Microscopic study of orbital textures

TL;DR

This paper derives microscopic Hamiltonians for orbital textures from tight-binding models, revealing mechanisms behind orbital hybridization and uncovering new orbital textures, aiding the design of spin-orbitronic materials.

Contribution

It introduces a microscopic derivation of orbital texture Hamiltonians, identifying two key hybridization mechanisms and discovering new orbital textures like Dresselhaus and anisotropic textures.

Findings

Reproduces symmetry-based orbital Hamiltonians from microscopic models

Identifies lattice structure and orbital mediation as hybridization mechanisms

Uncovers new orbital textures such as Dresselhaus and anisotropic textures

Abstract

Many interesting spin and orbital transport phenomena originate from orbital textures, referring to $\vec{k}$-dependent orbital states. Most of previous works are based on symmetry analysis to model the orbital texture and analyze its consequences. However the microscopic origins of orbital texture and its strength are largely unexplored. In this work, we derive the orbital texture Hamiltonians from microscopic tight-binding models for various situations. To form an orbital texture, $\vec{k}$-dependent hybridization of orbital states are necessary. We reveal two microscopic mechanisms for the hybridization: (i) lattice structure effect and (ii) mediation by other orbital states. By considering the orbital hybridization, we not only reproduce the orbital Hamiltonian obtained by the symmetry analysis but also reveal previously unreported orbital textures like orbital Dresselhaus texture and anisotropic orbital texture. The orbital Hamiltonians obtained here would be useful for analyzing the orbital physics and designing the materials suitable for spin-orbitronic applications. We show that our theory also provides useful microscopic insight into physical phenomena such as the orbital Rashba effect and the orbital Hall effect. Our formalism is so generalizable that one can apply it to obtain effective orbital Hamiltonians for arbitrary orbitals in the presence of periodic lattice structures.