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Flat-band polaritons spotted in Lieb lattice


A lattice of semiconductor pillars that supports the conduction of polariton quasiparticles has been created by physicists at ITMO University in St Petersburg, Russia and the University of Sheffield, UK. The square “Lieb” lattice has a special symmetry that occurs in some high-temperature superconductors and the research could provide insights into that poorly-understood phenomenon.

In recent years, physicists have become intrigued by the properties of Lieb lattices. As well as occurring naturally in cuprate high-temperature superconductors, Lieb lattices have also been made using ultracold atoms and arrays of optical waveguides.

One fascinating property of electrons and other particles subject to the periodic potential of a Lieb lattice, is that they have “flat bands” in which there is no relationship between the energy and velocity of the particles. This gives the particles near infinite effective mass. Flat bands are of great interest to physicists because they are related to some types of superconductivity, magnetism and other quantum properties of solids.

L-shaped cells

This latest Lieb lattice system was created Dmitry Kryzhanovskii at the University of Sheffield, ITMO’s Ivan Shelykh and colleagues. Their micropillars are made of a compound semiconductor and are about 3 µm in diameter. The unit cell of their Lieb lattice contains three micropillars arranged in an L-shape (see figure). The unit cells are arranged in a square array with a lattice constant of about 6 µm.

The lattice supports the conduction of polaritons – which are particle-like entities formed when the electric field of a photon interacts with the conduction electrons in a material. “Such hybrid particles interact with each other, much like electrons do in a solid body,” explains Kryzhanovskii. “Now we know how polaritons condense in flat bands, how their interaction breaks the radiation symmetry and how their spin or polarization properties change.”

The system is particularly useful because the physical parameters that govern the behaviour of the polaritons can be fine-tuned by changing the properties of the lattice – something that is much more difficult to do in crystalline materials such as superconductors.

Quantum-tunnelling paths

With this ease of control, the researchers maintained continuous spin rotation in their polaritons, allowing for remarkably long observations of their polarization. “From a fundamental viewpoint, polariton crystals are interesting in that they provide a great variety of quantum phases and effects that we cannot study in standard crystals,” says Shelykh. These effects included distinctive emission patterns from different electron orbitals, revealing quantum-tunnelling paths that depend on polarization — an effect never previously observed.

The high tuneability of the polariton system could also have promising potential for applications in quantum computing. In this case the polarization state of a polariton could be used to represent a quantum bit (qubit) of information. “Polarization is an ideal candidate for quantum-level information processing,” says Shelykh.

Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling C. E. Whittaker, E. Cancellieri, P. M. Walker, D. R. Gulevich, H. Schomerus, D. Vaitiekus, B. Royall, D. M. Whittaker, E. Clarke, I. V. Iorsh, I. A. Shelykh, M. S. Skolnick, and D. N. Krizhanovskii Phys. Rev. Lett. 120, 097401 – Published 2 March 2018 DOI:

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