2.2 Fundamentals of 2D Materials
27
Here, the (complex) dielectric function of 2D semiconductors (cf. [115])
implies for very good-quality 2D materials with very high oscillator strength and
near-homogeneously broadened linewidth (such as achieved by [7, 52, 57–59, 142,
150]) a Reststrahlenbande
3 in the reflection spectrum
4 [149] and, thus, hybrid light–
matter states with very low effective masses of their composite particles [33, 52].
These hybrid quasi-particles can be regarded as highly-mobile, delocalised, macroscopically valley-polarised correlated electron–hole pairs dressed with light.
Previously, the link between coherent excitons and exciton–polaritons had been
widely disregarded for TMDCs, but this aspect has become more significant when
the occurrence of negative permittivities around exciton resonances is justified by the
narrow linewidths. These findings and many more leave plenty of room for deeper
investigations of this material class. Recently, also the concept of renormalisation of
longitudinal-mode energies within the light cone and the degeneracy lifting between
longitudinal and transverse exciton modes (previously discussed for III/V quantumwell systems [151, 152]) has been revisited (see [33] and references therein, and
Chap. 3). Furthermore, within the light cone, the exciton fine-structure’s pseudo-spin
and angle-resolved valley polarisation was optically probed in [33].
Impact of the Substrate and Environment on Monolayer TMDCs
Although 2D materials are an ideal (ultrathin) model system in which charge-carriers
are strongly confined to the layer of transition metals between the chalcogen layers, they are in fact still not perfect. First of all, many properties are only ideal for
a defect- and disorder-free suspended monolayer in vacuum. Besides the fact that
most samples are not (strain-free perfectly) suspended, defects in the material spoil
various optoelectronic properties, as summarised further below. Furthermore, optoelectronic properties of TMDC monolayers are affected by the dielectric environment
(screening) and substrate-induced effects, as early studies indicated.
An interesting overview of the many different values for excitonic energies and
linewidths (compared for the four prominent members of the TMDC family) from
the early characterisation efforts in the literature is provided as a table with references
in [40]—a work concerning the impact of the environment on excitonic resonances
following a similar investigation focusing on the influence of the substrate material
on optical properties of monolayers [87].
Naturally (well before these works occurred), the questions arose whether the
substrates induced doping and strain, what the roles of local roughness and chemical
affinities were, and how the band-structure was changed by the local environment.
For instance, it was shown by Lin et al. that the trion/exciton ratio changed in the
emission (PL) of monolayer MoS 2 and the peak positions changed as well, when a
covering solvant was systematically varied to span a range of solvant dielectric con3 The Reststrahlenbande is a high-reflectivity band (photonic stop band), which is the consequence
of the zero-crossings of the real part of , i.e. for Re {} = < 0.
4 Note that spatial dispersion discussed in Chap. 5 of [149] may affect the maximum reflectivity in
the spectral region between the transverse and longitudinal exciton, i.e. between their resonances
ω 0 and ω L , respectively.
27
Here, the (complex) dielectric function of 2D semiconductors (cf. [115])
implies for very good-quality 2D materials with very high oscillator strength and
near-homogeneously broadened linewidth (such as achieved by [7, 52, 57–59, 142,
150]) a Reststrahlenbande
3 in the reflection spectrum
4 [149] and, thus, hybrid light–
matter states with very low effective masses of their composite particles [33, 52].
These hybrid quasi-particles can be regarded as highly-mobile, delocalised, macroscopically valley-polarised correlated electron–hole pairs dressed with light.
Previously, the link between coherent excitons and exciton–polaritons had been
widely disregarded for TMDCs, but this aspect has become more significant when
the occurrence of negative permittivities around exciton resonances is justified by the
narrow linewidths. These findings and many more leave plenty of room for deeper
investigations of this material class. Recently, also the concept of renormalisation of
longitudinal-mode energies within the light cone and the degeneracy lifting between
longitudinal and transverse exciton modes (previously discussed for III/V quantumwell systems [151, 152]) has been revisited (see [33] and references therein, and
Chap. 3). Furthermore, within the light cone, the exciton fine-structure’s pseudo-spin
and angle-resolved valley polarisation was optically probed in [33].
Impact of the Substrate and Environment on Monolayer TMDCs
Although 2D materials are an ideal (ultrathin) model system in which charge-carriers
are strongly confined to the layer of transition metals between the chalcogen layers, they are in fact still not perfect. First of all, many properties are only ideal for
a defect- and disorder-free suspended monolayer in vacuum. Besides the fact that
most samples are not (strain-free perfectly) suspended, defects in the material spoil
various optoelectronic properties, as summarised further below. Furthermore, optoelectronic properties of TMDC monolayers are affected by the dielectric environment
(screening) and substrate-induced effects, as early studies indicated.
An interesting overview of the many different values for excitonic energies and
linewidths (compared for the four prominent members of the TMDC family) from
the early characterisation efforts in the literature is provided as a table with references
in [40]—a work concerning the impact of the environment on excitonic resonances
following a similar investigation focusing on the influence of the substrate material
on optical properties of monolayers [87].
Naturally (well before these works occurred), the questions arose whether the
substrates induced doping and strain, what the roles of local roughness and chemical
affinities were, and how the band-structure was changed by the local environment.
For instance, it was shown by Lin et al. that the trion/exciton ratio changed in the
emission (PL) of monolayer MoS 2 and the peak positions changed as well, when a
covering solvant was systematically varied to span a range of solvant dielectric con3 The Reststrahlenbande is a high-reflectivity band (photonic stop band), which is the consequence
of the zero-crossings of the real part of , i.e. for Re {} = < 0.
4 Note that spatial dispersion discussed in Chap. 5 of [149] may affect the maximum reflectivity in
the spectral region between the transverse and longitudinal exciton, i.e. between their resonances
ω 0 and ω L , respectively.