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TmMgGaO₄ is one of a number of recently-synthesized quantum magnets that are proposed to realize important theoretical models. Here the authors demonstrate the agreement between detailed experimental measurements and state-of-the-art predictions based on the 2D transverse-field triangular lattice Ising model.

A hybrid analogue–digital quantum simulator is used to demonstrate beyond-classical performance in benchmarking experiments and to study thermalization phenomena in an XY quantum magnet, including the breakdown of Kibble–Zurek scaling predictions and signatures of the Kosterlitz–Thouless phase transition.

Synthetic lattice systems are powerful platforms for studying the influence of intrinsic nonlinearities on topological phenomena. Here the authors elucidate the topological transport of solitons in terms of Wannier functions displacement and they introduce a nonlinearity-induced topological transport effect that could be observed in ultracold quantum mixtures.

Non-equilibrium two-dimensional melting is less understood than its equilibrium counterpart. Now it is shown that topologically driven melting in a two-dimensional crystal of charged colloids is the same irrespective of the mechanisms that generate the defects

EuCo₂Al₉ is identified as a metallic spin supersolid with high thermal conductivity, exhibiting coexisting spin orders, strong quantum fluctuations and a giant magnetocaloric effect enabling efficient sub-Kelvin refrigeration.

Terahertz microspectroscopic imaging at subgap millielectronvolt energies of a two-dimensional superfluid plasmon in few-layer Bi₂Sr₂CaCu₂O_8+x is demonstrated, allowing the spatial resolution of its deeply subdiffractive terahertz electrodynamics.

Superconducting-qubit quantum annealers have served as platforms for simulating condensed-matter phenomena. Sathe et al. use a quantum annealer to probe critical phenomena in classical magnets by reliably sampling thermal distributions, revealing universal signatures of phase transitions without classical slowdowns.

Owing to electron localization, two-dimensional materials are not expected to be metallic at low temperatures, but a field-induced quantum metal phase emerges in NbSe₂, whose behaviour is consistent with the Bose-metal model.

Heterostructures based on (111)-oriented KTaO₃crystals are a new platform for studying oxide interfaces. Gate-tunable superconductivity in 2D electron gases at the surface of (111)-oriented KTaO₃is now reported, with the superconducting transition being of the Berezinskii-Kosterlitz-Thouless type.

Demonstration of ballistic conduction and spin polarization of edge state currents in two dimensional topological insulators remains a challenge. Here, Muraniet al. report a direct signature of ballistic one dimensional transport along the topological surfaces of a bismuth nanowire connected to superconducting electrodes.

Josephson coupling over micrometres and at tens of kelvins is demonstrated across the half-metallic manganite La_0.7Sr_0.3MnO₃ combined with the superconducting cuprate YBa₂Cu₃O₇.

The authors propose that when an intervalley coherent (IVC) state is subjected to a static magnetic field, it develops an oscillating orbital magnetization at microwave frequency, an effect analogous to a Josephson oscillation in momentum space. The effect could provide an experimental diagnostic for identifying the IVC state.

Physical details of a Josephson junction may drastically modify the properties of supercurrent. Here, the authors observe a colossal enhancement of the critical supercurrent in a Josephson junction subject to a perpendicular magnetic field, indicating topological phase transitions.

When superconducting discs are deposited on graphene they induce local superconducting islands. The phase coupling between the islands can be controlled by a gate. Quantum phase fluctuations kill the superconductivity and lead to a metallic state, however, at higher magnetic fields superconductivity can return.

Electrical transport measurements of magic-angle twisted trilayer graphene are presented.

The mechanism of the multiple-q charge density wave phase in the antiferromagnetic kagome metal FeGe is not fully understood. Here the authors reveal dimerization-driven hexagonal charge-diffuse precursor and identify the fraction of dimerized/undimerized states as the key order parameter of the phase transition.

The authors present experimental evidence of three-dimensional superinsulation in a nanopatterned slab of NbTiN. In the electric Meissner state, they find polar nematic order arising from ferroelectric alignment of short electric strings excited by external electromagnetic fields.

The authors report the implementation of a bilayer system of 2D ultracold Bose gases with controllable Josephson coupling. This allows characterisation of coupling-induced superfluid phases and their microscopic origin tracing back to vortex binding.

Second-order topological insulators feature helical one-dimensional states located at crystal hinges. Running a supercurrent through such systems is now shown to lead to long-lived excited Andreev pairs due to their separation along hinges with opposite helicity.

The breakdown of superconductivity is described as a reduction in the amplitude of the order parameter or a breakdown in phase coherence of Cooper pairs. This Review Article highlights recent results that show both mechanisms may be at play simultaneously.

A superlattice consisting of SrIrO₃ and SrTiO₃ is shown to display a giant response to sub-tesla external magnetic fields—a direct consequence of its antiferromagnetic nature.

It takes extreme sensitivity to measure the elementary excitations in liquid helium-4. An optomechanical cavity with a thin film of superfluid inside can be used to both observe and control phonons in real time.

Using ultracold atoms trapped in an optical lattice, a Laughlin-like fractional quantum Hall state is prepared and mapped out on a microscopic level.

The Berry curvature is essential to the study of the topological properties of a system, be it solid-state, atomic or photonic. In 1D photonic lattices there is a new clever way of measuring the Berry curvature.

When performing quantum simulation, oftentimes the properties of interest are only a subset of the information contained in the entire state. Here, the authors devise a different type of quantum simulation, where they work with a compressed quantum state whose amplitudes are proportional to expected values of some specific observables of interest.

A quantum gas trapped in an optical lattice of triangular symmetry can now be driven from a paramagnetic to an antiferromagnetic state by a tunable artificial magnetic field.

Encapsulated graphene Josephson junctions are promising for microwave quantum circuits but so far haven’t been explored. Here, Schmidt and Jenkins et al. observe a gate-tunable Josephson inductance in a microwave circuit based on a ballistic graphene Josephson junction embedded in a superconducting cavity.

Josephson junctions composed of graphene are limited by incomplete gate control of the supercurrent, impeding their development for superconducting quantum devices. Here, the authors fabricate bipolar Josephson junctions of graphene, allowing supercurrent on/off switching through electrostatic gating.

Lattices of exciton-polariton condensates provide the base for a simulator that can be used to find the global minimum of the classical XY Hamiltonian.

Exotic states can be stabilized in strongly-correlated systems with non-trivial topological properties. Here, Wang et al. propose a topological p-wave excitonic insulator characterized by a chiral Chern number 1/2.

As a blueprint for high-precision quantum simulation, an 18-qubit algorithm that consists of more than 1,400 two-qubit gates is demonstrated, and reconstructs the energy eigenvalues of the simulated one-dimensional wire to a precision of 1 per cent.

The Tomonaga–Luttinger liquid framework can be used to describe 1D quantum systems, spanning fermions, bosons and anyons. In this Review, we discuss the various platforms that can host TLL states, including Josephson junctions, cold atoms and topological materials, and discuss the advances TLL theory can provide in quantum criticality, nonequilibrium dynamics and condensed-matter physics exploration.

As a material's thickness decreases towards the atomic-scale, dimensional confinement may promote behaviour not found in the bulk, with potential technological applications. Here, the authors study superconductivity in TaS₂as it is mechanically exfoliated towards the two-dimensional limit.

The fractional quantum Hall effect occurs when electrons move in Landau levels. In this study, using a theoretical flat-band lattice model, the fractional quantum Hall effect is observed in the presence of repulsive interactions when the band is one third full and in the absence of Landau levels.

Research on superconductivity in magic-angle twisted bilayer graphene reveals unconventional behaviour, an anisotropic gap and a significant role of quantum geometry, using combined d.c. transport and microwave measurements, suggesting new insights into superconductivity mechanisms.

Quantum annealers have been used to study equilibrium states of condensed matter models and recently extended to 1D quantum quench dynamics. Here the authors use a quantum annealer to study the quench dynamics of 2D quantum spin models that are hard to simulate classically.

What happens to correlated electronic phases—superconductivity and charge density wave ordering—as a material is thinned? Experiments show that both can remain intact in just a single layer of niobium diselenide.

A large-scale programmable quantum simulation is described, using a D-Wave quantum processor to simulate a two-dimensional magnetic lattice in the vicinity of a topological phase transition.

A TLAF is an archetypal geometrically frustrated magnetic system, which serves as the foundation for many exotic states, including quantum spin-liquids. Here, Park et al perform INS measurements on BLCTO, which, combined with theoretical calculations, reveal distinctive fingerprints of spinon excitations, thereby suggesting proximity to a spin liquid even in the presence of strong XXZ anisotropy.

Evidence of modulated metallic and superconducting states stemming from an incommensurate structural stripe motif is reported in the bulk van der Waals superlattice SrTa₂S₅.

Magnetic spin ice compounds are described by vertex models, which have been intensively studied for their exotic properties. Bovo et al. show thin films of Dy₂Ti₂O₇ have structures distinct from bulk crystals and come close to realising the two-dimensional F-model, which has an unusual ordering transition in the Berezinskii–Kosterlitz–Thouless class.