Orbital effects in elemental chalcogens

This thesis focuses on two materials in which orbital physics is key – the elemental chalcogens selenium and tellurium. These electronic properties of these systems were originally studied in the 50s and 60s of the last century, when their band structure was first described [1–3]. Since then, they have not drawn much attention in theoretical solid state research. Recently, there have been a few new developments in the field of chalcogens, notably the work by Silva et. al. [4]. To date, however, there has been no attempt to describe elemental chalcogens using modern concepts in orbital physics – such as orbital order and the multi-orbital Hubbard model – developed for the study of correlated systems. A full description of topology in chalcogens is also lacking. This thesis addresses these two areas, as well as identifies some novel phenomena in selenium and tellurium. After a general introduction (chapter 1), chapter 2 describes the crystal structure of selenium and tellurium, which consists of weakly-coupled helical chains (chalcogen chains) – it is these chains that are studied in the thesis. In a chalcogen crystal, these chains are arranged in a two-dimensional, hexagonal pattern, with helixes’ axes parallel to each other. The ground state of a single chalcogen chain is an orbitally-ordered state, called an orbital density wave (ODW), in which dfferent orbitals are occupied on each of the inequivalent sites in the single period of the helix. This situation is a result of the helical geometry and the p orbital shape, and leads to physics very different from that of simple, linear chains. Chapter 3 considers the effect of weak inter-orbital Coulomb repulsion on the ODW ground state of a spinless chalcogen chain. This question is related to previous research [4], which indicated that inter-orbital Coulomb repulsion might be responsible for the lattice deformation of a parent simple cubic lattice which stabilises the three dimensional crystal structure of elemental selenium and tellurium. The inclusion of an inter-orbital Coulomb term in the Hamiltonian, however, is known to destabilise simple chains, leading to a Peiers-type transition [5]. Is it the same for chalcogen chains? It turns out that such a deformation does not occur in chalcogen chains for realistic values of the electron-electron interaction parameter U. This is because of the insulating nature of the chains and their sizeable band gap, both a consequence of the p orbital valence. This is an important conclusion, as it shows that the deformation mechanism proposed in literature [4] is not inconsistent. Following a brief introduction to one-diemnsional topological insulators in chapter 4, chapter 5 considers the topology of a realistic, spinfull chalcogen chain with non zero spin-orbit coupling, which has not previously been studied in much detail. It is established that the chalcogen chain harbours a topological ground state, with end states protected by a 180-degree rotation symmetry. The exponentially decaying end states have a particular form, with the charge density exactly zero on every third site. This is linked to the physics of the period-three Su-Schrieffer-Heeger model (SSH 3) [6]. In terms of bulk topological properties, the relevant topological invariant is the Lau-Brink-Ortix (LBO) invariant, only recently defined [7]. These findings lead one to expect topological surface states in elemental chalcogens, which form from the end states of individual chalcogen chains via the weak inter-chain coupling.