5.3 Basic Material Response
157
(cf. Fig. 2.7a, b), and the exciton–polaron-formation picture has been supported
by temperature-dependent dispersion measurements [66]. Furthermore, the linearity factor can also show a change within density-dependent measurements at higher
excitation densities near to the Mott transition for TMDCs (Fig. 5.12). This gets manifest as a kink in the (double-logarithmical) input–output curve, which can be caused
by a different band renormalisation at K and -point [31, 84]. Thus, complementary
information for a material system can be obtained by different considerations. This
becomes further clear in another PL-measurement example related to interactions
with the phonon bath.
In addition, for different stacks of WSe 2 and hBN (i.e. substrate-supported, hBNsupported, hBN-capped and hBN-encapsulated), temperature-dependent energy
shifts were in parallel to the linearity factor evaluated in a series between 10 K and
300 K [5], indicating reduced exciton–phonon coupling strengths for capped and
encapsulated monolayers. To link the shifts with the role of optical phonon modes at
elevated temperatures, the phenomenological O’Donnell model can be for instance
useful [85]:
E(T ) = E 0 (T = 0) − S ω
coth ω
2k B T
− 1
,
(5.4)
with the two parameters ω and S denoting the mean energy of optical phonons
and the dimensionless coupling constant, respectively. The latter is also referred to
as Huang-Rhys factor. Interestingly, the extracted trion–phonon coupling parameter
was systematically weaker than the exciton–phonon counterpart (S X ± < S X 0 ). Note
that with regard to such temperature-series evaluation, if the emphasis is not on the
discussion of exciton–phonon coupling, also the phenomenological Varshni equation
[86] typically describes the data well (also the case for [5]). Therefor, the second
term −S... in (5.4) is replaced with −αT
2
/(T + β), with parameters α and β.
In 2D semiconductors with excitons arising from different bands such as the A and
B (and C) excitons of TMDCs [87], an additional possibility of injecting excitons is
given by resonantly addressing the A or B type, for instance. However, decay channels
to lower-lying excitons cause depopulation and introduce additional depolarisation
pathways in valley-sensitive materials. Unless the free-carrier energy gap is above
the addressed species, resonance excitation of higher energy excitons automatically
leads to direct-gap hot carrier excitation. This might become even more relevant
when combining TMDC monolayers to form heterostructures (cf. [2, 5, 88–90]).
Last, but not least, excitation and detection can be purposefully adjusted to be in
a certain polarisation of light. This can be particularly useful when dealing with valleytronic materials such as the valley-polarisable TMDCs (see for instance [91–93]).
TMDCs as monolayers exhibit considerable polarisation anisotropy, which can be
in the case of bilayers further dependent on the bilayer configuration (for instance
discussed in [8]). In [8], superachromatic wave-plates and polarisers were used for
polarisation-resolved measurements. Typically, co- and cross-/counter- polarisation
are of interest to determine the degree of linear/circular polarisation. The degree of
157
(cf. Fig. 2.7a, b), and the exciton–polaron-formation picture has been supported
by temperature-dependent dispersion measurements [66]. Furthermore, the linearity factor can also show a change within density-dependent measurements at higher
excitation densities near to the Mott transition for TMDCs (Fig. 5.12). This gets manifest as a kink in the (double-logarithmical) input–output curve, which can be caused
by a different band renormalisation at K and -point [31, 84]. Thus, complementary
information for a material system can be obtained by different considerations. This
becomes further clear in another PL-measurement example related to interactions
with the phonon bath.
In addition, for different stacks of WSe 2 and hBN (i.e. substrate-supported, hBNsupported, hBN-capped and hBN-encapsulated), temperature-dependent energy
shifts were in parallel to the linearity factor evaluated in a series between 10 K and
300 K [5], indicating reduced exciton–phonon coupling strengths for capped and
encapsulated monolayers. To link the shifts with the role of optical phonon modes at
elevated temperatures, the phenomenological O’Donnell model can be for instance
useful [85]:
E(T ) = E 0 (T = 0) − S ω
coth ω
2k B T
− 1
,
(5.4)
with the two parameters ω and S denoting the mean energy of optical phonons
and the dimensionless coupling constant, respectively. The latter is also referred to
as Huang-Rhys factor. Interestingly, the extracted trion–phonon coupling parameter
was systematically weaker than the exciton–phonon counterpart (S X ± < S X 0 ). Note
that with regard to such temperature-series evaluation, if the emphasis is not on the
discussion of exciton–phonon coupling, also the phenomenological Varshni equation
[86] typically describes the data well (also the case for [5]). Therefor, the second
term −S... in (5.4) is replaced with −αT
2
/(T + β), with parameters α and β.
In 2D semiconductors with excitons arising from different bands such as the A and
B (and C) excitons of TMDCs [87], an additional possibility of injecting excitons is
given by resonantly addressing the A or B type, for instance. However, decay channels
to lower-lying excitons cause depopulation and introduce additional depolarisation
pathways in valley-sensitive materials. Unless the free-carrier energy gap is above
the addressed species, resonance excitation of higher energy excitons automatically
leads to direct-gap hot carrier excitation. This might become even more relevant
when combining TMDC monolayers to form heterostructures (cf. [2, 5, 88–90]).
Last, but not least, excitation and detection can be purposefully adjusted to be in
a certain polarisation of light. This can be particularly useful when dealing with valleytronic materials such as the valley-polarisable TMDCs (see for instance [91–93]).
TMDCs as monolayers exhibit considerable polarisation anisotropy, which can be
in the case of bilayers further dependent on the bilayer configuration (for instance
discussed in [8]). In [8], superachromatic wave-plates and polarisers were used for
polarisation-resolved measurements. Typically, co- and cross-/counter- polarisation
are of interest to determine the degree of linear/circular polarisation. The degree of