70
3 Light–Matter Interactions for Photonic Applications
Fig. 3.4 a Schematic band structure depiction for a direct-gap semiconductor with electronic transitions from the valence band (VB) to the conduction band (CB). Here, the photo-induced electronic
excitation is indicated by arrows (nearly vertical, as the photon momentum is negligible compared
to the relevant phase space ranges for crystal electrons). The bands in the energy–momentum-space
diagram around the Γ point are oversimplified. q denotes the quasi-momentum for electrons/holes
in the lattice. This single-particle excitation picture does not take into account the formation of
correlated electron–hole pairs and cannot represent its energetics. b Rydberg-series of energy states
for the hydrogen-like electronic quasi-particle, which represents a fundamental electronic matter
excitation. The formation of Coulomb-bound electron–hole pairs, referred to as excitons, is sketched
with centre of mass (dot), envelope function (shaded area) and size (ring), typically given by the
Bohr radius for the main quantum number n (states 1s, 2s, ...). c In contrast to a, the quasi-particle
excitation picture displays the properties of excitons with centre-of-mass momentum Q that are the
dispersions for different resonances (1s, 2s or higher) and the corresponding effective mass (approximated from the parabolic dispersion around Γ ≡ Q = 0 point). Resonant (into bound states) and
off-resonant (into continuum states, i.e. ionised excitons) optical excitation are indicated by red
and dark-red arrows, respectively. By returning to the crystal ground state, the electronic excitation
releases its energy to the environment/system either radiatively (photon emission) or nonradiatively
(e.g. through Auger-like processes). Note that in the sketches (a–c) the energies are not correctly
scaled and merely serve visualisation purposes
The Long Path to Exciton Condensates
Even after long-lasting intensive research following the predictions of exciton condensation [133, 134] and pioneering work on collective properties of such quasiparticles [125], the desired results were lacking. A high decoherence rate via phonon
scattering in appropriate structures posed a major challenge, whereas the Mott transition [135, 136] from an insulator state of matter in the bosonic state to a metallic
(electron–hole) plasma in the fermionic regime above a critical particle density [137]
set an upper limit to the critical densities for condensation experiments. Many systems such as coupled quantum wells and spatially indirect excitons were considered
to circumvent such constraints [130]. Nevertheless, the effective mass of the quasiparticle required experiments to be carried out in the milli-Kelvin range in solids.
3 Light–Matter Interactions for Photonic Applications
Fig. 3.4 a Schematic band structure depiction for a direct-gap semiconductor with electronic transitions from the valence band (VB) to the conduction band (CB). Here, the photo-induced electronic
excitation is indicated by arrows (nearly vertical, as the photon momentum is negligible compared
to the relevant phase space ranges for crystal electrons). The bands in the energy–momentum-space
diagram around the Γ point are oversimplified. q denotes the quasi-momentum for electrons/holes
in the lattice. This single-particle excitation picture does not take into account the formation of
correlated electron–hole pairs and cannot represent its energetics. b Rydberg-series of energy states
for the hydrogen-like electronic quasi-particle, which represents a fundamental electronic matter
excitation. The formation of Coulomb-bound electron–hole pairs, referred to as excitons, is sketched
with centre of mass (dot), envelope function (shaded area) and size (ring), typically given by the
Bohr radius for the main quantum number n (states 1s, 2s, ...). c In contrast to a, the quasi-particle
excitation picture displays the properties of excitons with centre-of-mass momentum Q that are the
dispersions for different resonances (1s, 2s or higher) and the corresponding effective mass (approximated from the parabolic dispersion around Γ ≡ Q = 0 point). Resonant (into bound states) and
off-resonant (into continuum states, i.e. ionised excitons) optical excitation are indicated by red
and dark-red arrows, respectively. By returning to the crystal ground state, the electronic excitation
releases its energy to the environment/system either radiatively (photon emission) or nonradiatively
(e.g. through Auger-like processes). Note that in the sketches (a–c) the energies are not correctly
scaled and merely serve visualisation purposes
The Long Path to Exciton Condensates
Even after long-lasting intensive research following the predictions of exciton condensation [133, 134] and pioneering work on collective properties of such quasiparticles [125], the desired results were lacking. A high decoherence rate via phonon
scattering in appropriate structures posed a major challenge, whereas the Mott transition [135, 136] from an insulator state of matter in the bosonic state to a metallic
(electron–hole) plasma in the fermionic regime above a critical particle density [137]
set an upper limit to the critical densities for condensation experiments. Many systems such as coupled quantum wells and spatially indirect excitons were considered
to circumvent such constraints [130]. Nevertheless, the effective mass of the quasiparticle required experiments to be carried out in the milli-Kelvin range in solids.