Spin currents in a coherent exciton gas

Moiré pattern of interference dislocations in condensate of indirect excitons

Interference patterns provide direct measurement of coherent propagation of matter waves in quantum systems. Superfluidity in Bose-Einstein condensates of excitons can enable long-range ballistic exciton propagation and can lead to emerging long-scale interference patterns. Indirect excitons (IXs) are formed by electrons and holes in separated layers. The theory predicts that the reduced IX recombination enables IX superfluid propagation over macroscopic distances. Here, we present dislocation-like phase singularities in interference patterns produced by condensate of IXs. We analyze how exciton vortices and skyrmions should appear in the interference experiments and show that the observed interference dislocations are not associated with these phase defects. We show that the observed interference dislocations originate from the moiré effect in combined interference patterns of propagating condensate matter waves. The interference dislocations are formed by the IX matter waves ballistically propagating over macroscopic distances. The long-range ballistic IX propagation is the evidence for IX condensate superfluidity.

Indirect Excitons and Trions in MoSe2/WSe2 van der Waals Heterostructures

Indirect excitons (IX) in semiconductor heterostructures are bosons, which can cool below the temperature of quantum degeneracy and can be effectively controlled by voltage and light. IX quantum Bose gases and IX devices were explored in GaAs heterostructures where an IX range of existence is limited to low temperatures due to low IX binding energies. IXs in van der Waals transition-metal dichalcogenide (TMD) heterostructures are characterized by large binding energies giving the opportunity for exploring excitonic quantum gases and for creating excitonic devices at high temperatures. TMD heterostructures also offer a new platform for studying single-exciton phenomena and few-particle complexes. In this work, we present studies of IXs in MoSe₂/WSe₂ heterostructures and report on two IX luminescence lines whose energy splitting and temperature dependence identify them as neutral and charged IXs. The experimentally found binding energy of the indirect charged excitons, that is, indirect trions, is close to the calculated binding energy of 28 meV for negative indirect trions in TMD heterostructures [Deilmann, T.; Thygesen, K. S. Nano Lett. 2018, 18, 1460]. We also report on the realization of IXs with a luminescence line width reaching 4 meV at low temperatures. An enhancement of IX luminescence intensity and the narrow line width are observed in localized spots.

Exciton condensation in quantum wells with defects of macroscopic sizes

Formation of the excitonic condensed phase in quantum wells with defects of macroscopic size is investigated in the case of a specific kind of defect arising in local areas of planar quantum wells where the wells are thicker or thinner by an atomic monolayer or two. The excitonic system in the wells is non-equilibrium as the excitons are constantly created by an irradiation and decay due to the finite lifetime. The condensation considered in the paper is not the Bose-Einstein condensation but rather the classical condensation due an interaction between excitons with additional peculiarities caused by non-equilibrium conditions. The main contribution to the exciton's energy in the defect's area comes from the energy of the exciton's confinement along the growth axis and the respective quantization of the exciton's levels. The condensation manifests itself by an enhancement the exciton accumulation in the defect's area with increasing pumping and by an appearance of different types of structures in the exciton density distribution when the defect's size is large. The condensed phase may appear in the form of islands or in the form of rings on the defect's boundary. It is shown, that the value of the exciton's lifetime plays an important role in the spatial distribution of the exciton density. The similarity and the difference of density structures for wells with the extra or lacking atomic monolayer in the defect's area are investigated. The specific features of the manifestation of the exciton luminescence at the condensation in the defect's region is analyzed.

Dynamical formation of a strongly correlated dark condensate of dipolar excitons

Strongly interacting bosons display a rich variety of quantum phases, the study of which has so far been focused in the dilute regime, at a fixed number of particles. Here we demonstrate the formation of a dense Bose-Einstein condensate in a long-lived dark spin state of 2D dipolar excitons. A dark condensate of weakly interacting excitons is very fragile, being unstable against a coherent coupling of dark and bright spin states. Remarkably, we find that strong dipole-dipole interactions stabilize the dark condensate. As a result, the dark phase persists up to densities high enough for a dark quantum liquid to form. The striking experimental observation of a step-like dependence of the exciton density on the pump power is reproduced quantitatively by a model describing the nonequilibrium dynamics of driven coupled dark and bright condensates. This unique behavior marks a dynamical condensation to dark states with lifetimes as long as a millisecond, followed by a brightening transition at high densities.

Spin current generation and relaxation in a quenched spin-orbit-coupled Bose-Einstein condensate

Understanding the effects of spin-orbit coupling (SOC) and many-body interactions on spin transport is important in condensed matter physics and spintronics. This topic has been intensively studied for spin carriers such as electrons but barely explored for charge-neutral bosonic quasiparticles (including their condensates), which hold promises for coherent spin transport over macroscopic distances. Here, we explore the effects of synthetic SOC (induced by optical Raman coupling) and atomic interactions on the spin transport in an atomic Bose-Einstein condensate (BEC), where the spin-dipole mode (SDM, actuated by quenching the Raman coupling) of two interacting spin components constitutes an alternating spin current. We experimentally observe that SOC significantly enhances the SDM damping while reducing the thermalization (the reduction of the condensate fraction). We also observe generation of BEC collective excitations such as shape oscillations. Our theory reveals that the SOC-modified interference, immiscibility, and interaction between the spin components can play crucial roles in spin transport.

Spin-orbit coupling is interesting for fundamental understanding of spin transport and quench dynamics. Here the authors demonstrate spin-current generation and its relaxation in spin-orbit-coupled Bose-Einstein condensates of Rb atoms in different spin states.

Bose Condensation of Long-Living Direct Excitons in an Off-Resonant Cavity

We propose a way to increase the lifetime of two-dimensional direct excitons and show the possibility to observe their macroscopically coherent state at temperatures much higher than that of indirect exciton condensation. For a single GaAs quantum well embedded in photonic layered heterostructures with subwavelength period, we predict the exciton radiative decay to be strongly suppressed. Quantum hydrodynamics joined with the Bogoliubov approach are used to study the Berezinskii-Kosterlitz-Thouless crossover in a finite exciton system with intermediate densities. Below the estimated critical temperatures, drastic growth of the correlation length is shown to be accompanied by a manyfold increase of the photoluminescence intensity.

Pancharatnam-Berry phase in condensate of indirect excitons

The Pancharatnam-Berry phase is a geometric phase acquired over a cycle of parameters in the Hamiltonian governing the evolution of the system. Here, we report on the observation of the Pancharatnam-Berry phase in a condensate of indirect excitons (IXs) in a GaAs-coupled quantum well structure. The Pancharatnam-Berry phase is directly measured by detecting phase shifts of interference fringes in IX interference patterns. Correlations are found between the phase shifts, polarization pattern of IX emission, and onset of IX spontaneous coherence. The evolving Pancharatnam-Berry phase is acquired due to coherent spin precession in IX condensate and is observed with no decay over lengths exceeding 10 μm indicating long-range coherent spin transport.

Exciton Diffusion and Halo Effects in Monolayer Semiconductors

We directly monitor exciton propagation in freestanding and SiO_{2}-supported WS_{2} monolayers through spatially and time-resolved microphotoluminescence under ambient conditions. We find a highly nonlinear behavior with characteristic, qualitative changes in the spatial profiles of the exciton emission and an effective diffusion coefficient increasing from 0.3 to more than 30  cm^{2}/s, depending on the injected exciton density. Solving the diffusion equation while accounting for Auger recombination allows us to identify and quantitatively understand the main origin of the increase in the observed diffusion coefficient. At elevated excitation densities, the initial Gaussian distribution of the excitons evolves into long-lived halo shapes with μm-scale diameter, indicating additional memory effects in the exciton dynamics.

Indirect excitons in van der Waals heterostructures at room temperature

Indirect excitons (IXs) are explored both for studying quantum Bose gases in semiconductor materials and for the development of excitonic devices. IXs were extensively studied in III-V and II-VI semiconductor heterostructures where IX range of existence has been limited to low temperatures. Here, we present the observation of IXs at room temperature in van der Waals transition metal dichalcogenide (TMD) heterostructures. This is achieved in TMD heterostructures based on monolayers of MoS₂ separated by atomically thin hexagonal boron nitride. The IXs we realize in the TMD heterostructure have lifetimes orders of magnitude longer than lifetimes of direct excitons in single-layer TMD and their energy is gate controlled. The realization of IXs at room temperature establishes the TMD heterostructures as a material platform both for a field of high-temperature quantum Bose gases of IXs and for a field of high-temperature excitonic devices.

Chaotization of internal motion of excitons in ultrathin layers by spin-orbit coupling

We show that Rashba spin-orbit coupling (SOC) can generate chaotic behavior of excitons in two-dimensional semiconductor structures. To model this chaos, we study a Kepler system with spin-orbit coupling and numerically obtain a transition to chaos at a sufficiently strong coupling. The chaos emerges since the SOC reduces the number of integrals of motion as compared to the number of degrees of freedom. Dynamically, the dependence of the exciton energy on the spin orientation in the presence of SOC produces an anomalous spin-dependent velocity resulting in chaotic motion. We observe numerically the critical dependence of the dynamics on the initial conditions, where the system can return to and exit a stability domain through very small changes in the initial spin orientation. This chaos can have a strong influence on the lifetime of optically injected carriers in semiconductors and organometallic perovskites. Hence, this effect should be taken into account while designing structures for photovoltaic and optical spintronics applications, where excitons play a significant role.

Bose-Einstein condensation and indirect excitons: a review

We review recent progress on Bose-Einstein condensation (BEC) of semiconductor excitons. The first part deals with theory, the second part with experiments. This Review is written at a time where the problem of exciton Bose-Einstein condensation has just been revived by the understanding that the exciton condensate must be dark because the exciton ground state is not coupled to light. Here, we theoretically discuss this missed understanding before providing its experimental support through experiments that scrutinize indirect excitons made of spatially separated electrons and holes. The theoretical part first discusses condensation of elementary bosons. In particular, the necessary inhibition of condensate fragmentation by exchange interaction is stressed, before extending the discussion to interacting bosons with spin degrees of freedom. The theoretical part then considers composite bosons made of two fermions like semiconductor excitons. The spin structure of the excitons is detailed, with emphasis on the crucial fact that ground-state excitons are dark: indeed, this imposes the exciton Bose-Einstein condensate to be not coupled to light in the dilute regime. Condensate fragmentations are then reconsidered. In particular, it is shown that while at low density, the exciton condensate is fully dark, it acquires a bright component, coherent with the dark one, beyond a density threshold: in this regime, the exciton condensate is 'gray'. The experimental part first discusses optical creation of indirect excitons in quantum wells, and the detection of their photoluminescence. Exciton thermalisation is also addressed, as well as available approaches to estimate the exciton density. We then switch to specific experiments where indirect excitons form a macroscopic fragmented ring. We show that such ring provides efficient electrostatic trapping in the region of the fragments where an essentially-dark exciton Bose-Einstein condensate is formed at sub-Kelvin bath temperatures. The macroscopic spatial coherence of the photoluminescence observed in this essentially dark region confirms this conclusion.

Dark High Density Dipolar Liquid of Excitons

The possible phases and the nanoscale particle correlations of two-dimensional interacting dipolar particles is a long-sought problem in many-body physics. Here we observe a spontaneous condensation of trapped two-dimensional dipolar excitons with internal spin degrees of freedom from an interacting gas into a high density, closely packed liquid state made mostly of dark dipoles. Another phase transition, into a bright, highly repulsive plasma, is observed at even higher excitation powers. The dark liquid state is formed below a critical temperature Tc ≈ 4.8 K, and it is manifested by a clear spontaneous spatial condensation to a smaller and denser cloud, suggesting an attractive part to the interaction which goes beyond the purely repulsive dipole-dipole forces. Contributions from quantum mechanical fluctuations are expected to be significant in this strongly correlated, long living dark liquid. This is a new example of a two-dimensional atomic-like interacting dipolar liquid, but where the coupling of light to its internal spin degrees of freedom plays a crucial role in the dynamical formation and the nature of resulting condensed dark ground state.

Effects of fermion exchange on the polarization of exciton condensates

Exchange interaction is responsible for the stability of elementary boson condensates with respect to momentum fragmentation. This remains true for composite bosons when single fermion exchanges are included but spin degrees of freedom are ignored. Here, we show that their inclusion can produce a spin fragmentation of the dark exciton condensate, i.e., an unpolarized condensate with an equal amount of spin (+2) and (-2) excitons not coupled to light. The composite boson many-body formalism allows us to predict that, for spatially indirect excitons, the condensate polarization switches from unpolarized to fully polarized when the distance between the layers confining electrons and holes increases. Importantly, the threshold distance for this switch lies in a regime fully accessible to experiments.

Space- and time-dependent quantum dynamics of spatially indirect excitons in semiconductor heterostructures

We study the unitary propagation of a two-particle one-dimensional Schrödinger equation by means of the Split-Step Fourier method, to study the coherent evolution of a spatially indirect exciton (IX) in semiconductor heterostructures. The mutual Coulomb interaction of the electron-hole pair and the electrostatic potentials generated by external gates and acting on the two particles separately are taken into account exactly in the two-particle dynamics. As relevant examples, step/downhill and barrier/well potential profiles are considered. The space- and time-dependent evolutions during the scattering event as well as the asymptotic time behavior are analyzed. For typical parameters of GaAs-based devices, the transmission or reflection of the pair turns out to be a complex two-particle process, due to comparable and competing Coulomb, electrostatic, and kinetic energy scales. Depending on the intensity and anisotropy of the scattering potentials, the quantum evolution may result in excitation of the IX internal degrees of freedom, dissociation of the pair, or transmission in small periodic IX wavepackets due to dwelling of one particle in the barrier region. We discuss the occurrence of each process in the full parameter space of the scattering potentials and the relevance of our results for current excitronic technologies.