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This reference book explains the fundamentals of Bose Einstein Condensation (BEC) in excitons and polaritons. It presents five chapters exploring fundamental concepts and recent developments on the subject. Starting with a historical overview of BEC, the book progresses into the origins and behaviors of excitons and polaritons. Chapters also cover the unique thermalization and relaxation kinetics of excitons, and the distinctive features of polaritons, such as lasing, superfluidity, and quantized vortices. The chapters dedicated to BEC in excitons and polaritons detail experimental techniques, theoretical modeling, recent advancements, and practical applications in a simplified way for beginners. This book serves as a resource for researchers, physicists, and students interested in the phenomena of BEC, providing insights into both the theoretical foundations and the practical implications of excitons and polaritons. Readership Graduate and undergraduate students and academics studying particle and contended matter physics.

Two-dimensional materials and their heterostructures constitute a promising platform to study correlated electronic states, as well as the many-body physics of excitons. Transport measurements on twisted graphene bilayers have revealed a plethora of intertwined electronic phases, including Mott insulators, strange metals and superconductors 1 – 5 . However, signatures of such strong electronic correlations in optical spectroscopy have hitherto remained unexplored. Here we present experiments showing how excitons that are dynamically screened by itinerant electrons to form exciton-polarons 6 , 7 can be used as a spectroscopic tool to investigate interaction-induced incompressible states of electrons. We study a molybdenum diselenide/hexagonal boron nitride/molybdenum diselenide heterostructure that exhibits a long-period moiré superlattice, as evidenced by coherent hole-tunnelling-mediated avoided crossings of an intralayer exciton with three interlayer exciton resonances separated by about five millielectronvolts. For electron densities corresponding to half-filling of the lowest moiré subband, we observe strong layer pseudospin paramagnetism, demonstrated by an abrupt transfer of all the (roughly 1,500) electrons from one molybdenum diselenide layer to the other on application of a small perpendicular electric field. Remarkably, the electronic state at half-filling of each molybdenum diselenide layer is resilient towards charge redistribution by the applied electric field, demonstrating an incompressible Mott-like state of electrons. Our experiments demonstrate that optical spectroscopy provides a powerful tool for investigating strongly correlated electron physics in the bulk and paves the way for investigating Bose–Fermi mixtures of degenerate electrons and dipolar excitons. Optical spectroscopy is used to probe correlated electronic states in a moiré heterostructure, showing many-body effects such as strong layer paramagnetism and an incompressible Mott-like state of electrons.

The design and control of material interfaces is a foundational approach to realize technologically useful effects and engineer material properties. This is especially true for two-dimensional (2D) materials, where van der Waals stacking allows disparate materials to be freely stacked together to form highly customizable interfaces. This has underpinned a recent wave of discoveries based on excitons in stacked double layers of transition metal dichalcogenides (TMDs), the archetypal family of 2D semiconductors. In such double-layer structures, the elegant interplay of charge, spin and moiré superlattice structure with many-body effects gives rise to diverse excitonic phenomena and correlated physics. Here we review some of the recent discoveries that highlight the versatility of TMD double layers to explore quantum optics and many-body effects. We identify outstanding challenges in the field and present a roadmap for unlocking the full potential of excitonic physics in TMD double layers and beyond, such as incorporating newly discovered ferroelectric and magnetic materials to engineer symmetries and add a new level of control to these remarkable engineered materials. This Review discusses the exciton physics of transition metal dichalcogenides, focusing on moiré patterns and exciton many-body physics, and outlines future research directions in the field.

A Bose–Einstein condensate is the ground state of a dilute gas of bosons, such as atoms cooled to temperatures close to absolute zero 1 . With much smaller mass, excitons (bound electron–hole pairs) are expected to condense at considerably higher temperatures 2 – 7 . Two-dimensional van der Waals semiconductors with very strong exciton binding are ideal systems for the study of high-temperature exciton condensation. Here we study electrically generated interlayer excitons in MoSe 2 –WSe 2 atomic double layers with a density of up to 10 12 excitons per square centimetre. The interlayer tunnelling current depends only on the exciton density, which is indicative of correlated electron–hole pair tunnelling 8 . Strong electroluminescence arises when a hole tunnels from WSe 2 to recombine with an electron in MoSe 2 . We observe a critical threshold dependence of the electroluminescence intensity on exciton density, accompanied by super-Poissonian photon statistics near the threshold, and a large electroluminescence enhancement with a narrow peak at equal electron and hole densities. The phenomenon persists above 100 kelvin, which is consistent with the predicted critical condensation temperature 9 – 12 . Our study provides evidence for interlayer exciton condensation in two-dimensional atomic double layers and opens up opportunities for exploring condensate-based optoelectronics and exciton-mediated high-temperature superconductivity 13 . Condensation of interlayer excitons at temperatures above 100 kelvin is demonstrated in a van der Waals heterostructure consisting of two-dimensional atomic double layers of transition metal chalcogenides.

Excitonic insulators (EIs) arise from the formation of bound electron–hole pairs (excitons) 1 , 2 in semiconductors and provide a solid-state platform for quantum many-boson physics 3 – 8 . Strong exciton–exciton repulsion is expected to stabilize condensed superfluid and crystalline phases by suppressing both density and phase fluctuations 8 – 11 . Although spectroscopic signatures of EIs have been reported 6 , 12 – 14 , conclusive evidence for strongly correlated EI states has remained elusive. Here we demonstrate a strongly correlated two-dimensional (2D) EI ground state formed in transition metal dichalcogenide (TMD) semiconductor double layers. A quasi-equilibrium spatially indirect exciton fluid is created when the bias voltage applied between the two electrically isolated TMD layers is tuned to a range that populates bound electron–hole pairs, but not free electrons or holes 15 – 17 . Capacitance measurements show that the fluid is exciton-compressible but charge-incompressible—direct thermodynamic evidence of the EI. The fluid is also strongly correlated with a dimensionless exciton coupling constant exceeding 10. We construct an exciton phase diagram that reveals both the Mott transition and interaction-stabilized quasi-condensation. Our experiment paves the path for realizing exotic quantum phases of excitons 8 , as well as multi-terminal exciton circuitry for applications 18 – 20 . So far only signatures of excitonic insulators have been reported, but here direct thermodynamic evidence is provided for a strongly correlated excitonic insulating state in transition metal dichalcogenide semiconductor double layers.

Silicon dominates contemporary solar cell technologies 1 . But when absorbing photons, silicon (like other semiconductors) wastes energy in excess of its bandgap 2 . Reducing these thermalization losses and enabling better sensitivity to light is possible by sensitizing the silicon solar cell using singlet exciton fission, in which two excited states with triplet spin character (triplet excitons) are generated from a photoexcited state of higher energy with singlet spin character (a singlet exciton) 3 – 5 . Singlet exciton fission in the molecular semiconductor tetracene is known to generate triplet excitons that are energetically matched to the silicon bandgap 6 – 8 . When the triplet excitons are transferred to silicon they create additional electron–hole pairs, promising to increase cell efficiencies from the single-junction limit of 29 per cent to as high as 35 per cent 9 . Here we reduce the thickness of the protective hafnium oxynitride layer at the surface of a silicon solar cell to just eight angstroms, using electric-field-effect passivation to enable the efficient energy transfer of the triplet excitons formed in the tetracene. The maximum combined yield of the fission in tetracene and the energy transfer to silicon is around 133 per cent, establishing the potential of singlet exciton fission to increase the efficiencies of silicon solar cells and reduce the cost of the energy that they generate. A silicon and tetracene solar cell employing singlet fission uses an eight-angstrom-thick hafnium oxynitride interlayer to promote efficient triplet transfer, increasing the efficiency of the cell.

In non-Hermitian systems, spectral degeneracies can arise that can cause unusual, counter-intuitive effects; here exciton-polaritons—hybrid light–matter particles—within a semiconductor microcavity are found to display non-trivial topological modal structure exclusive to such systems. Non-Hermitian dynamics in a quantum chaotic exciton-polariton system In non-Hermitian systems, which are open and subject to gain and loss, exceptional points can arise, spectral degeneracies that can cause unusual, counter-intuitive effects. Recent efforts to observe non-Hermitian physics have concentrated on various optical systems, but not yet on exciton-polaritons. These are hybrid light–matter particles, formed by strongly interacting photons and excitons (electron–hole pairs) in semiconductor microcavities. Such systems require constant pumping of energy and continuously decays releasing coherent radiation, so are a profoundly open quantum system. In a striking experiment involving a chaotic exciton-polariton billiard —a two-dimensional area enclosed by a curved potential barrier — these authors demonstrate this non-Hermitian nature for the first time. The experiment reveals the non-trivial topological modal structure exclusive to non-Hermitian systems. These findings open the way for novel types of operating principles for polariton-based optoelectronic devices. Exciton-polaritons are hybrid light–matter quasiparticles formed by strongly interacting photons and excitons (electron–hole pairs) in semiconductor microcavities 1 , 2 , 3 . They have emerged as a robust solid-state platform for next-generation optoelectronic applications as well as for fundamental studies of quantum many-body physics. Importantly, exciton-polaritons are a profoundly open (that is, non-Hermitian 4 , 5 ) quantum system, which requires constant pumping of energy and continuously decays, releasing coherent radiation 6 . Thus, the exciton-polaritons always exist in a balanced potential landscape of gain and loss. However, the inherent non-Hermitian nature of this potential has so far been largely ignored in exciton-polariton physics. Here we demonstrate that non-Hermiticity dramatically modifies the structure of modes and spectral degeneracies in exciton-polariton systems, and, therefore, will affect their quantum transport, localization and dynamical properties 7 , 8 , 9 . Using a spatially structured optical pump 10 , 11 , 12 , we create a chaotic exciton-polariton billiard—a two-dimensional area enclosed by a curved potential barrier. Eigenmodes of this billiard exhibit multiple non-Hermitian spectral degeneracies, known as exceptional points 13 , 14 . Such points can cause remarkable wave phenomena, such as unidirectional transport 15 , anomalous lasing/absorption 16 , 17 and chiral modes 18 . By varying parameters of the billiard, we observe crossing and anti-crossing of energy levels and reveal the non-trivial topological modal structure exclusive to non-Hermitian systems 9 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 . We also observe mode switching and a topological Berry phase for a parameter loop encircling the exceptional point 23 , 24 . Our findings pave the way to studies of non-Hermitian quantum dynamics of exciton-polaritons, which may uncover novel operating principles for polariton-based devices.

The formation of excitons in organic molecules by charge injection is an essential process in organic light-emitting diodes (OLEDs) 1 – 7 . According to a simple model based on spin statistics, the injected charges form spin-singlet (S 1 ) excitons and spin-triplet (T 1 ) excitons in a 1:3 ratio 2 – 4 . After the first report of a highly efficient OLED 2 based on phosphorescence, which is produced by the decay of T 1 excitons, more effective use of these excitons has been the primary strategy for increasing the energy efficiency of OLEDs. Another route to improving OLED energy efficiency is reduction of the operating voltage 2 – 6 . Because T 1 excitons have lower energy than S 1 excitons (owing to the exchange interaction), use of the energy difference could—in principle—enable exclusive production of T 1 excitons at low OLED operating voltages. However, a way to achieve such selective and direct formation of these excitons has not yet been established. Here we report a single-molecule investigation of electroluminescence using a scanning tunnelling microscope 8 – 20 and demonstrate a simple method of selective formation of T 1 excitons that utilizes a charged molecule. A 3,4,9,10-perylenetetracarboxylicdianhydride (PTCDA) molecule 21 – 25 adsorbed on a three-monolayer NaCl film atop Ag(111) shows both phosphorescence and fluorescence signals at high applied voltage. In contrast, only phosphorescence occurs at low applied voltage, indicating selective formation of T 1 excitons without creating their S 1 counterparts. The bias voltage dependence of the phosphorescence, combined with differential conductance measurements, reveals that spin-selective electron removal from a negatively charged PTCDA molecule is the dominant formation mechanism of T 1 excitons in this system, which can be explained by considering the exchange interaction in the charged molecule. Our findings show that the electron transport process accompanying exciton formation can be controlled by manipulating an electron spin inside a molecule. We anticipate that designing a device taking into account the exchange interaction could realize an OLED with a lower operating voltage. Recombination of excitons to produce molecular light emission is made more efficient by controlling electron spin within the molecule to produce spin-triplet excitons only, without the usual accompanying spin-singlet excitons.

The generation, control and transfer of triplet excitons in molecular and hybrid systems is of great interest owing to their long lifetime and diffusion length in both solid-state and solution phase systems, and to their applications in light emission 1 , optoelectronics 2 , 3 , photon frequency conversion 4 , 5 and photocatalysis 6 , 7 . Molecular triplet excitons (bound electron–hole pairs) are ‘dark states’ because of the forbidden nature of the direct optical transition between the spin-zero ground state and the spin-one triplet levels 8 . Hence, triplet dynamics are conventionally controlled through heavy-metal-based spin–orbit coupling 9 – 11 or tuning of the singlet–triplet energy splitting 12 , 13 via molecular design. Both these methods place constraints on the range of properties that can be modified and the molecular structures that can be used. Here we demonstrate that it is possible to control triplet dynamics by coupling organic molecules to lanthanide-doped inorganic insulating nanoparticles. This allows the classically forbidden transitions from the ground-state singlet to excited-state triplets to gain oscillator strength, enabling triplets to be directly generated on molecules via photon absorption. Photogenerated singlet excitons can be converted to triplet excitons on sub-10-picosecond timescales with unity efficiency by intersystem crossing. Triplet exciton states of the molecules can undergo energy transfer to the lanthanide ions with unity efficiency, which allows us to achieve luminescent harvesting of the dark triplet excitons. Furthermore, we demonstrate that the triplet excitons generated in the lanthanide nanoparticle–molecule hybrid systems by near-infrared photoexcitation can undergo efficient upconversion via a lanthanide–triplet excitation fusion process: this process enables endothermic upconversion and allows efficient upconversion from near-infrared to visible frequencies in the solid state. These results provide a new way to control triplet excitons, which is essential for many fields of optoelectronic and biomedical research. Optically dark (non-emitting) triplet excitons on organic molecules may be rendered bright by coupling the molecules to lanthanide-doped nanoparticles, providing a way to control such excitons in optoelectronic systems.