Surface states

Résumé

Surface states are electronic states found at the surface of materials. They are formed due to the sharp transition from solid material that ends with a surface and are found only at the atom layers closest to the surface. The termination of a material with a surface leads to a change of the electronic band structure from the bulk material to the vacuum. In the weakened potential at the surface, new electronic states can be formed, so called surface states. Origin at condensed matter interfaces As stated by Bloch's theorem, eigenstates of the single-electron Schrödinger equation with a perfectly periodic potential, a crystal, are Bloch waves : \begin{align} \Psi_{n\boldsymbol{k}} &=\mathrm{e}^{i\boldsymbol{k}\cdot\boldsymbol{r}}u_{n\boldsymbol{k}}(\boldsymbol{r}). \end{align} Here u_{n\boldsymbol{k}}(\boldsymbol{r}) is a function with the same periodicity as the crystal, n is the band index and k is the wave number. The allowed wave numbers fo

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The topology of the electron wavefunctions in certain band insulators can give rise to novel topological phases. Materials harbouring such topological phases are termed topological insulators (TI). A gapped bulk electronic spectrum, described by a topological invariant, and gapless boundary modes, tend to characterize the non-trivial topology. This work describes a theoretical investigation of the Z2 topological insulator phase in Bi2Se3 and Bi2Te3, and the topological crystalline insulator (TCI) phase in SnTe, subject to nanoscale confinement. Specifically, it details the electronic structure, and properties of low-dimensional nanostructures derived from the bulk topological phase. For the bismuth chalcogenides, a first principles methodology is applied to compute the energetics of high-index surfaces, followed by an analysis of the electronic properties of corresponding topological surface state charge carriers. Our calculations find several stable terminations of high-index surfaces, which can be realized at different values of the chemical potential of one of constituent elements. For the uniquely defined stoichiometric termination, the Dirac fermion surface states exhibit a strong anisotropy, with a clear dependence of Fermi velocities and spin polarization on the surface orientation. Non-stoichiometric surfaces undergo self-doping effects, which results in the presence of topologically trivial mid-gap states. These findings guide the construction of Bi2Se3 nanostructures of a nanowire (NW) and nanoribbon (NR) morphology. A tight-binding formalism is utilised to study, firstly, the impact of finite-size effects on the electronic spectrum of each nanostructure. Secondly, the effects of confinement on the topological properties of two-dimensional (2D) Dirac fermion surface states. Quantum confinement around each nanostructure perimeter entails the formation of a series of discrete one-dimensional (1D) sub-bands in the bulk gap. An analysis of how the band gap varies as a function of nanostructure dimensions finds that the dependence is highly sensitive to nanostructure morphology. We reveal a clear correspondence between the spin helicity of the 2D surface Dirac cone and the spin properties of the 1D sub-bands. This is exemplified in the real space spin textures of each nanostructure. For the NW morphology, this correspondence gives rise to an energy dependent spin polarization density. Whereas for the NR morphology the presence of two separate surface types results in a more complex relationship. Finally, via a similar tight-binding formalism, we establish how the crystal-symmetry-dependent topological phases of SnTe (001) thin films are exhibited in lower dimensional nanowires. SnTe (001) thin films, defined by either mirror or glide symmetry, realise distinct 2D TCI phases. As the band dispersion of NWs are characterised by which of these symmetry classes they belong to, we subsequently connect the distinctive NW surface states to the respective parent 2D TCI phase. Lastly, we show that the robust topological protection offered by the mirror symmetry protected 2D TCI phase is manifested in robust surface states of NWs of equivalent symmetry.

EPFL2016

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Dirac fermions at high-index surfaces of bismuth chalcogenide topological insulator nanostructures

Naunidh Singh Virk, Oleg Yazyev

Binary bismuth chalcogenides Bi2Se3, Bi2Te3, and related materials are currently being extensively investigated as the reference topological insulators (TIs) due to their simple surface-state band dispersion (single Dirac cone) and relatively large bulk band gaps. Nanostructures of TIs are of particular interest as an increased surface-to-volume ratio enhances the contribution of surfaces states, meaning they are promising candidates for potential device applications. So far, the vast majority of research efforts have focused on the low-energy (0001) surfaces, which correspond to natural cleavage planes in these layered materials. However, the surfaces of low-dimensional nanostructures (nanoplatelets, nanowires, nanoribbons) inevitably involve higher-index facets. We perform a systematic ab initio investigation of the surfaces of bismuth chalcogenide TI nanostructures characterized by different crystallographic orientations, atomic structures and stoichiometric compositions. We find several stable terminations of high-index surfaces, which can be realized at different values of the chemical potential of one of the constituent elements. For the uniquely defined stoichiometric termination, the topological Dirac fermion states are shown to be strongly anisotropic with a clear dependence of Fermi velocities and spin polarization on the surface orientation. Self-doping effects and the presence of topologically trivial mid-gap states are found to characterize the non-stoichiometric surfaces. The results of our study pave the way towards experimental control of topologically protected surface states in bismuth chalcogenide nanostructures.

Nature Publishing Group2016

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Electron hopping at the Si(111):B-root 3 surface: Insight from local impurity spectroscopy

Cédric Tournier-Colletta

Boron vacancies at the Si( 111):B-root 3 surface are model systems in the comprehension of strongly correlated semiconductor surfaces. By using scanning tunneling spectroscopy, the origin of the single-vacancy electronic structure is addressed. It is shown to originate from the localization of a well-identified dangling-bond surface state with significant B character. The bivacancy defect, which is characterized by energy-split bonding and antibonding states, is interpreted within the textbook diatomic molecule picture. From the hopping parameter, we determine the bandwidth of the surface state from which the impurity state derives and evaluate the strength of many-body effects. Our analysis supports the realization of the Mott-Hubbard insulator state in half-filled dangling-bond surface states on root 3-reconstructed surfaces, as proposed recently for SiC(0001), Sn/Ge(111), and Sn/Si(111). DOI: 10.1103/PhysRevB.87.075427

American Physical Society2013

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EPFL2016