Abstract
We theoretically investigate the magnetic brightening, valley Zeeman
splitting, and valley dynamics of long-lived A and B dark excitons
(A-DEs and B-DEs) in monolayer WS2, subjected to tilted magnetic fields.
Biexciton states and indirect intervalley excitons, with the latter
composed of a hole in the K valley and an electron in the A valley, are
also taken into account. We reveal that both in-plane and out-of-plane
field components greatly affect the magnetic brightening process due to
correlations among different excitonic quasiparticles but in distinct
roles. Specifically, the in-plane component primarily enables the
dark-state brightening, while the perpendicular one not only modifies
the bright-dark splitting inside a given valley, but also lifts the
valley degeneracy of either bright or dark excitonic states. Moreover,
in the presence of a tilted magnetic field with a nonzero in-plane
component, we observe that both A-DEs and B-DEs can be brightened, with
the latter requiring a much stronger field for a certain intensity of
light emission. Remarkably, we find that the valley splitting of A-DEs
is around twice as large as that of A bright excitons but vanishes for
B-DEs, as a result of the combined effect of the spin and orbital
magnetic moments on the energy shifts of the two valleys. In addition,
as the tilt angle of the field with respect to the normal direction of
WS2 sheet increases from 0 degrees to 180 degrees, the bright-dark
splittings for A and B excitons exhibit an opposite behavior, but both
feature an ``X''-like pattern when the field is oriented in-plane.
Finally, it is observed that the temperature greatly affects the light
emission of bright and brightened dark states, while the corresponding
temperature dependence is distinct for A and B excitons.
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