L. V. Butov

Macroscopically ordered state in an exciton system.

There is a rich variety of quantum liquids—such as superconductors, liquid helium and atom Bose–Einstein condensates—that exhibit macroscopic coherence in the form of ordered arrays of vortices. Experimental observation of a macroscopically ordered electronic state in semiconductors has, however, remained a challenging and relatively unexplored problem. A promising approach for the realization of such a state is to use excitons, bound pairs of electrons and holes that can form in semiconductor systems. At low densities, excitons are Bose-particles, and at low temperatures, of the order of a few kelvin, excitons can form a quantum liquid—that is, a statistically degenerate Bose gas or even a Bose–Einstein condensate. Here we report photoluminescence measurements of a quasi-two-dimensional exciton gas in GaAs/AlGaAs coupled quantum wells and the observation of a macroscopically ordered exciton state. Our spatially resolved measurements reveal fragmentation of the ring-shaped emission pattern into circular structures that form periodic arrays over lengths up to 1 mm.

Control of Exciton Fluxes in an Excitonic Integrated Circuit

Efficient signal communication uses photons. Signal processing, however, uses an optically inactive medium, electrons. Therefore, an interconnection between electronic signal processing and optical communication is required at the integrated circuit level. We demonstrated control of exciton fluxes in an excitonic integrated circuit. The circuit consists of three exciton optoelectronic transistors and performs operations with exciton fluxes, such as directional switching and merging. Photons transform into excitons at the circuit input, and the excitons transform into photons at the circuit output. The exciton flux from the input to the output is controlled by a pattern of the electrode voltages. The direct coupling of photons, used in communication, to excitons, used as the device-operation medium, may lead to the development of efficient exciton-based optoelectronic devices.

High-temperature superfluidity with indirect excitons in van der Waals heterostructures

All known superfluid and superconducting states of condensed matter are enabled by composite bosons (atoms, molecules and Cooper pairs) made of an even number of fermions. Temperatures where such macroscopic quantum phenomena occur are limited by the lesser of the binding energy and the degeneracy temperature of the bosons. High-critical temperature cuprate superconductors set the present record of ~100 K. Here we propose a design for artificially structured materials to rival this record. The main elements of the structure are two monolayers of a transition metal dichalcogenide separated by an atomically thin spacer. Electrons and holes generated in the system would accumulate in the opposite monolayers and form bosonic bound states--the indirect excitons. The resultant degenerate Bose gas of indirect excitons would exhibit macroscopic occupation of a quantum state and vanishing viscosity at high temperatures.

Spontaneous coherence in a cold exciton gas

If bosonic particles are cooled down below the temperature of quantum degeneracy, they can spontaneously form a coherent state in which individual matter waves synchronize and combine. Spontaneous coherence of matter waves forms the basis of a number of fundamental phenomena in physics, including superconductivity, superfluidity and Bose–Einstein condensation. Spontaneous coherence is the key characteristic of condensation in momentum space. Excitons—bound pairs of electrons and holes—form a model system to explore the quantum physics of cold bosons in solids. Cold exciton gases can be realized in a system of indirect excitons, which can cool down below the temperature of quantum degeneracy owing to their long lifetimes. Here we report measurements of spontaneous coherence in a gas of indirect excitons. We found that spontaneous coherence of excitons emerges in the region of the macroscopically ordered exciton state and in the region of vortices of linear polarization. The coherence length in these regions is much larger than in a classical gas, indicating a coherent state with a much narrower than classical exciton distribution in momentum space, characteristic of a condensate. A pattern of extended spontaneous coherence is correlated with a pattern of spontaneous polarization, revealing the properties of a multicomponent coherent state. We also observed phase singularities in the coherent exciton gas. All these phenomena emerge when the exciton gas is cooled below a few kelvin.

Excitons in electrostatic traps

We consider in-plane electrostatic traps for indirect excitons in coupled quantum wells, where the traps are formed by a laterally modulated gate voltage. An intrinsic obstacle for exciton confinement in electrostatic traps is an in-plane electric field that can lead to exciton dissociation. We propose a design to suppress the in-plane electric field and, at the same time, to effectively confine excitons in the electrostatic traps. We present calculations for various classes of electrostatic traps and experimental proof of principle for trapping of indirect excitons in electrostatic traps.

Formation mechanism and low-temperature instability of exciton rings.

The macroscopic exciton rings observed in the photoluminescence (PL) patterns of excitons in coupled quantum wells (CQWs) are explained by a series of experiments and a theory based on the idea of carrier imbalance, transport and recombination. The rings are found to be a source of cold excitons with temperature close to that of the lattice. We explored states of excitons in the ring over a range of temperatures down to 380 mK. These studies reveal a sharp, albeit continuous, second order phase transition to a low-temperature ordered exciton state, characterized by ring fragmentation into a periodic array of aggregates. An instability at the onset of degeneracy in the cold exciton system, due to stimulated exciton formation, is proposed as the transition mechanism.

From spatially indirect excitons to momentum-space indirect excitons by an in-plane magnetic field

An in-plane magnetic field is found to change drastically the photoluminescence spectra and kinetics of interwell excitons in

Exciton optoelectronic transistor

\mathrm{GaAs}/{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}

Coherence Length of Cold Exciton Gases in Coupled Quantum Wells

coupled quantum wells. This effect is due to the in-plane magnetic-field-induced displacement of the interwell exciton dispersion in momentum space, which results in the transition from the momentum-space direct exciton ground state to the momentum-space indirect exciton ground state. An in-plane magnetic field is, therefore, an effective tool for exciton dispersion engineering.

Condensation of excitons in a trap.

We demonstrate experimental proof of principle for an optoelectronic transistor based on the modulation of exciton flux via gate voltage. The exciton optoelectronic transistor (EXOT) implements electronic operation on photons by using excitons as intermediate media; the intensity of light emitted at the optical output is proportional to the intensity of light at the optical input and is controlled electronically by the gate. We demonstrate a contrast ratio of 30 between an on state and an off state of the EXOT and its operation at speeds greater than 1 GHz. Our studies also demonstrate high-speed control of both the flux and the potential energy of excitons on a time scale much shorter than the exciton lifetime.