A supersolid is a counter-intuitive phase of matter where its constituent particles are arranged into a crystalline structure, yet they are free to flow without friction. This requires the particles to share a global macroscopic phase while being able to reduce their total energy by spontaneous, spatial self-organisation. This exotic state of matter has been achieved in different systems using Bose-Einstein condensates coupled to cavities, possessing spin-orbit coupling, or dipolar interactions. Here we provide experimental evidence of a new implementation of the supersolid phase in a novel non-equilibrium context based on exciton-polaritons condensed in a topologically non-trivial, bound-in-the-continuum state with exceptionally low losses. We measure the density modulation of the polaritonic state indicating the breaking of translational symmetry with a remarkable precision of a few parts in a thousand. Direct access to the phase of the wavefunction allows us to additionally measure the local coherence of the superfluid component. We demonstrate the potential of our synthetic photonic material to host phonon dynamics and a multimode excitation spectrum.
At a very low-temperature of 9 mK, electrons in the second Landau level of an extremely high-mobility two-dimensional electron system exhibit a very complex electronic behavior. With a varying filling factor, quantum liquids of different origins compete with several insulating phases leading to an irregular pattern in the transport parameters. We observe a fully developed nu=2+2/5 state separated from the even-denominator nu=2+1/2 state by an insulating phase and a nu=2+2/7 and nu=2+1/5 state surrounded by such phases. A developing plateau at nu=2+3/8 points to the existence of other even-denominator states.
We have measured magnetotransport at half-filled high Landau levels in a quantum well with two occupied electric subbands. We find resistivities that are isotropic in perpendicular magnetic field but become strongly anisotropic at nu = 9/2 and 11/2 on tilting the field. The anisotropy appears at an in-plane field, B(ip) approximately 2.5 T, with the easy-current direction parallel to B(ip) but rotates by 90 degrees at B(ip) approximately 10 T and points now in the same direction as in single-subband samples. This complex behavior is in quantitative agreement with theoretical calculations based on a unidirectional charge density wave state model.
We study two dimensional electron systems confined in wide quantum wells whose subband separation is comparable with the Zeeman energy. Two N = 0 Landau levels from different subbands and with opposite spins are pinned in energy when they cross each other and electrons can freely transfer between them. When the disorder is strong, we observe clear hysteresis in our data corresponding to instability of the electron distribution in the two crossing levels. When the intra-layer interaction dominates, multiple minima appear when a Landau level is 1/3 or 2/3 filled and fractional quantum hall effect can be stabilized.
Magnetotransport measurements were performed in an ultrahigh mobility $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum well of density $\ensuremath{\sim}3.0\ifmmode\times\else\texttimes\fi{}{10}^{11}\text{ }\text{ }{\mathrm{c}\mathrm{m}}^{\ensuremath{-}2}$. The temperature dependence of the magnetoresistance ${R}_{xx}$ was studied in detail in the vicinity of $\ensuremath{\nu}=\frac{9}{2}$. In particular, we discovered new minima in ${R}_{xx}$ at a filling factor $\ensuremath{\nu}\ensuremath{\simeq}4\frac{1}{5}$ and $4\frac{4}{5}$, but only at intermediate temperatures $80\ensuremath{\lesssim}T\ensuremath{\lesssim}120\text{ }\text{ }\mathrm{m}\mathrm{K}$. We interpret these as evidence for a fractional quantum Hall liquid forming in the $N=2$ Landau level and competing with bubble and Wigner crystal phases favored at lower temperatures. Our data suggest that a magnetically driven insulator-insulator quantum phase transition occurs between the bubble and Wigner crystal phases at $T=0$.
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