidence: 99%

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Pushing the limit of quantum transport simulations

Istas

Groth

Waintal

2019

Phys. Rev. Research

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Simulations of quantum transport in coherent conductors have evolved into mature techniques that are used in fields of physics ranging from electrical engineering to quantum nanoelectronics and material science. The most efficient general-purpose algorithms have a computational cost that scales as L 6...7 in 3D, which on the one hand is a substantial improvement over older algorithms, but on the other hand still severely restricts the size of the simulation domain, limiting the usefulness of simulations through strong finite-size effects. Here, we present a novel class of algorithms that, for certain systems, allows to directly access the thermodynamic limit. Our approach, based on the Green's function formalism for discrete models, targets systems which are mostly invariant by translation, i.e. invariant by translation up to a finite number of orbitals and/or quasi-1D electrodes and/or the presence of edges or surfaces. Our approach is based on an automatic calculation of the poles and residues of series expansions of the Green's function in momentum space. This expansion allows to integrate analytically in one momentum variable. We illustrate our algorithms with several applications: devices with graphene electrodes that consist of half an infinite sheet; Friedel oscillation calculations of infinite 2D systems in presence of an impurity; quantum spin Hall physics in presence of an edge; the surface of a Weyl semi-metal in presence of impurities and electrodes connected to the surface. In this last example, we study the conduction through the Fermi arcs of the topological material and its resilience to the presence of disorder. Our approach provides a practical route for simulating 3D bulk systems or surfaces as well as other setups that have so far remained elusive.

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A general algorithm for computing bound states in infinite tight-binding systems

Cited by 18 publications

References 28 publications

Linear scaling quantum transport methodologies

Linear scaling quantum transport methodologies

Amorphous topological phases protected by continuous rotation symmetry

Pushing the limit of quantum transport simulations

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