Bose-Einstein condensation (BEC) is normally limited to temperatures near absolute zero but researchers have now seen it at a much warmer 100 Kelvin for excitons (electron-hole pairs) in atomically thin double layers of semiconductors. The finding will be important for coherent optoelectronics applications and perhaps even high-temperature superconductivity, they say.
BEC happens when a gas of bosonic atoms or particles is cooled until the de Broglie wavelength of the atoms or particles becomes comparable to the distance between them. The atoms or particles then collapse into the same quantum ground state and can therefore be described by the same wavefunction.
The phenomenon, which allows the atoms or particles to become a superfluid (in which they flow without friction) was predicted nearly a hundred years ago by Albert Einstein and Satyendra Nath Bose. The first such condensate (made from rubidium atoms) saw the light of day in 1995. It has since also been observed in particles including polaritons, photons and magnons.
Excitons should Bose condense at much higher temperatures
BEC is normally only seen at extremely low temperatures – not more than a few kelvins – and researchers would dearly like to increase this BEC “transition temperature”. Theory predicts that excitons (bound states of a negatively charged electron and a positively charged hole – or electron vacancy – that have a much smaller mass than atoms and can be packed to a much higher density) might be good particles to study in this context. This is because they should Bose condense at much higher temperatures.
Electrons and holes on their own are classified as fermions and so cannot form Bose-Einstein condensates, but a bound state of two fermions is a boson, so excitons can condense. Until now, however, experiments (on semiconductor quantum wells and graphene, for example) have shown condensation temperatures of only up to about 1 K because of the small exciton binding energy in the material systems studied.
Huge exciton binding energy
In this new work, researchers led by Zefang Wang, Jie Shan and Kin Fai Mak of Cornell University together with co-workers at Columbia University and NIMS in Japan did their experiments on the 2D semiconductors molybdenum diselenide (MoSe2) and tungsten disulphide (WSe2). These materials belong to the transition metal dichalcogenide family of semiconductors, which become direct band gap semiconductors when made into monolayers. One of their unique features is their huge exciton binding energy, which is almost two orders of magnitude higher than that of conventional semiconductor quantum wells.
“This huge exciton binding energy means that the excitons in these materials can, in principle, undergo high-temperature condensation, but the short exciton lifetime in monolayer materials means that it is difficult to achieve in reality,” says Mak.
Double layer boosts exciton condensation to 100 K
“One solution to this problem is a double layer system (which was first put forward by researchers in 2014) instead of a single layer one. This system significantly increases the exciton lifetime and favours exciton condensation without comprising the strong exciton binding. It is thus an ideal platform in which to realize high-temperature exciton condensation.
“By building an electron-hole double layer based on MoSe2 and WSe2, we have now shown that we can boost the exciton condensation by nearly two orders of magnitude – to about 100 K.”
Electroluminescence depends on the exciton density at a critical threshold density
When electrons and holes find themselves in the same region in a semiconductor, they can recombine and release energy in the form of electroluminescence (EL). In their experiments, Mak and colleagues found that the intensity of this EL has a threshold dependence on the exciton density, which they discovered quite by accident in devices made using monolayers of MoSe2 and WSe2 separated by an insulating layer of hexagonal boron nitride (hBN). hBN serves to limit electron and hole tunnelling between the two semiconductors and thus supresses electron-hole recombination.
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“We applied a bias voltage to this device via contact electrodes (made from graphene),” explains Mak. “As we cranked up this voltage, we first observed the creation of an electron-hole gas in the double layer. As we further increased it – and thus increased the exciton density – the EL suddenly increased by nearly two orders of magnitude.
“This phenomenon reminded us of laser diodes, in which a threshold increase in the light emission intensity emerges with a small increase in electrical pumping (similar to the bias voltage we apply). In fact, exciton condensation is closely related to lasing, which can itself be regarded as a non-equilibrium BEC of photons in a single optical cavity mode.”
Electron and hole densities need to be equal
Accompanied by this dramatic phase transition is the enhanced photon noise at the threshold, also known as critical fluctuations in phase transition theory, he tells Physics World. “The so-called super-Poissonian photon statistics we observed at this threshold are very similar to the enhanced photon noise at the lasing threshold for lasers. Although quite distinct from lasing, this enhanced photon noise does nonetheless provide important evidence for exciton condensation.”
We found that EL enhancement occurs when the density of electrons and holes in the system is the same, he adds. “This observation backs up theory calculations that predict that exciton condensation indeed requires almost perfect electron-hole ‘Fermi surface nesting’, which means that the condensate quickly falls apart if the electron and hole densities are not equal.”
Towards coherent optoelectronics applications and perhaps even high-temperature superconductivity?
The study will have implications for coherent optoelectronics applications in which the excitons in the condensed phase couple to light cooperatively – instead of independently of each other as in classical devices like light-emitting diodes, explains Mak. It might also be important for high-temperature superconductivity.
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“In 1976, theoretical physicists Lozovik and Yudson put forward a route to achieving such superconductivity via exciton condensation. Instead of trying to pair up like-charged particles in a single material (as researchers are trying to do in existing superconductors), they proposed pairing up oppositely charged particles (such as electrons and holes) spatially separated in two layers. Superconductivity might emerge in each individual layer of the system when the electron-hole pairs condense. The physicists predicted that the maximum superconducting temperature in this case would be limited by a fraction of the exciton binding energy, which could approach room temperature.”
The team, reporting its work in Nature 10.1038/s41586-019-1591-7, says that it would indeed like to experimentally demonstrate such superconductivity in each of the individual layers of MoSe2 and WSe2 in the future. Such experiments are feasible thanks to the simplicity of the set up.
“We are also working on measuring the exciton correlation length, which can become macroscopic in the condensed phase,” says Mak. “This is a unique feature of macroscopic quantum coherence.
“Finally, we also wish to combine our exciton condensates with moiré superlattices, like those recently demonstrated in twisted bilayer graphene, to realize a Bose-Hubbard model in a solid-state system,” he reveals.
