Quantum-electrodynamical approach to the exciton spectrum in transition-metal dichalcogenides

Manipulation of intrinsic electron degrees of freedom, such as charge and spin gives rise to electronics and spintronics, respectively. Electrons in monolayer materials with a honeycomb lattice structure, such as the Transition-Metal Dichalcogenides (TMD's), exhibit an additional degree of freedom, known as the valley, which may assume two values according to the region of the Brillouin zone the electron belongs. Valleytronics is expected to set up a new era in the realm of electronic devices by manipulating valley properties of electrons. In this work, we accurately determine the energy spectrum and lifetimes of exciton (electron-hole) bound-states for different TMD materials, namely WSe$_2$, WS$_2$ and MoS$_2$. Our approach, which employs quantum-field theory (QFT) techniques based on the Bethe-Salpeter equation and the Schwinger-Dyson formalism, takes into account the full electromagnetic interaction among the electrons. As a unique distinguishing feature, our method allows one to easily determine to which valley an exciton belongs, without the use of any external agents. We report here a splitting of 170 meV between the exciton energies from different valleys, corresponding to an effective Zeeman magnetic field of 1400 T. The valley selection mechanism operates through the dynamical breakdown of the time-reversal (TR) symmetry, which originally interconnects the two valleys. This is spontaneously broken whenever the full electromagnetic interaction vertex is used to probe the response of the system to an external field.