As few as five electrons in a semiconductor can exhibit collective behaviour, forming a “Coulomb liquid”, according to researchers in Europe. This extends the study of correlated systems to electron plasmas, and could lead to the study of other exotic phases of matter.
A conventional plasma is a hot, ionized gas of free electrons and positive ions. However, the conduction band of a semiconductor can be considered a one-component plasma. “The effect of the positive charges, as they are locked into the lattice, can be modelled as a uniform background of positive charge,” says team member Vyacheslavs Kashcheyevs of the University of Latvia in Riga. In conventional electronics and semiconductor physics, the conduction band is modelled as a 2D Fermi gas of non-interacting particles, with the Coulomb interaction between the electrons neglected.
The new work focused on electron–electron correlations in the conduction band of gallium arsenide at millikelvin temperatures. The team created a Y-shaped junction. Electrons emitted from a quantum dot were steered through the device by an externally-generated surface acoustic wave (SAW) potential. Part-way through, the path divided, and each electron could either go left or right. The number taking each path was measured by separate quantum dots. The researchers are uncertain, and the model is agnostic, about the extent to which the randomness of left or right arose from quantum mechanics.
When no more than one electron was loaded into each potential minimum, each electron’s choice was random, and the number of electrons counted at each detector after multiple trials could be modelled by a binomial distribution. However, when the researchers tuned the apparatus such that each minimum contained multiple electrons, they found changes in the distribution, with groups of particles less likely to travel to the same detector than would be naïvely expected.
Calculating “cumulants”
The researchers quantified the changes in the distributions using probability theory, calculating “cumulants” of the distributions. “We not only have a cumulant of order two, which would say that two particles are repulsing,” says Hermann Sellier of Institut Néel in Grenoble, France, who led the experimental research. “We have a cumulant of order four for four particles or five for five particles, showing that each particle is talking to all the other particles of the droplet. That’s much stronger and something that has not been measured before.”
This shows, say the researchers, that the 2D electron gas condenses into a strongly correlated Coulomb liquid. This a phase of matter seen in quark–gluon plasma, which is created by the high-energy collision of heavy ions, but never previously identified in electronic matter.
“It’s not like you have atoms which, below a certain temperature, go from the gas phase to the liquid phase because of an attractive interaction,” explains Sellier. “We say that the correlated behaviour is like that of a liquid, but a very special liquid made of repulsive interactions. You push on the right, it pushes on the left.” This is possible only at low temperatures because heating increases the entropy to the point where the correlated state of matter is disfavoured.
The team now wants to look at larger systems approaching the macroscopic limit. They believe similar systems could potentially be used to study many-body physics with other, exotic particles such as anyons – quasiparticles that have properties intermediate to bosons and fermions. Potential technological applications include cold atom quantum simulation.
Considerable interest
Ravi Rau of Louisiana State University in the US says, “It is an interesting method, novel to me, of controlling electron droplets and being able to measure correlations of two, three and up to a maximum of five-particles so far, and addressing the general question of the transition in few-body systems to the statistical limit from explicit dynamics when the number of particles is small”. He adds, “This study, such a system, and the results presented will of course be of considerable interest.”
Rau does however, note that very similar results were achieved in the past in studies of electron collisions with cold atoms and molecules. “[That technique] went under the name of COLTRIMS (cold target recoil-ion momentum spectroscopy) allowed measuring multiple differential cross sections and studying electron–electron correlations in atoms,” he says. “It was the exact analogue of this [work], except that instead of an artificially created and controlled droplet cluster, the electrons were naturally inside the atom.”
The researchers acknowledge the similarity, and thank Rau for bringing the previous work to their attention. However, Kashcheyevs argues that the new work has a generality that allows it to tackle new problems, finding the scaling law that connects the properties of individual electrons to the properties of incompressible Coulomb plasma. “Applying our method at lower temperatures in the future can probe the quantum regime of the phase diagram of this electronic fluid, which is known to support exotic quasiparticles impossible in the 3D vacuum of the Standard Model,” he says.
The research is described in Nature.
