A Theoretical Investigation of Topological Insulator Nanostructures

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.

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

Electronic Transport in 2D Materials with Strong Spin-orbit Coupling

Artem Pulkin

The thesis describes the computational study of structural, electonic and transport properties of monolayer transition metal dichalcogenides (TMDs) in the stable 2H and the metastable 1T' phases. Several aspects have been covered by the study including the electronic properties of the topological quantum spin Hall (QSH) state in the 1T' monolayer phase as well as the effects of strain, periodic line defects, interfaces and edges of monolayer TMDs. The electronic properties of the bulk monolayer phases were described by the ab-initio density functional theory framework while the electronic and transport properties of 1D defects were calculated using the non-equilibrium Green's function formalism. A specific focus was made on the transport of spin-polarized charge carriers across line defects in the monolayer 2H phase. Subject to energy, pseudomomentum and spin conservation, the size of the transport gap is governed by both bulk properties of a material and symmetries of a line defect. Outside the transport gap energy region, the charge carriers are discriminated with respect to their spin resulting in the spin polarization of the transmitted current. Next, the properties of the metastable monolayer 1T' phase were studied. The presence of a sufficiently large band gap is crucial to observe the QSH phase in the family of materials by probing the topological boundary states. The meV-order band gaps of the 1T' phase of monolayer TMDs were found to be sensitive to materials' lattice constants suggesting the control of the band gap size by strain. In particular, the electronic band structure and the size of the band gap in monolayer 1T'-WSe2 were found to be in agreement with spectroscopy studies. The topologically protected states at the edges of the monolayer 1T' phase as well as at the boundaries between the topological 1T' phase and the trivial 2H phase of monolayer TMDs were studied. Specific atomic structure configurations were suggested to observe experimentally the topological protection of the charge carrier transport against back-scattering. Finally, in the context of lateral semiconducting device engineering, the electronic and transverse transport properties of 2H-1T' phase boundaries as well as the dimerization defects in the 1T' phase were investigated. Both kinds of defects considered exhibit a relatively large transmission probability for the charge carriers crossing the defects. However, the differences between the shapes of bulk bands of the two phases open a sizeable transport gap for charge carriers crossing periodic domain boundaries between the monolayer 2H and 1T' phases. The calculated formation energies of dimerization defects were found to be relatively low suggesting their high concentration in real samples of monolayer 1T'-TMDs. Additionally, the thesis includes studies of magnetic dopants on the surface of Bi2Te3 and atomic vacancies in monolayer 2H-MoSe2 where the electronic properties of point defects were calculated and compared to experimental results. The two possible adsorption sites of Fe on the surface of Bi2Te3 both show a large out-of-plane magnetic anisotropy in agreement with experiments. The calculated local electronic properties of Se vacancies in monolayer 2H-MoSe2 show the presence of in-gap states which are not observed in experiment. Nevertheless, the combination of theoretical and experimental scanning tunneling microscopy images allowed the unambiguous identification of the vacancy defect.

EPFL2017

Experimental studies of the equilibrium and out-of-equilibrium electronic structure of non-symmorphic topological materials

Gianmarco Gatti

Symmetry and topology are fundamental properties of nature. Mathematics provides us with a general framework to understand these concepts. On one side, symmetry describes the invariance properties of an object for specific transformations. On the other side, topology classifies objects under continuous deformations. Two objects with different topologies cannot be deformed one into each other without creating or annihilating a singularity, sometimes referred to as 'node'. These concepts gradually found applications in physics, namely in the description of the electronic properties of solids, which is the focus of this thesis. Symmetry and topology protect special nodes in the band structure of a crystal, where several states are degenerate in energy. Close to a node, the electron wave function obeys the Dirac or Weyl Hamiltonians, which were formally introduced to describe fermions in high-energy particle physics. These exotic fermions exhibit unique optical and transport properties, fully manifesting their quantum nature. Symmetry guides us in the search for which classes of materials may host topological nodes. Recently the attention of the scientific community has been attracted by crystals with non-symmorphic symmetries (screw axes and glide planes), as promising candidates for topological phases. This thesis focuses on two families of non-symmorphic crystals, whose topological properties have been investigated by combining conventional angle-resolved photoelectron spectroscopy (ARPES) with state-of-the-art spin-resolved (spARPES) and time-resolved ARPES (trARPES). The experimental results are supported by calculations carried out in collaboration with theory groups. ZrSiTe and ZrSiSe belong to the same class of non-trivial semimetals. They host Dirac electrons with large mobility. The results of my spARPES experiments clarify that spin-orbit interaction (SOI) not only removes the topological nodes in ZrSiTe, but also induces a 'hidden' spin polarization of its bulk electronic states, otherwise forbidden by the inversion symmetry of the lattice. Moreover, trARPES data provide evidence that the electron-electron interaction is only partially screened in the metallic state of ZrSiSe. As a consequence, the band velocity is enhanced, at odds with general expectations. More importantly, I show that this band renormalization can be controlled at the ultrafast time scale (namely fs scale, with 1 fs=10^{-15} s) via intense optical excitation, paving the way for engineering the band structure of Dirac semimetals. Tellurium is a chiral semiconductor, with a small and direct band gap. The low-symmetry of its lattice and the simple chemical composition make it the ideal case to study the interplay between symmetry and topology. With ARPES I determine several Weyl nodes in its electronic structure. By means of spARPES, I demonstrate that in their surrounding the spin exhibits a hedgehog configuration. This observation is new and it highlights the connection between spin-dependent and topology-related properties in Te. Finally, I illustrate promising preliminary results based on trARPES that explore the appealing possibility of optically controlling the topology of the electronic structure of Te upon excitation of coherent phonons.