Green Function Approach to Interface States in Band‐Invert ed Junctions

Domı́nguez-Adame, F.

doi:10.1002/pssb.2221860231

Cited by 8 publications

(14 citation statements)

References 14 publications

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“…Since the interface momentum is conserved, the envelope function can be written as χ χ χ(r r r) = χ χ χ(z) exp(ir r r ⊥ · k k k ⊥ ), where χ χ χ(z) decays exponentially on each semiconductor. In the case of symmetric and same-sized gaps, namely V C (z) = 0 and E G (z) = 2∆ sgn(z), it is found that χ χ χ(z) ∼ exp(−|z|/d), with d =hv ⊥ /∆ and the interface dispersion relation is a single Dirac cone 23 for further details).…”

Section: Ti/s Junction Under Bias: Continuum Modelmentioning

confidence: 99%

Tuning the Fermi velocity in Dirac materials with an electric field

Díaz‐Fernández

Chico

González

et al. 2017

Sci Rep

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Dirac materials are characterized by energy-momentum relations that resemble those of relativistic massless particles. Commonly denominated Dirac cones, these dispersion relations are considered to be their essential feature. These materials comprise quite diverse examples, such as graphene and topological insulators. Band-engineering techniques should aim to a full control of the parameter that characterizes the Dirac cones: the Fermi velocity. We propose a general mechanism that enables the fine-tuning of the Fermi velocity in Dirac materials in a readily accessible way for experiments. By embedding the sample in a uniform electric field, the Fermi velocity is substantially modified. We first prove this result analytically, for the surface states of a topological insulator/semiconductor interface, and postulate its universality in other Dirac materials. Then we check its correctness in carbon-based Dirac materials, namely graphene nanoribbons and nanotubes, thus showing the validity of our hypothesis in different Dirac systems by means of continuum, tight-binding and ab-initio calculations.

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Section: Ti/s Junction Under Bias: Continuum Modelmentioning

confidence: 99%

Tuning the Fermi velocity in Dirac materials with an electric field

Díaz‐Fernández

Chico

González

et al. 2017

Sci Rep

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“…In the absence of external fields, it is well known that band-inverted junctions support topologically protected states located at the interface. Their energy lies within the common gap of the two semiconductors and the dispersion relation is a Dirac cone [ 13 , 15 – 16 20 ]. The Dirac cone remains even if an electric field perpendicular to the junction is applied, but it widens and the Fermi velocity is quadratically reduced with the electric field [ 25 , 28 ].…”

Section: Discussionmentioning

confidence: 99%

“…The interface momentum is conserved and the envelope function can be expressed as , where it is understood that the subscript “ ” in a vector indicates the nullification of its z -component. In the case of aligned and same-sized gaps, it is found that , with and the interface dispersion relation is a single Dirac cone , where the origin of energy is taken at the center of the gaps [ 20 ]. v is the group velocity at the Fermi level in undoped samples and it will be referred to as Fermi velocity hereafter.…”

Section: Theoretical Modelmentioning

confidence: 99%

“…The equation governing the conduction- and valence-band envelope functions reduces to a Dirac-like equation after neglecting far-band corrections. In view of this analogy, exact solutions can be then straightforwardly found by means of supersymmetric [ 16 ] or Green’s function approaches [ 20 ]. In the context of symmetry-protected topological phases, our model can be applied not only to topological crystalline insulators, like the ones mentioned above [ 8 ], but also to more general three-dimensional topological insulators, such as Bi 2 Se 3 , in contact with a trivial insulator [ 21 – 22 ].…”

Section: Introductionmentioning

confidence: 99%

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Robust midgap states in band-inverted junctions under electric and magnetic fields

Díaz‐Fernández¹,

Valle²,

Domı́nguez-Adame³

2018

Beilstein J. Nanotechnol.

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Several IV–VI semiconductor compounds made of heavy atoms, such as Pb1 −xSnxTe, may undergo band-inversion at the L point of the Brillouin zone upon variation of their chemical composition. This inversion gives rise to topologically distinct phases, characterized by a change in a topological invariant. In the framework of the k·p theory, band-inversion can be viewed as a change of sign of the fundamental gap. A two-band model within the envelope-function approximation predicts the appearance of midgap interface states with Dirac cone dispersions in band-inverted junctions, namely, when the gap changes sign along the growth direction. We present a thorough study of these interface electron states in the presence of crossed electric and magnetic fields, the electric field being applied along the growth direction of a band-inverted junction. We show that the Dirac cone is robust and persists even if the fields are strong. In addition, we point out that Landau levels of electron states lying in the semiconductor bands can be tailored by the electric field. Tunable devices are thus likely to be realizable, exploiting the properties studied herein.

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“…A subclass of topological insulators that rely on crystalline symmetries has also been experimentally realized in Pb 1−x Sn x Te [68,77,78] and Pb 1−x Sn x Se [79]. All these topological states of matter were already encountered in a series of seminal papers by Volkov and Pankratov in the 1980s [80][81][82][83][84][85]. Remarkably, these states can be reshaped by means of external electric and magnetic fields [86][87][88][89] and doping [90,91].…”

Section: Topological Insulator Nanowiresmentioning

confidence: 99%

Nanowires: A route to efficient thermoelectric devices

Domı́nguez-Adame

Martín‐González

Sánchez

et al. 2019

Physica E: Low-dimensional Systems and Nanostructures

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Miniaturization of electronic devices aims at manufacturing ever smaller products, from mesoscopic to nanoscopic sizes. This trend is challenging because the increased levels of dissipated power demands a better understanding of heat transport in small volumes. A significant amount of the consumed energy in electronics is transformed into heat and dissipated to the environment. Thermoelectric materials offer the possibility to harness dissipated energy and make devices less energy-demanding. Heat-to-electricity conversion requires materials with a strongly suppressed thermal conductivity but still high electronic conduction. Nanowires can meet nicely these two requirements because enhanced phonon scattering at the surface and defects reduces the lattice thermal conductivity while electric conductivity is not deteriorated, leading to an overall remarkable thermoelectric efficiency. Therefore, nanowires are regarded as a promising route to achieving valuable thermoelectric materials at the nanoscale. In this paper, we present an overview of key experimental and theoretical results concerning the thermoelectric properties of nanowires. The focus of this review is put on the physical mechanisms by which the efficiency of nanowires can be improved. Phonon scattering at surfaces and interfaces, enhancement of the power factor by quantum effects and topological protection of electron states to prevent the degradation of electrical conductivity in nanowires are thoroughly discussed.

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Green Function Approach to Interface States in Band‐Invert ed Junctions

Cited by 8 publications

References 14 publications

Tuning the Fermi velocity in Dirac materials with an electric field

Tuning the Fermi velocity in Dirac materials with an electric field

Robust midgap states in band-inverted junctions under electric and magnetic fields

Nanowires: A route to efficient thermoelectric devices

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