Dirac cone

Dirac cones, named after Paul Dirac, are features that occur in some electronic band structures that describe unusual electron transport properties of materials like graphene and topological insulators. In these materials, at energies near the Fermi level, the valence band and conduction band take the shape of the upper and lower halves of a conical surface, meeting at what are called Dirac points. Typical examples include graphene, topological insulators, bismuth antimony thin films and some other novel nanomaterials, in which the electronic energy and momentum have a linear dispersion relation such that the electronic band structure near the Fermi level takes the shape of an upper conical surface for the electrons and a lower conical surface for the holes. The two conical surfaces touch each other and form a zero-band gap semimetal. The name of Dirac cone comes from the Dirac equation that can describe relativistic particles in quantum mechanics, pr

A Theoretical Investigation of Topological Insulator Nanostructures

Naunidh Singh Virk

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

Controlling magnetic order, magnetic anisotropy, and band topology in the semimetals Sr(Mn0.9Cu0.1)Sb-2 and Sr(Mn0.9Zn0.1)Sb-2

Yong Liu

Neutron diffraction and magnetic susceptibility studies show that orthorhombic single-crystals of topological semimetals Sr(Mn0.9Cu0.1)Sb-2 and Sr(Mn0.9Zn0.1)Sb-2 undergo three-dimensional C-type antiferromagnetic (AFM) ordering of the Mn2+ moments at T-N = 200 +/- 10 and 210 +/- 12 K, respectively, significantly lower than that of the parent SrMnSb2 with T-N = 297 +/- 3 K. Magnetization versus applied magnetic field (perpendicular to MnSb planes) below T-N exhibits slightly modified de Haas van Alphen oscillations for the Zn-doped crystal as compared to that of the parent compound. By contrast, the Cu-doped system does not show de Haas van Alphen magnetic oscillations, suggesting that either Cu substitution for Mn changes the electronic structure of the parent compound substantially, or that the Cu sites are strong scatterers of carriers that significantly shorten their mean free path thus diminishing the oscillations. Density functional theory (DFT) calculations including spin-orbit coupling predict the C-type AFM state for the parent, Cu-, and Zn-doped systems and identify the a-axis (i.e., perpendicular to the Mn layer) as the easy magnetization direction in the parent and 12.5% of Cu or Zn substitutions. In contrast, 25% of Cu content changes the easy magnetization to the b-axis (i.e., within the Mn layer). We find that the incorporation of Cu and Zn in SrMnSb2 tunes electronic bands near the Fermi level resulting in different band topology and semimetallicity. The parent and Zn-doped systems have coexistence of electron and hole pockets with opened Dirac cone around the Y-point whereas the Cu-doped system has dominant hole pockets around the Fermi level with a distorted Dirac cone. The tunable electronic structure may point out possibilities of rationalizing the experimentally observed de Haas van Alphen magnetic oscillations.

2020

A Theoretical Investigation of Topological Insulator Nanostructures

Naunidh Singh Virk

EPFL2016

Controlling magnetic order, magnetic anisotropy, and band topology in the semimetals Sr(Mn0.9Cu0.1)Sb-2 and Sr(Mn0.9Zn0.1)Sb-2

Yong Liu

2020

Dirac Structures and Generalized Complex Structures on $TM \times \mathbf{R}^{h}$

A Theoretical Investigation of Topological Insulator Nanostructures

Controlling magnetic order, magnetic anisotropy, and band topology in the semimetals Sr(Mn0.9Cu0.1)Sb-2 and Sr(Mn0.9Zn0.1)Sb-2

A Theoretical Investigation of Topological Insulator Nanostructures

Dirac Structures and Generalized Complex Structures on $TM \times \mathbf{R}^{h}$

Controlling magnetic order, magnetic anisotropy, and band topology in the semimetals Sr(Mn0.9Cu0.1)Sb-2 and Sr(Mn0.9Zn0.1)Sb-2