Orbital magneto-optical response of periodic insulators from first principles

Abstract

Magneto-optical response, i.e. optical response in the presence of a magnetic field, is commonly used for characterization of materials and in optical communications. However, quantum mechanical description of electric and magnetic fields in crystals is not straightforward as the position operator is ill defined. We present a reformulation of the density matrix perturbation theory for timedependent electromagnetic fields under periodic boundary conditions, which allows us to treat the orbital magneto-optical response of solids at the ab initio level. The efficiency of the computational scheme proposed is comparable to standard linear-response calculations of absorption spectra and the results of tests for molecules and solids agree with the available experimental data. A clear signature of the valley Zeeman effect is revealed in the continuum magneto-optical spectrum of a single layer of hexagonal boron nitride. The present formalism opens the path towards the study of magneto-optical effects in strongly driven low-dimensional systems.arXiv:1806.09886v4 [cond-mat.mtrl-sci]

Valley Zeeman effect and Landau levels in two-dimensional transition metal dichalcogenides

“…The effects of electron-hole interactions on the exciton g-factors have been discussed by some authors [50]. Our consideration of electron-hole interactions will be published separately [51].…”

Valley Zeeman effect and Landau levels in Two-Dimensional Transition Metal Dichalcogenides

“…The effects of e-h interactions have been discussed by some authors [47]. Our consideration of e-h interactions will be published separately [48].…”

Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems

“…106,107 While magneto-optical spectra can be straightforwardly computed for molecules, [108][109][110][111][112] the theory for solids has been developed only re-cently. 113 The reason is that external electromagnetic fields break the translational symmetry of periodic systems, which is formally expressed through the unboundness of the position operator. [114][115][116] The orbital response to magnetic fields is especially complicated to describe, as such fields lead to non-perturbative changes in wavefunctions and introduce vector coupling to electron dynamics.…”

“…19,[120][121][122] To treat uniform magnetic fields in periodic systems, we use the approach based on perturbation theory for the one-particle density matrix. 113,117,119 Such an approach allows us to work under purely periodic boundary conditions and to automatically take into account gauge invariance. A periodic and gauge-invariant counterpart Õ is distinguished for any operator O = O r 1 r 2 defined for two points r 1 and r 2 in real space…”

“…Instead, α νµ,γ is expressed through the first-order derivatives to the perturbations P = E µ , B γ and a supplementary perturbation corresponding to a vector potential P = A ν at frequency −Ω. 113 To test the developed formalism for solids, it has been applied to bulk silicon and the corresponding results are shown in Fig. 10.…”