Abstract

We study the optical properties of semiconducting transition metal dichalcogenide monolayers under the influence of strong out-of-plane magnetic fields, using the effective massive Dirac model. We pay attention to the role of spin-orbit coupling effects, doping level and electron-electron interactions, treated at the Hartree-Fock level. We find that optically-induced valley and spin imbalance, commonly attained with circularly polarized light, can also be obtained with linearly polarized light in the doped regime. Additionally, we explore an exchange-driven mechanism to enhance the spin-orbit splitting of the conduction band, in n-doped systems, controlling both the carrier density and the intensity of the applied magnetic field.

Highlights

  • The discovery of two-dimensional (2D) systems whose quasiparticles are described in terms of a Dirac theory [1] has been one of the major breakthroughs over the last two decades in condensed matter physics and has fueled research in the area of 2D materials [2,3]

  • We study the optical response of massive Dirac systems under the influence of applied out-ofplane magnetic fields

  • We focus on the case of transition metal dichalcogenide (TMD) monolayers MX 2, where M = Mo,W and X = S,Se, whose magneto-optical properties

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Summary

INTRODUCTION

The discovery of two-dimensional (2D) systems whose quasiparticles are described in terms of a Dirac theory [1] has been one of the major breakthroughs over the last two decades in condensed matter physics and has fueled research in the area of 2D materials [2,3]. There are 2D semiconductors that require a description through a massive Dirac equation [5,6], instead of a Schrödinger-type model Whereas both Dirac and Schrödinger theories would yield similar energy bands, their wave functions and linear response are distinct. Have attracted considerable interest both from the experimental [10,11,12,13] and theoretical [14,15] sides These directband-gap semiconductors are the object of intense scrutiny because of their strong light-matter coupling [16,17], strong spin-orbit interactions [5,9], rich excitonic effects [18,19,20,21], and potential applications in the emergent field of valleytronics [22,23].

MODEL HAMILTONIAN
MAGNETO-OPTICAL RESPONSE
Dipole matrix elements
Electric susceptibility
Circularly polarized light
LONGITUDINAL SUSCEPTIBILITY
Undoped regime
Doped system with optical transitions to zeroth
Doped system with a single Landau level polarized
TRANSVERSE SUSCEPTIBILITY
RESPONSE TO CIRCULARLY POLARIZED LIGHT
EXCHANGE SELF-ENERGY CORRECTIONS
Keldysh potential
Exchange self-energy
Renormalized optical transition energies
Renormalization of the spin-orbit splitting
VIII. DISCUSSION AND CONCLUSIONS
Limits of the model
Main results
Interacting equation of motion
Exchange self-energy terms
Coulomb integrals

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