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Quantum ferrofluids A paper in this issue addresses a hot topic in the physics of ultracold atoms — quantum ferrofluids, which are superfluid quantum gases that consist of polarized dipoles, either electric or magnetic. The symmetry-breaking interaction between such dipoles is expected to lead to new physical phenomena. Now a group from Stuttgart University has succeeded in producing a chromium Bose–Einstein condensate with strong anisotropic magnetic dipole–dipole interaction between the atoms, which induces a pronounced change of the aspect ratio of the cloud. This much-sought form of matter should enable fundamental studies of physical systems in previously unexplored regimes. This paper reports the realization of a chromium Bose-Einstein condensate (BEC) with strong anisotropic magnetic dipole–dipole interaction between the atoms, which induces a pronounced change of the aspect ratio of the cloud. The experiment opens the way for exploration of the unique properties of quantum ferrofluids. Symmetry-breaking interactions have a crucial role in many areas of physics, ranging from classical ferrofluids to superfluid 3 He and d -wave superconductivity. For superfluid quantum gases, a variety of new physical phenomena arising from the symmetry-breaking interaction between electric or magnetic dipoles are expected 1 . Novel quantum phases in optical lattices, such as chequerboard or supersolid phases, are predicted for dipolar bosons 2 , 3 . Dipolar interactions can also enrich considerably the physics of quantum gases with internal degrees of freedom 4 , 5 , 6 . Arrays of dipolar particles could be used for efficient quantum information processing 7 . Here we report the realization of a chromium Bose–Einstein condensate with strong dipolar interactions. By using a Feshbach resonance, we reduce the usual isotropic contact interaction, such that the anisotropic magnetic dipole–dipole interaction between 52 Cr atoms becomes comparable in strength. This induces a change of the aspect ratio of the atom cloud; for strong dipolar interactions, the inversion of ellipticity during expansion (the usual ‘smoking gun’ evidence for a Bose–Einstein condensate) can be suppressed. These effects are accounted for by taking into account the dipolar interaction in the superfluid hydrodynamic equations governing the dynamics of the gas, in the same way as classical ferrofluids can be described by including dipolar terms in the classical hydrodynamic equations. Our results are a first step in the exploration of the unique properties of quantum ferrofluids.

The electron–hole plasma in charge-neutral graphene is predicted to realize a quantum critical system in which electrical transport features a universal hydrodynamic description, even at room temperature 1 , 2 . This quantum critical ‘Dirac fluid’ is expected to have a shear viscosity close to a minimum bound 3 , 4 , with an interparticle scattering rate saturating 1 at the Planckian time, the shortest possible timescale for particles to relax. Although electrical transport measurements at finite carrier density are consistent with hydrodynamic electron flow in graphene 5 – 8 , a clear demonstration of viscous flow at the charge-neutrality point remains elusive. Here we directly image viscous Dirac fluid flow in graphene at room temperature by measuring the associated stray magnetic field. Nanoscale magnetic imaging is performed using quantum spin magnetometers realized with nitrogen vacancy centres in diamond. Scanning single-spin and wide-field magnetometry reveal a parabolic Poiseuille profile for electron flow in a high-mobility graphene channel near the charge-neutrality point, establishing the viscous transport of the Dirac fluid. This measurement is in contrast to the conventional uniform flow profile imaged in a metallic conductor and also in a low-mobility graphene channel. Via combined imaging and transport measurements, we obtain viscosity and scattering rates, and observe that these quantities are comparable to the universal values expected at quantum criticality. This finding establishes a nearly ideal electron fluid in charge-neutral, high-mobility graphene at room temperature 4 . Our results will enable the study of hydrodynamic transport in quantum critical fluids relevant to strongly correlated electrons in high-temperature superconductors 9 . This work also highlights the capability of quantum spin magnetometers to probe correlated electronic phenomena at the nanoscale. Viscous Dirac fluid flow in room-temperature graphene is imaged using quantum diamond magnetometry, revealing a parabolic Poiseuille profile for electron flow in a high-mobility graphene channel near the charge-neutrality point.

We review the physics of helium nanodroplets with emphasis on theoretical aspects that have been the subject of recent research, like 3He and mixed 3He− 4He droplets, vortices in droplets and droplets on weakly attractive substrates, and in others that have not been previously reviewed in detail. Whenever possible, we compare results from different theoretical methods, with the aim of assessing the capabilities and limitations of the more phenomenological ones, that often constitute the only instrument to address some of the questions raised by current experiments.

Moiré superlattices can be used to engineer strongly correlated electronic states in two-dimensional van der Waals heterostructures, as recently demonstrated in the correlated insulating and superconducting states observed in magic-angle twisted-bilayer graphene and ABC trilayer graphene/boron nitride moiré superlattices 1 – 4 . Transition metal dichalcogenide moiré heterostructures provide another model system for the study of correlated quantum phenomena 5 because of their strong light–matter interactions and large spin–orbit coupling. However, experimental observation of correlated insulating states in this system is challenging with traditional transport techniques. Here we report the optical detection of strongly correlated phases in semiconducting WSe 2 /WS 2 moiré superlattices. We use a sensitive optical detection technique and reveal a Mott insulator state at one hole per superlattice site and surprising insulating phases at 1/3 and 2/3 filling of the superlattice, which we assign to generalized Wigner crystallization on the underlying lattice 6 – 11 . Furthermore, the spin–valley optical selection rules 12 – 14 of transition metal dichalcogenide heterostructures allow us to optically create and investigate low-energy excited spin states in the Mott insulator. We measure a very long spin relaxation lifetime of many microseconds in the Mott insulating state, orders of magnitude longer than that of charge excitations. Our studies highlight the value of using moiré superlattices beyond graphene to explore correlated physics. Strongly correlated insulating Mott and generalized Wigner phases are detected in WSe 2 /WS 2 moiré superlattices, and their electrical properties and excited spin states are studied using an optical technique.

Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice 1 . A variety of two-dimensional systems have shown evidence for Wigner crystals 2 – 11 (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν  ≈ 0.13 and ν  ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Analysis of individual lattice sites shows signatures that may be related to the quantum zero-point motion of electrons in the WC lattice. A magnetic-field-induced Wigner crystal in Bernal-stacked bilayer graphene was directly imaged using high-resolution scanning tunnelling microscopy and its structural properties as a function of electron density, magnetic field and temperature were examined.

The Wigner crystal 1 has fascinated condensed matter physicists for nearly 90 years 2 – 14 . Signatures of two-dimensional (2D) Wigner crystals were first observed in 2D electron gases under high magnetic field 2 – 4 , and recently reported in transition metal dichalcogenide moiré superlattices 6 – 9 . Direct observation of the 2D Wigner crystal lattice in real space, however, has remained an outstanding challenge. Conventional scanning tunnelling microscopy (STM) has sufficient spatial resolution but induces perturbations that can potentially alter this fragile state. Here we demonstrate real-space imaging of 2D Wigner crystals in WSe 2 /WS 2 moiré heterostructures using a specially designed non-invasive STM spectroscopy technique. This employs a graphene sensing layer held close to the WSe 2 /WS 2 moiré superlattice. Local STM tunnel current into the graphene layer is modulated by the underlying Wigner crystal electron lattice in the WSe 2 /WS 2 heterostructure. Different Wigner crystal lattice configurations at fractional electron fillings of n  = 1/3, 1/2 and 2/3, where n is the electron number per site, are directly visualized. The n  = 1/3 and n  = 2/3 Wigner crystals exhibit triangular and honeycomb lattices, respectively, to minimize nearest-neighbour occupations. The n  = 1/2 state spontaneously breaks the original C3 symmetry and forms a stripe phase. Our study lays a solid foundation for understanding Wigner crystal states in WSe 2 /WS 2 moiré heterostructures and provides an approach that is generally applicable for imaging novel correlated electron lattices in other systems. So far, only indirect evidence of Wigner crystals has been reported, but a specially designed scanning tunnelling microscope is used here to directly image them in a moiré heterostructure.

Graphene moiré superlattices display electronic flat bands. At integer fillings of these flat bands, energy gaps due to strong electron–electron interactions are generally observed. However, the presence of other correlation-driven phases in twisted graphitic systems at non-integer fillings is unclear. Here, we report the existence of three-fold rotational ( C 3 ) symmetry breaking in twisted double bilayer graphene. Using spectroscopic imaging over large and uniform areas to characterize the direction and degree of C 3 symmetry breaking, we find it to be prominent only at energies corresponding to the flat bands and nearly absent in the remote bands. We demonstrate that the magnitude of the rotational symmetry breaking does not depend on the degree of the heterostrain or the displacement field, being instead a manifestation of an interaction-driven electronic nematic phase. We show that the nematic phase is a primary order that arises from the normal metal state over a wide range of doping away from charge neutrality. Our modelling suggests that the nematic instability is not associated with the local scale of the graphene lattice, but is an emergent phenomenon at the scale of the moiré lattice. Observations of an electronic nematic phase in twisted double bilayer graphene expand the number of moiré materials where this interaction-driven state exists.

Electrons on helium form a unique two-dimensional system on the interface of liquid helium and vacuum. A small number of trapped electrons on helium exhibits strong interactions in the absence of disorder, and can be used as a qubit. Trapped electrons typically have orbital frequencies in the microwave regime and can therefore be integrated with circuit quantum electrodynamics (cQED), which studies light–matter interactions using microwave photons. Here, we experimentally realize a cQED platform with the orbitals of single electrons on helium. We deterministically trap one to four electrons in a dot integrated with a microwave resonator, allowing us to study the electrons’ response to microwaves. Furthermore, we find a single-electron-photon coupling strength of g ∕ 2 π = 4.8 ± 0.3  MHz, greatly exceeding the resonator linewidth κ ∕ 2 π = 0.5  MHz. These results pave the way towards microwave studies of Wigner molecules and coherent control of the orbital and spin state of a single electron on helium. Electrons on the surface of helium have strong interactions with each other but weak coupling to dissipation mechanisms, providing opportunities for many-body physics and storing quantum information. Here the authors demonstrate a circuit QED platform for manipulating and probing few-electron clusters.

One of the first theoretically predicted manifestations of strong interactions in many-electron systems was the Wigner crystal 1 – 3 , in which electrons crystallize into a regular lattice. The crystal can melt via either thermal or quantum fluctuations 4 . Quantum melting of the Wigner crystal is predicted to produce exotic intermediate phases 5 , 6 and quantum magnetism 7 , 8 because of the intricate interplay of Coulomb interactions and kinetic energy. However, studying two-dimensional Wigner crystals in the quantum regime has often required a strong magnetic field 9 – 11 or a moiré superlattice potential 12 – 15 , thus limiting access to the full phase diagram of the interacting electron liquid. Here we report the observation of bilayer Wigner crystals without magnetic fields or moiré potentials in an atomically thin transition metal dichalcogenide heterostructure, which consists of two MoSe 2 monolayers separated by hexagonal boron nitride. We observe optical signatures of robust correlated insulating states at symmetric (1:1) and asymmetric (3:1, 4:1 and 7:1) electron doping of the two MoSe 2 layers at cryogenic temperatures. We attribute these features to bilayer Wigner crystals composed of two interlocked commensurate triangular electron lattices, stabilized by inter-layer interaction 16 . The Wigner crystal phases are remarkably stable, and undergo quantum and thermal melting transitions at electron densities of up to 6 × 10 12 per square centimetre and at temperatures of up to about 40 kelvin. Our results demonstrate that an atomically thin heterostructure is a highly tunable platform for realizing many-body electronic states and probing their liquid–solid and magnetic quantum phase transitions 4 – 8 , 17 . Optical signatures reveal correlated insulating Wigner crystals—electron solids—in a bilayer of a two-dimensional transition metal dichalcogenide, MoSe 2 , with hexagonal boron nitride between the layers.

Interacting electrons confined to their lowest Landau level in a high magnetic field can form a variety of correlated states, some of which manifest themselves in a Hall effect. Although such states have been predicted to occur in three-dimensional semimetals, a corresponding Hall response has not yet been experimentally observed. Here, we report the observation of an unconventional Hall response in the quantum limit of the bulk semimetal HfTe 5 , adjacent to the three-dimensional quantum Hall effect of a single electron band at low magnetic fields. The additional plateau-like feature in the Hall conductivity of the lowest Landau level is accompanied by a Shubnikov-de Haas minimum in the longitudinal electrical resistivity and its magnitude relates as 3/5 to the height of the last plateau of the three-dimensional quantum Hall effect. Our findings are consistent with strong electron-electron interactions, stabilizing an unconventional variant of the Hall effect in a three-dimensional material in the quantum limit. There is a long-standing experimental effort to observe field-induced correlated states in three-dimensional materials. Here, the authors observe an unconventional Hall response in the quantum limit of the bulk semimetal HfTe 5 with a plateau-like feature in the Hall conductivity.