  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), can be distinguished according to the
region (valley) of the Brillouin zone to which they belong. Valleytronics, the
manipulation of this electron's property, is expected to set up a new era in
the realm of electronic devices. 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$_2$. For all of them,
we obtain a splitting of the order of 170 meV between the exciton energies from
different valleys, corresponding to an effective Zeeman magnetic field of 1400
T. 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. The valley
selection mechanism operates through the dynamical breakdown of the
time-reversal (TR) symmetry, which originally interconnects the two valleys.
This symmetry is spontaneously broken whenever the full electromagnetic
interaction vertex is used to probe the response of the system to an external
field.
