198
6 Effects of Quantisation
their room-temperature excitons promise further advances towards practical polariton
systems [51].
To conclude this very compact part, it shall be highlighted that there are two main
reasons to consider 2D semiconductors for BEC studies at room temperature. Firstly,
their robust excitons with their extraordinary high binding energies for inorganic
crystalline materials allows to study density-dependent effects at room temperature.
Their exciton Bohr radius locates them somewhere between Wannier–Mott [52, 53]
and Frenkel-like [54] excitons
10 (see table in [55] and references therein). Secondly,
in optical microcavities, they can couple strongly with the confined light field (even in
relatively-low-quality resonators) and form extremely light quasi-particles—hybrid
states with composite-bosonic character well below the electron–hole plasma (Mott)
density. For fundamentals on semiconductor optics, the interested reader is referred
to textbooks such as [21, 56, 57]. For a general discussion of BEC and topical
overview on some examples, see [43, 58–62]. Condensation phenomena involving
2D-materials excitons are furthermore investigated without cavities at cryogenic
temperatures, e.g. for bilayer systems [63].
6.3.1 Charge-Carrier Localisation and Tailored Transitions
Historically, the introduction of confinement schemes has both step-wise (for each
major design change of active media) and continuously (due to maturity of the underlying technology) improved the performance of optical devices such as laser diodes.
Beginning with bare pn-junctions, laser thresholds and operation temperatures benefited strongly from the introduction of double heterostructures (cf. [64, 65]) owing to
an improved overlap between charge carriers and optical fields. Currently, quantumwell structures are indispensable elements of semiconductor gain media, whereas
quantum dots open new pathways to ultra-efficient nanolasers [12, 66, 67], which
are attractive for “green photonics” (e.g. [68]), and more uniquely for single-photon
sources and cQED experiments (cf. [12, 69–73]). Beyond that, they find application
in photodetectors, nanoelectronics and nonlinear materials. Ultimately, novel concepts for quantum technological devices fully rely on the control of electronic and
optical properties of/by quantum structures.
In semiconductor lasers, the modification of the DOS yields noticeable improvements regarding the onset of lasing at reduced charge-carrier densities, as the number
of available states right at the band-gap energy for the stimulated emission process is
governed by the dimensionality. While bulk semiconductors with square-root DOS
have exactly a minimum of states at the lowest transition energy between bands,
quantum wells with their step function directly provide a constant number of states
at a well-defined ground-state transition energy. Quantum dots further localise charge
10 For details on these two exciton types and the differences between Wannier–Mott and Frenkel
excitons, i.e. delocalised crystal lattice and localised molecule site excitons, respectively, see for
instance [21].
6 Effects of Quantisation
their room-temperature excitons promise further advances towards practical polariton
systems [51].
To conclude this very compact part, it shall be highlighted that there are two main
reasons to consider 2D semiconductors for BEC studies at room temperature. Firstly,
their robust excitons with their extraordinary high binding energies for inorganic
crystalline materials allows to study density-dependent effects at room temperature.
Their exciton Bohr radius locates them somewhere between Wannier–Mott [52, 53]
and Frenkel-like [54] excitons
10 (see table in [55] and references therein). Secondly,
in optical microcavities, they can couple strongly with the confined light field (even in
relatively-low-quality resonators) and form extremely light quasi-particles—hybrid
states with composite-bosonic character well below the electron–hole plasma (Mott)
density. For fundamentals on semiconductor optics, the interested reader is referred
to textbooks such as [21, 56, 57]. For a general discussion of BEC and topical
overview on some examples, see [43, 58–62]. Condensation phenomena involving
2D-materials excitons are furthermore investigated without cavities at cryogenic
temperatures, e.g. for bilayer systems [63].
6.3.1 Charge-Carrier Localisation and Tailored Transitions
Historically, the introduction of confinement schemes has both step-wise (for each
major design change of active media) and continuously (due to maturity of the underlying technology) improved the performance of optical devices such as laser diodes.
Beginning with bare pn-junctions, laser thresholds and operation temperatures benefited strongly from the introduction of double heterostructures (cf. [64, 65]) owing to
an improved overlap between charge carriers and optical fields. Currently, quantumwell structures are indispensable elements of semiconductor gain media, whereas
quantum dots open new pathways to ultra-efficient nanolasers [12, 66, 67], which
are attractive for “green photonics” (e.g. [68]), and more uniquely for single-photon
sources and cQED experiments (cf. [12, 69–73]). Beyond that, they find application
in photodetectors, nanoelectronics and nonlinear materials. Ultimately, novel concepts for quantum technological devices fully rely on the control of electronic and
optical properties of/by quantum structures.
In semiconductor lasers, the modification of the DOS yields noticeable improvements regarding the onset of lasing at reduced charge-carrier densities, as the number
of available states right at the band-gap energy for the stimulated emission process is
governed by the dimensionality. While bulk semiconductors with square-root DOS
have exactly a minimum of states at the lowest transition energy between bands,
quantum wells with their step function directly provide a constant number of states
at a well-defined ground-state transition energy. Quantum dots further localise charge
10 For details on these two exciton types and the differences between Wannier–Mott and Frenkel
excitons, i.e. delocalised crystal lattice and localised molecule site excitons, respectively, see for
instance [21].