2.1 The Rise of the 2D Materials
19
Exciton
Negative Trion
Positive Trion
Biexciton
Negative Biexciton
K
K'
X
K
K'
K
K'
K
K'
K
K'
K
K'
K
K'
K
K'
K
K'
K
K'
K
K'
X d,t
X d,s
X - s
X - t
X - d
X +
X + d
X-X d,s
X-X d,t
XX -
e
-
h
+
XX
X
+
X
-
X
XX
-
X
XX or X-X annihilation
Fig. 2.2 A zoo of excitonic species and so-called multi-particle states across valleys can be obtained
in 2D semiconductors owing to the three-fold symmetry and the correspondingly peculiar spin–
valley locking. Here, a schematic overview diagram of possible exciton complexes is shown, drawn
freely after [41, 54, 55], indicating intra- and intervalley configurations for excitons (X), biexcitons
(XX) and their charged analogues, the trions (X ± ) and charged biexcitons (XX − ). The index d
denotes optically-dark states (grey-shaded boxes), s and t denote singlet and triplet state, respectively.
Black solid and open circles represent electrons and holes, respectively. By displaying here solely
the underlying charge carriers in their different host bands, Coulomb-binding energies are not
represented. Here, K and K represent the two distinct spin-opposite direct gap symmetry points
for monolayers. Black arrows indicate spin up/down corresponding to the colour-coded (red/blue)
band dispersions. Inset: Sketch of a 2D semiconductor layer with different crystal quasi-particles
52], excitation-detuning-dependent formation of macroscopic polarisation (coherent
excitons, also valley-polarised) [33], radiation patterns [47], phonon-assisted modes
[53] and the multi-particle states across valleys in 2D semiconductors [54, 55] have
been unraveled.
2D Excitons in Quantum Materials
Quantum materials such as monolayer TMDCs are particularly interesting due to the
zoo of exciton species hosted in their lattices after optical excitation (see Fig. 2.2), and
more importantly due to their strong light–matter interactions and the inherent spin–
valley locking [21, 56], which have attracted unmatched attention by the research
community. The former peculiar feature of these 2D semiconductors results from
their extraordinarily large oscillator strength as well as binding energy, whereas the
latter property is a consequence of the symmetry-breaking in the plane of the 2D
crystal.
Semiconducting few-layer and monolayer materials with their sharp optical resonances such as WSe 2 , which recently were reported close to the homogeneous
linewidth limit [7, 52, 57–60], have been extensively studied and envisioned for
applications in the weak [61–63] as well as strong light–matter coupling [64–69]
regimes. Also, they have been extensively studied for effective nanolaser operation
19
Exciton
Negative Trion
Positive Trion
Biexciton
Negative Biexciton
K
K'
X
K
K'
K
K'
K
K'
K
K'
K
K'
K
K'
K
K'
K
K'
K
K'
K
K'
X d,t
X d,s
X - s
X - t
X - d
X +
X + d
X-X d,s
X-X d,t
XX -
e
-
h
+
XX
X
+
X
-
X
XX
-
X
XX or X-X annihilation
Fig. 2.2 A zoo of excitonic species and so-called multi-particle states across valleys can be obtained
in 2D semiconductors owing to the three-fold symmetry and the correspondingly peculiar spin–
valley locking. Here, a schematic overview diagram of possible exciton complexes is shown, drawn
freely after [41, 54, 55], indicating intra- and intervalley configurations for excitons (X), biexcitons
(XX) and their charged analogues, the trions (X ± ) and charged biexcitons (XX − ). The index d
denotes optically-dark states (grey-shaded boxes), s and t denote singlet and triplet state, respectively.
Black solid and open circles represent electrons and holes, respectively. By displaying here solely
the underlying charge carriers in their different host bands, Coulomb-binding energies are not
represented. Here, K and K represent the two distinct spin-opposite direct gap symmetry points
for monolayers. Black arrows indicate spin up/down corresponding to the colour-coded (red/blue)
band dispersions. Inset: Sketch of a 2D semiconductor layer with different crystal quasi-particles
52], excitation-detuning-dependent formation of macroscopic polarisation (coherent
excitons, also valley-polarised) [33], radiation patterns [47], phonon-assisted modes
[53] and the multi-particle states across valleys in 2D semiconductors [54, 55] have
been unraveled.
2D Excitons in Quantum Materials
Quantum materials such as monolayer TMDCs are particularly interesting due to the
zoo of exciton species hosted in their lattices after optical excitation (see Fig. 2.2), and
more importantly due to their strong light–matter interactions and the inherent spin–
valley locking [21, 56], which have attracted unmatched attention by the research
community. The former peculiar feature of these 2D semiconductors results from
their extraordinarily large oscillator strength as well as binding energy, whereas the
latter property is a consequence of the symmetry-breaking in the plane of the 2D
crystal.
Semiconducting few-layer and monolayer materials with their sharp optical resonances such as WSe 2 , which recently were reported close to the homogeneous
linewidth limit [7, 52, 57–60], have been extensively studied and envisioned for
applications in the weak [61–63] as well as strong light–matter coupling [64–69]
regimes. Also, they have been extensively studied for effective nanolaser operation