Abstract
We show that the magnetic response of atomically thin materials with Dirac spectrum and spin-orbit interactions can exhibit strong dependence on electron-electron interactions. While graphene itself has a very small spin-orbit coupling, various two-dimensional (2D) compounds "beyond graphene" are good candidates to exhibit the strong interplay between spin-orbit and Coulomb interactions. Materials in this class include dichalcogenides (such as MoS$_2$ and WSe$_2$), silicene, germanene, as well as 2D topological insulators described by the Kane-Mele model. We present a unified theory for their in-plane magnetic field response leading to "anomalous", i.e. electron interaction dependent transition moments. Our predictions can be potentially used to construct unique magnetic probes with high sensitivity to electron correlations.
Highlights
Two-dimensional quantum materials are characterized by low-energy quasiparticle excitations that can be fully described by an effective (2 + 1)-dimensional Dirac equation
While most studies related to anomalous quantum Hall physics have been conducted within the context of massless two-dimensional (2D) Dirac fermions [5,6,8,9], recent research has elucidated similar magnetic phenomena arising in the regime of massive 2D Dirac fermions [10,11]
In this paper we explore the magnetic response of the massive 2D Dirac fermions, with a special focus on the effect of electron-electron interactions
Summary
Two-dimensional quantum materials are characterized by low-energy quasiparticle excitations that can be fully described by an effective (2 + 1)-dimensional Dirac equation. We will extend and apply our formalism and calculations of anomalous transition magnetic moments to two other systems, which include the atomically thin TMDCs and silicene-germanene class of materials Besides being gapped, these materials display strong intrinsic spin-orbit coupling effects [14,24,25,26,27,28,29,30,31]. The Kane-Mele model describes the general 2D Dirac Hamiltonian with a mass term that originates from the spinorbit coupling This SOC renders the system gapped, and much of this section will be devoted to understanding the interplay of Coulomb interactions and the SOC in relation to the transverse magnetic response. To display the effects of the Coulomb interaction correction, we show the dependence of the total transition moment μ + δμ with the dimensionless band momenta for various values of the coupling α in the bottom panel of Fig. 2. We extend this formalism to calculate the one-loop Coulomb interaction correction for the transition moment in atomically thin dichalcogenides
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