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\begin{document}

\title{Disclosed: quasiparticle properties and dynamics in real and momentum
space}



\author[1]{Ursula Wurstbauer}%
\affil[1]{University of Münster Department of Physics}%


\vspace{-1em}



  
  \date{June 17, 2024}


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Disclosed: quasiparticle properties and dynamics in real and momentum
space

Ursula Wurstbauer

\selectlanguage{ngerman}\emph{Institute of Physics and Center for Soft Nanoscience (SoN),
Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str.10, 48149
Münster, Germany.}

\selectlanguage{english}\textbf{+ wurstbauer@uni-muenster.de}

Physical properties of solid-state materials and other systems are
determined by manifold interactions. While for weakly interacting
systems their description in a single-particle picture is often
sufficient, this approach fails when the interactions become stronger
and many particles are involved. The quantum-mechanical problem of
describing elementary excitations and collective behavior in many-body
systems is often solved by introducing quasiparticles, thereby
transforming the problem of strongly interacting particles to that of
weakly interacting quasiparticles.

Prominent examples are band-electrons in crystals that are described by
electrons with an effective mass acting as free electrons in vacuum
despite being surrounded by many other electrons and the atoms of the
solid . Further examples are Cooper pairs -- quasiparticles in
superconductors -- that are composite bosons comprised of two electrons
coupled by exchange of virtual phonons ; composite fermions --
quasiparticles of fractional quantum Hall effect states -- consisting of
electrons coupled with an even number of flux quanta ; and also phonons,
the quasiparticles of collective lattice vibrations, or plasmons, the
quasiparticles describing collective excitation of free electrons in
solids . Quasiparticles are often connected with emergent phenomena such
as superconductivity, superfluidity or others and can have different
quasiparticle statistics than the underlying real-particles, e.g.
transforming two fermions into a composite boson as, e.g., for Cooper
pairs and excitons. The latter amounts to a bound electron-hole pair in
a solid or a molecule.

The concept of employing weakly interacting quasiparticles to describe
many-body phenomena in a solid-state system was pioneered by Y. Frenkel
in 1930 when he described the neutral excitation of a solid with light
by an exciton -- a photo-excited electron-hole pair bound together by
attractive Coulomb force. Excitons can be viewed as analogues of the
hydrogen atom model, featuring Rydberg states and a fine structure, also
with respect to spin alignment. Excitons exist in semiconductors,
insulators and molecules, in zero-dimensional quantum dots,
one-dimensional wires and tubes, two-dimensional systems as well as in
bulk materials. Recently, the exciton-dominated light-matter interaction
in ultimately thin two-dimensional semiconductors has been intensely
studied because of the strong exciton binding energies on the order of
0.5 eV caused by reduced screening . The most prominent ambassador of
such systems is the class of air-stable transition metal dichalcogenides
(TMDCs) as, e.g., MoS\textsubscript{2} or WSe\textsubscript{2} that
transition from an indirect to a direct gap material when approaching
the monolayer limit . The single-particle states for two valleys in the
conduction band are very close in energy and prone to external stimuli
such as strain doping or dielectric environment. Therefore, the nature
of the lowest energy neutral interband excitation forming the exciton is
under debate. The exciton could hold vanishing crystal momentum or
finite crystal momentum such that the decay is typically phonon-assisted
in order to fulfill the momentum conservation law . The all-surface
nature of those materials allows modifying the excitonic properties by
dielectric engineering , defect engineering by creating individual
emitter sites as well stacking into van der Waals heterostructures
enabling the formation of charge transfer excitons (a.k.a interlayer
excitons) with one electron localized in one crystal plane and another
electron in the other plane .

Excitons are electrically neutral and can be generated electrically or
optically and are either localized around an individual lattice site
(Frenkel exciton) or freely moving in a crystal (Wannier-Mott exciton) .
Excitons can act as single photon sources emitting just one exciton at a
time or gather into dense exciton ensembles. Excitons play also a
crucial role in the origin of life as energy transfer mechanisms in
biology via Forster resonance energy transfer (FRET) processes , but
also in solid-state lighting, solar energy harvesting, and information
and quantum-information technologies. In particular the latter requires
detailed knowledge of the quantum properties of the exciton
quasiparticle including its wave-function in real as well as momentum
(\emph{k} )-space. In addition, exciton formation, relaxation and decay
dynamics as well as their interaction with the solid or free charge
carriers are of particular interest since those are, e.g., sources of
decoherence hampering applications in the quantum information and
computation sector.

Excitons can have finite crystal momentum with electrons and holes
confined at different valleys in \emph{k} -space. Exciton energies and
the dynamics of excitons with vanishing center of mass momentum can be
easily determined by (time-resolved) optical interband measurements.
Binding and Rydberg energies can be determined either by absorption
experiments or a combination of optical experiments and
scanning-tunneling experiments and even the inner structure, independent
of their center of mass momentum, can be accessed by time-resolved
intraband spectroscopy . Direct experimental access to spin-forbidden or
momentum dark excitons is more challenging because optical interband
transitions need to be mediated, e.g., by phonons to fulfill the
momentum conservation law. Still, the wavefunction properties and the
dispersion relation E(\emph{k} ) of those quasiparticles describing the
neutral excitation cannot be unraveled by such techniques. The
dispersion relation of the underlying single-particle states can be
accessed in the case of occupied states by angle-resolved photo-emission
spectroscopy (ARPES) and in the case of unoccupied states by inverse
photoemission experiments (IPE) .

Excitons like other quasiparticles possess a quantum mechanical
wavefunction as well as energy-momentum relation that are distinctly
different from those of the underlying single particle states. The
concept of a quasiparticle is a great success story significantly
simplifying the understanding and description of complex many-body
phenomena. However, direct measurement of the spatial distribution of
the quasiparticle wave-function {[}Dong21{]} and direct visualization of
finite momentum excitons {[}Dong21, remains challenging and was achieved
only more than 90 years after the quasi-particle invention. Dong and
coworkers {[}Dong21{]} employed a multi-dimensional photoemission
spectroscopy scheme to directly access the time-, momentum-, and
energy-resolved properties of excitons in the layered semiconductor
WSe\textsubscript{2}.The decay dynamics of bright excitons was monitored
through time-resolved and angle-resolved photoemission spectroscopy
(tr-ARPES) measurements. The material is first excited with a pump pulse
of energy close to the fundamental band gap and probed with a
time-delayed XUV probe pulse to study the photoemission characteristics
in dependence of the excitation in the energy and time domain.
Near-resonant excitation conditions are fulfilled if the energy of the
absorbed photon is just sufficient to promote an electron from the
valence band at the \emph{K} -point in the
1\textsuperscript{st}Brillouin Zone (BZ) to the conduction band at the
\emph{K} -point leaving a hole behind. The \emph{K} -points are high
symmetry point located at the corners of the 1\textsuperscript{st} BZ
with the lowest energy direct interband transition in the band structure
. For near resonance excitation, the generated particles have vanishing
of just little access energy. For such a near-resonant excitation
scheme, Dong et al. report the generation of a coherent excitonic
polarization. The neutral elementary excitations decay to a bright
exciton population within a dephasing time of about 17 fs. Rather fast
within a time of about 18 fs the quasiparticles scatter into an exciton
ensemble with finite center of mass momentum with the electron state
residing at another high symmetry point - the \selectlanguage{greek}Σ \selectlanguage{english}point inside the BZ and
the hole state at the \emph{K} -point at the corner of the BZ. By
Fourier transformation of the momentum distribution, real space
information of the excitonic state could be extracted {[}Dong21{]}. In
this way, the isotropic quasiparticle wave function envelope is
determined and an exciton Bohr radius of 1.78 nm is obtained, which is
consistent with the theoretically expected valued.

In the future, the method of Dong et al. holds the promise to also
uncover the spatial distribution of the quasiparticle wavefunction along
with the distinct properties of other many-body states of interest.
Among these are charge-transfer excitons. Due to reduced overlap of the
underlying single-particle wave-functions, charge-transfer excitons
exhibit enhanced lifetimes that allow the formation of thermalized dense
ensembles. Such ensembles of bosonic quasiparticles are expected to show
emergent correlation phenomena at high densities and low temperatures
due to their bosonic nature . Valley selective hybridization effects
enable electric-field and hence gate-tunable switching of charge
excitons and direct excitons that might serve as quasiparticle qubits .
For integration into realistic quantum-circuitries, it would be highly
beneficial to know their quantum mechanical properties. The extension of
the method introduced by Dong et al. {[}Dong21{]} can thus be expected
to advance our current understanding of interaction-driven emergent
phenomena in solid state systems.

{[}Dong21{]}

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