Crystal momentum | EPFL Graph Search

In solid-state physics crystal momentum or quasimomentum is a momentum-like vector associated with electrons in a crystal lattice. It is defined by the associated wave vectors \mathbf{k} of this lattice, according to :{\mathbf{p}}_{\text{crystal}} \equiv \hbar {\mathbf{k}} (where \hbar is the reduced Planck's constant). Frequently, crystal momentum is conserved like mechanical momentum, making it useful to physicists and materials scientists as an analytical tool. Lattice symmetry origins A common method of modeling crystal structure and behavior is to view electrons as quantum mechanical particles traveling through a fixed infinite periodic potential V(x) such that :V({\mathbf{x}}+{\mathbf{a}})=V({\mathbf{x}}), where \mathbf{a} is an arbitrary lattice vector. Such a model is sensible because crystal ions that form the lattice structure are typically on the order of tens of thousands of times more

Crystalline and correlated phases in two-dimensional transition metal dichalcogenides

Diego José Pasquier

This thesis is dedicated to the study of various aspects of the electronic structure of two-dimensional transition metal dichalcogenides (TMDs) of chemical composition MX

_2

(where M is a transition metal atom and X= S, Se, Te), using a combination of \textit{ab inito} density-functional methods. We first address the relative stability of the

1T

and

1H

phases of two-dimensional TMDs as a function of the column of the transition metal atom in the periodic table. Using a Wannier-function approach, we calculate crystal field and ligand field parameters for a broad range of members of this family of materials. Taking TaS

_2

as an example, we show how the splitting of the

d

electron states arises from an interplay of electrostatic effects and hybridization with the ligands'

s

p

and

d

states. We show that the ligand field alone cannot explain the stabilization of the

1H

polymorph for

d^1

and

d^2

TMDs, and that band structure effects are dominant. We present trends of the calculated parameters across the periodic table, and argue that these allow developing simple chemical intuition. Secondly, we study the occurrence of charge density wave phases and periodic lattice distortion in metallic

1T

transition metal dichalcogenides. The phonon dispersion and fermiology of representative examples with different

d

electron counts are studied as a function of doping. Two qualitatively different behaviours are found as a function of the filling of the

t_{2g}

subshell. We argue that away from half-filling, weak-coupling nesting arguments are a useful starting point for understanding, whereas closer to half-filling a strong-coupling real-space picture is more correct. Using Wannier functions, it is shown that strong metal-metal bonds are formed and that simple bond-counting arguments apply. Thirdly, the recently synthesized

1T

phase of NbSe

_2

, in monolayer form, is investigated from first principles. We find that

1T

-NbSe

_2

is unstable towards the formation of an incommensurate charge density wave phase, whose periodicity can be understood from the Fermi surface topology. We investigate different scenarios for the experimentally observed superlattice and insulating behaviour, and conclude that the star-of-David phase is the most stable commensurate charge density wave phase. We study the electronic properties of the star-of-David phase at various levels of theory and confirm its Mott insulating character, as speculated and in analogy with TaS

_2

. The Heisenberg exchange couplings are found to be ferromagnetic, which suggests a parallel with the so-called flat-band ferromagnetism in certain multiband Hubbard models. Finally, we address the possibility of the occurrence of the excitonic insulator phase in single-layer TiSe

_2

. The relative role of electron-electron and electron-phonon interactions in driving the charge density wave in layered and two-dimensional TiSe

_2

has been disputed and is still unresolved. We calculate the electronic structure and finite-momentum exciton spectrum from hybrid density functional theory. We find that in a certain range of parameters, excitonic effects are strong and the material is close to a pure excitonic insulator instability. A possible necessary condition for the physical realization of a pure excitonic insulator is proposed.

EPFL2019

Direct observation of the spin texture in SmB6 as evidence of the topological Kondo insulator

Kazimierz Conder, Jan Hugo Dil, Joël Mesot, Stefan Peter Muff

Topological Kondo insulators have been proposed as a new class of topological insulators in which non-trivial surface states reside in the bulk Kondo band gap at low temperature due to strong spin-orbit coupling. In contrast to other three-dimensional topological insulators, a topological Kondo insulator is truly bulk insulating. Furthermore, strong electron correlations are present in the system, which may interact with the novel topological phase. By applying spin- and angle-resolved photoemission spectroscopy, here we show that the surface states of SmB6 are spin polarized. The spin is locked to the crystal momentum, fulfilling time reversal and crystal symmetries. Our results provide strong evidence that SmB6 can host topological surface states in a bulk insulating gap stemming from the Kondo effect, which can serve as an ideal platform for investigating of the interplay between novel topological quantum states with emergent effects and competing orders induced by strongly correlated electrons.

Nature Publishing Group2014