Complex band structures of crystalline solids: An eigenvalue method

Chang, Yia‐Chung; Schulman, J. N.

doi:10.1103/physrevb.25.3975

Cited by 167 publications

(91 citation statements)

References 19 publications

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“…Equation (3) is a nonlinear eigenvalue problem that can be rewritten as a linear generalized eigenvalue problem of double the size and can be solved numerically in a straightforward fashion [22,23]. The corresponding spectrum of complex energy-dependent k x values is known collectively as the CBS.…”

Section: B Complex Band Structurementioning

confidence: 99%

Complex band structure of topologically protected edge states

et al. 2014

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One of the great successes of modern condensed matter physics is the discovery of topological insulators (TIs). A thorough investigation of their properties could bring such materials from fundamental research to potential applications. Here, we report on theoretical investigations of the complex band structure (CBS) of two-dimensional (2D) TIs. We utilize the tight-binding form of the Bernevig, Hughes, and Zhang model as a prototype for a generic 2D TI. Based on this model, we outline the conditions that the CBS must satisfy in order to guarantee the presence of topologically protected edge states. Furthermore, we use the Green's function technique to show how these edge states are localized, highlighting the fact that the decay of the edge-state wave functions into the bulk of a TI is not necessarily monotonic and, in fact, can exhibit an oscillatory behavior that is consistent with the predicted CBS of the bulk TI. These results may have implications for electronic and spin transport across a TI when it is used as a tunnel barrier.

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Section: B Complex Band Structurementioning

confidence: 99%

Complex band structure of topologically protected edge states

et al. 2014

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“…19 Several approaches to obtain the complex band structure from ab initio density functional theory (DFT) calculations have been developed (e.g., Refs. [20][21][22]. In such calculations, one usually aims at solving the inverse problem of the standard DFT, i.e., instead of fixing the Bloch vector and solving for the energy eigenstates, one fixes the energy and solves for the real and complex Bloch vectors.…”

Section: Complex Band Structure Of Ferroelectricsmentioning

confidence: 99%

Influence of the electronic structure on tunneling through ferroelectric insulators: Application to BaTiO3and PbTiO33

Wortmann

Blügel

2011

Phys. Rev. B

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Electronic tunneling through ferroelectric insulators is considered to be a key ingredient of future oxide electronics. We investigate the role of the electronic band structure of the decaying electronic states in the band gap by first discussing the expected behavior of tunneling in the effective mass model. We demonstrate that, even for the simple prototype ferroelectric oxides in the perovskite structures PbTiO 3 and BaTiO 3 , the basic assumption of the effective mass model is not appropriate, and that the correct interpretation of tunneling in these materials requires a material-specific description of the evanescent states as provided by the complex band structure.

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“…They enable calculations on semi-infinite structures with a single well-defined edge, or on infinite structures containing a single grain boundary, and they generally do not require the use of large supercells. Green's function techniques have been pioneered for calculations on surface states of three-dimensional (3D) materials [38][39][40][41][42]. Here, we formulate a special Green's function technique for calculating edge and grain boundary states.…”

Section: Introductionmentioning

confidence: 99%

Green's function approach to edge states in transition metal dichalcogenides

2016

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The semiconducting two-dimensional transition metal dichalcogenides MX 2 show an abundance of onedimensional metallic edges and grain boundaries. Standard techniques for calculating edge states typically model nanoribbons, and require the use of supercells. In this paper, we formulate a Green's function technique for calculating edge states of (semi-)infinite two-dimensional systems with a single well-defined edge or grain boundary. We express Green's functions in terms of Bloch matrices, constructed from the solutions of a quadratic eigenvalue equation. The technique can be applied to any localized basis representation of the Hamiltonian. Here, we use it to calculate edge states of MX 2 monolayers by means of tight-binding models. Aside from the basic zigzag and armchair edges, we study edges with a more general orientation, structurally modifed edges, and grain boundaries. A simple three-band model captures an important part of the edge electronic structures. An 11-band model comprising all valence orbitals of the M and X atoms is required to obtain all edge states with energies in the MX 2 band gap. Here, states of odd symmetry with respect to a mirror plane through the layer of M atoms have a dangling-bond character, and tend to pin the Fermi level.

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Complex band structures of crystalline solids: An eigenvalue method

Cited by 167 publications

References 19 publications

Complex band structure of topologically protected edge states

Complex band structure of topologically protected edge states

Influence of the electronic structure on tunneling through ferroelectric insulators: Application to BaTiO3and PbTiO33

Green's function approach to edge states in transition metal dichalcogenides

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