Tightly bound excitons in monolayer semiconductors represent a versatile platform to study two-dimensional propagation of neutral quasiparticles. Their intrinsic properties, however, can be severely obscured by spatial energy fluctuations due to a high sensitivity to the immediate environment. Here, we take advantage of the encapsulation of individual layers in hexagonal boron nitride to strongly suppress environmental disorder. Diffusion of excitons is then directly monitored using time-and spatially-resolved emission microscopy at ambient conditions. We consistently find very efficient propagation with linear diffusion coefficients up to 10 cm 2 /s, corresponding to room temperature effective mobilities as high as 400 cm 2 /Vs as well as a correlation between rapid diffusion and short population lifetime. At elevated densities we detect distinct signatures of many-particle interactions and consequences of strongly suppressed Auger-like exciton-exciton annihilation. Combination of analytical and numerical theoretical approaches is employed to provide pathways towards comprehensive understanding of the observed linear and non-linear propagation phenomena. We emphasize the role of dark exciton states and present a mechanism for diffusion facilitated by free electron hole plasma from entropy-ionized excitons.

The interplay of optics, dynamics and transport is crucial for the design of novel optoelectronic devices, such as photodetectors and solar cells. In this context, transition metal dichalcogenides (TMDs) have received much attention. Here, strongly bound excitons dominate optical excitation, carrier dynamics and diffusion processes. While the first two have been intensively studied, there is a lack of fundamental understanding of non-equilibrium phenomena associated with exciton transport that is of central importance e.g. for high efficiency light harvesting. In this work, we provide microscopic insights into the interplay of exciton propagation and many-particle interactions in TMDs. Based on a fully quantum mechanical approach and in excellent agreement with photoluminescence measurements, we show that Auger recombination and emission of hot phonons act as a heating mechanism giving rise to strong spatial gradients in excitonic temperature. The resulting thermal drift leads to an unconventional exciton diffusion characterized by spatial exciton halos.

While exciton relaxation in transition metal dichalcogenides (TMDs) has been intensively studied, spatial exciton propagation has received only little attention -in spite of being a key process for optoelectronics and having already shown interesting unconventional behaviours (e.g. spatial halos).Here, we study the spatiotemporal dynamics in TMDs and track the way of optically excited excitons in time, momentum, and space. In particular, we investigate the temperature-dependent exciton diffusion including the remarkable exciton landscape constituted by bright and dark states. Based on a fully quantum mechanical approach, we show at low temperatures an unexpected negative transient diffusion. This phenomenon can be traced back to the existence of dark exciton states in TMDs and is a result of an interplay between spatial exciton diffusion and intervalley exciton-phonon scattering.arXiv:1908.07735v1 [cond-mat.mes-hall]

A recently proposed Markov approach provides Lindblad-type scattering superoperators, which ensure the physical (positive-definite) character of the many-body density matrix. We apply the mean-field approximation to such a many-body equation, in the presence of one-and two-body scattering mechanisms, and we derive a closed equation of motion for the electronic single-particle density matrix, which turns out to be nonlinear as well as non-Lindblad. We prove that, in spite of its nonlinear and non-Lindblad structure, the mean-field approximation does preserve the positive-definite character of the single-particle density matrix, an essential prerequisite of any reliable kinetic treatment of semiconductor quantum devices. This result is in striking contrast with conventional (non-Lindblad) Markov approaches, where the single-particle mean-field equations can lead to positivity violations and thus to unphysical results. Furthermore, the proposed single-particle formulation is extended to the case of quantum systems with spatial open boundaries, providing a formal derivation of a recently proposed density-matrix treatment based on a Lindblad-like system-reservoir scattering superoperator.

The Wigner-function formalism is a well-known approach to model charge transport in semiconductor nanodevices. The primary goal of the present article is to point out and explain the intrinsic limitations of the conventional quantum-device modeling based on such a Wigner-function paradigm, providing a definite answer to open questions related to the application of the conventional spatial boundary condition scheme to the Wigner transport equation. Our analysis shows that (i) in the absence of energy dissipation (coherent limit) the solution of the Wigner equation equipped with given boundary conditions is not unique, and (ii) when dissipation and decoherence phenomena are taken into account via a relaxation-time approximation, the solution, although unique, is not necessarily a physical Wigner function. l right rese rvoir left rese rvoir quan tum devic e (left conta ct) (righ t conta ct) z = + l 2 z z = -l 2 z FIG. 1. (Color online) Schematic representation of a typical semiconductor-based quantum device as an open system connected to two external charge reservoirs.Here, the distance between the interfaces is l, and z is the longitudinal transport direction. dissipation (coherent limit) the solution of the Wigner equation (compatible with given boundary conditions) is not unique, and (ii) also when the solution is unique, the latter is not necessarily a Wigner function, i.e., a Weyl-Wigner transform of a single-particle density matrix.The article is organized as follows: In Sec. II, we shall summarize the fundamentals of quantum-device modeling, with a special focus on the problem of quantum systems with open space boundaries, corresponding, e.g., to the case of a semiconductor nanodevice inserted into an electric circuit. In Sec. III, we shall discuss in very general terms the intrinsic limitations of the conventional boundary condition scheme applied to a quantum-mechanical problem, thus addressing the main topic of the article, i.e., the physical versus unphysical nature of the Wigner-equation solutions corresponding to given spatial boundaries. Section IV is devoted to an investigation of the coherent limit and of the corresponding Wigner equation, while Sec. V deals with the inclusion of energy-dissipation and decoherence phenomena. Finally, in Sec. VI we shall summarize and draw a few conclusions.