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A quantum-liquid state of spin–orbital-entangled magnetic moments is observed in the 5 d -electron honeycomb iridate H 3 LiIr 2 O 6 , evidenced by the absence of magnetic ordering down to 0.05 kelvin. Honeycomb hosts quantum spin liquid When materials with interacting spins are cooled, magnetic states with long-range ordering usually emerge. However, quantum effects have been predicted to prevent long-range ordering all the way down to temperatures close to absolute zero in materials known as quantum spin liquids, where the term 'liquid' refers to the disordered state of the spins. The realization of such a state in a material with a honeycomb lattice, such as graphene, is expected to also reveal topological excitations. Hidenori Takagi and colleagues demonstrate a quantum-spin-liquid state in the 5 d honeycomb iridate H 3 LiIrO 6 , which shows no magnetic ordering down to 0.05 kelvin. Signatures of unusual excitations suggest that this material is a topological quantum-spin-liquid candidate. The honeycomb lattice is one of the simplest lattice structures. Electrons and spins on this simple lattice, however, often form exotic phases with non-trivial excitations. Massless Dirac fermions can emerge out of itinerant electrons, as demonstrated experimentally in graphene 1 , and a topological quantum spin liquid with exotic quasiparticles can be realized in spin-1/2 magnets, as proposed theoretically in the Kitaev model 2 . The quantum spin liquid is a long-sought exotic state of matter, in which interacting spins remain quantum-disordered without spontaneous symmetry breaking 3 . The Kitaev model describes one example of a quantum spin liquid, and can be solved exactly by introducing two types of Majorana fermion 2 . Realizing a Kitaev model in the laboratory, however, remains a challenge in materials science. Mott insulators with a honeycomb lattice of spin–orbital-entangled pseudospin-1/2 moments have been proposed 4 , including the 5 d -electron systems α-Na 2 IrO 3 (ref. 5 ) and α-Li 2 IrO 3 (ref. 6 ) and the 4 d -electron system α-RuCl 3 (ref. 7 ). However, these candidates were found to magnetically order rather than form a liquid at sufficiently low temperatures 8 , 9 , 10 , owing to non-Kitaev interactions 6 , 11 , 12 , 13 . Here we report a quantum-liquid state of pseudospin-1/2 moments in the 5 d -electron honeycomb compound H 3 LiIr 2 O 6 . This iridate does not display magnetic ordering down to 0.05 kelvin, despite an interaction energy of about 100 kelvin. We observe signatures of low-energy fermionic excitations that originate from a small number of spin defects in the nuclear-magnetic-resonance relaxation and the specific heat. We therefore conclude that H 3 LiIr 2 O 6 is a quantum spin liquid. This result opens the door to finding exotic quasiparticles in a strongly spin–orbit-coupled 5 d -electron transition-metal oxide.

The excitonic insulator is a long conjectured correlated electron phase of narrow-gap semiconductors and semimetals, driven by weakly screened electron–hole interactions. Having been proposed more than 50 years ago, conclusive experimental evidence for its existence remains elusive. Ta 2 NiSe 5 is a narrow-gap semiconductor with a small one-electron bandgap E G of <50 meV. Below T C =326 K, a putative excitonic insulator is stabilized. Here we report an optical excitation gap E op ∼0.16 eV below T C comparable to the estimated exciton binding energy E B . Specific heat measurements show the entropy associated with the transition being consistent with a primarily electronic origin. To further explore this physics, we map the T C – E G phase diagram tuning E G via chemical and physical pressure. The dome-like behaviour around E G ∼0 combined with our transport, thermodynamic and optical results are fully consistent with an excitonic insulator phase in Ta 2 NiSe 5 . The nature of an insulating phase in Ta 2 NiSe 5 is an open question. Here, Lu et al . report transport, thermodynamic and optical evidences being fully consistent with an excitonic insulator phase in this material.

The nature of the pseudogap phase of cuprates remains a major puzzle 1 , 2 . One of its signatures is a large negative thermal Hall conductivity 3 , whose origin is as yet unknown. This is observed even in the undoped Mott insulator La 2 CuO 4 , in which the charge carriers are localized and therefore cannot be responsible. Here, we show that the thermal Hall conductivity of La 2 CuO 4 is roughly isotropic; that is, for heat transport parallel and normal to the CuO 2 planes, it is nearly the same. This shows that the Hall response must come from phonons, as they are the only heat carriers that are able to move with the same ease both normal and parallel to the planes 4 . For doping levels higher than the critical doping level at which the pseudogap phase ends, both La 1.6 −x Nd 0.4 Sr x CuO 4 and La 1.8 −x Eu 0.2 Sr x CuO 4 show no thermal Hall signal for a heat current normal to the planes, which establishes that phonons have zero Hall response outside the pseudogap phase. Inside the pseudogap phase, the phonons must become chiral to generate the Hall response, but the mechanism by which this happens remains to be identified. It must be intrinsic (from a coupling of phonons to their electronic environment) rather than extrinsic (from structural defects or impurities), as these are the same on both sides of critical doping. Thermal transport measurements show that there is a thermal Hall effect in the out-of-plane direction in two cuprates in the pseudogap regime. This indicates that phonons are carrying the heat and that they have a handedness of unknown origin.

The nature of the pseudogap phase of the copper oxides (‘cuprates’) remains a puzzle. Although there are indications that this phase breaks various symmetries, there is no consensus on its fundamental nature 1 . Fermi-surface, transport and thermodynamic signatures of the pseudogap phase are reminiscent of a transition into a phase with antiferromagnetic order, but evidence for an associated long-range magnetic order is still lacking 2 . Here we report measurements of the thermal Hall conductivity (in the x – y plane, κ xy ) in the normal state of four different cuprates—La 1.6− x Nd 0.4 Sr x CuO 4 , La 1.8− x Eu 0.2 Sr x CuO 4 , La 2− x Sr x CuO 4 and Bi 2 Sr 2− x La x CuO 6+ δ . We show that a large negative κ xy signal is a property of the pseudogap phase, appearing at its critical hole doping, p *. It is also a property of the Mott insulator at p  ≈ 0, where κ xy has the largest reported magnitude of any insulator so far 3 . Because this negative κ xy signal grows as the system becomes increasingly insulating electrically, it cannot be attributed to conventional mobile charge carriers. Nor is it due to magnons, because it exists in the absence of magnetic order. Our observation is reminiscent of the thermal Hall conductivity of insulators with spin-liquid states 4 – 6 , pointing to neutral excitations with spin chirality 7 in the pseudogap phase of cuprates. The so-called pseudogap phase in hole-doped cuprate superconductors is associated with an unusually large thermal Hall effect that attains unprecedented levels as the parent Mott insulator is approached.

The three central phenomena of cuprate (copper oxide) superconductors are linked by a common doping level p* —at which the enigmatic pseudogap phase ends and the resistivity exhibits an anomalous linear dependence on temperature, and around which the superconducting phase forms a dome-shaped area in the phase diagram 1 . However, the fundamental nature of p * remains unclear, in particular regarding whether it marks a true quantum phase transition. Here we measure the specific heat C of the cuprates Eu-LSCO and Nd-LSCO at low temperature in magnetic fields large enough to suppress superconductivity, over a wide doping range 2 that includes p* . As a function of doping, we find that C el / T is strongly peaked at p*  (where C el is the electronic contribution to C ) and exhibits a log(1/ T ) dependence as temperature T tends to zero. These are the classic thermodynamic signatures of a quantum critical point 3 – 5 , as observed in heavy-fermion 6 and iron-based 7 superconductors at the point where their antiferromagnetic phase comes to an end. We conclude that the pseudogap phase of cuprates ends at a quantum critical point, the associated fluctuations of which are probably involved in d -wave pairing and the anomalous scattering of charge carriers. Measurements of the specific heat of two cuprate materials at low temperature in magnetic fields large enough to suppress superconductivity and over a wide doping range reveal that the pseudogap phase of cuprates ends at a quantum critical point.

One of the most intriguing features of some high-temperature cuprate superconductors is the interplay between one-dimensional \"striped\" spin order and charge order, and superconductivity. We used mid-infrared femtosecond pulses to transform one such stripe-ordered compound, nonsuperconducting La₁.₆₇₅Eu₀.₂Sr₀.₁₂₅CuO₄, into a transient three-dimensional superconductor. The emergence of coherent interlayer transport was evidenced by the prompt appearance of a Josephson plasma resonance in the c-axis optical properties. An upper limit for the time scale needed to form the superconducting phase is estimated to be 1 to 2 picoseconds, which is significantly faster than expected. This places stringent new constraints on our understanding of stripe order and its relation to superconductivity.

The coupling between spin, valley and layer degrees of freedom in transition-metal dichalcogenides is shown to give rise to spin-polarized electron states, providing opportunities to create and manipulate spin and valley polarizations in bulk solids. Methods to generate spin-polarized electronic states in non-magnetic solids are strongly desired to enable all-electrical manipulation of electron spins for new quantum devices 1 . This is generally accepted to require breaking global structural inversion symmetry 1 , 2 , 3 , 4 , 5 . In contrast, here we report the observation from spin- and angle-resolved photoemission spectroscopy of spin-polarized bulk states in the centrosymmetric transition-metal dichalcogenide WSe 2 . Mediated by a lack of inversion symmetry in constituent structural units of the bulk crystal where the electronic states are localized 6 , we show how spin splittings up to ∼0.5 eV result, with a spin texture that is strongly modulated in both real and momentum space. Through this, our study provides direct experimental evidence for a putative locking of the spin with the layer and valley pseudospins in transition-metal dichalcogenides 7 , 8 , of key importance for using these compounds in proposed valleytronic devices.

Angle-resolved photoemission measurements of electron-doped layers of tungsten diselenide reveal signatures of negative electronic compressibility that survive to much higher carrier densities than in conventional 2D electron gases. Tunable bandgaps 1 , extraordinarily large exciton-binding energies 2 , 3 , strong light–matter coupling 4 and a locking of the electron spin with layer and valley pseudospins 5 , 6 , 7 , 8 have established transition-metal dichalcogenides (TMDs) as a unique class of two-dimensional (2D) semiconductors with wide-ranging practical applications 9 , 10 . Using angle-resolved photoemission (ARPES), we show here that doping electrons at the surface of the prototypical strong spin–orbit TMD WSe 2 , akin to applying a gate voltage in a transistor-type device, induces a counterintuitive lowering of the surface chemical potential concomitant with the formation of a multivalley 2D electron gas (2DEG). These measurements provide a direct spectroscopic signature of negative electronic compressibility (NEC), a result of electron–electron interactions, which we find persists to carrier densities approximately three orders of magnitude higher than in typical semiconductor 2DEGs that exhibit this effect 11 , 12 . An accompanying tunable spin splitting of the valence bands further reveals a complex interplay between single-particle band-structure evolution and many-body interactions in electrostatically doped TMDs. Understanding and exploiting this will open up new opportunities for advanced electronic and quantum-logic devices.

The minimal ingredients to explain the essential physics of layered copper-oxide (cuprates) materials remains heavily debated. Effective low-energy single-band models of the copper–oxygen orbitals are widely used because there exists no strong experimental evidence supporting multi-band structures. Here, we report angle-resolved photoelectron spectroscopy experiments on La-based cuprates that provide direct observation of a two-band structure. This electronic structure, qualitatively consistent with density functional theory, is parametrised by a two-orbital ( d x 2 - y 2 and d z 2 ) tight-binding model. We quantify the orbital hybridisation which provides an explanation for the Fermi surface topology and the proximity of the van-Hove singularity to the Fermi level. Our analysis leads to a unification of electronic hopping parameters for single-layer cuprates and we conclude that hybridisation, restraining d -wave pairing, is an important optimisation element for superconductivity. The essential physics of cuprate superconductors is often described by single-band models. Here, Matt et al. report direct observation of a two-band electronic structure in La-based cuprates.

Josephson plasma waves are linear electromagnetic modes that propagate along the planes of cuprate superconductors, sustained by interlayer tunnelling supercurrents. For strong electromagnetic fields, as the supercurrents approach the critical value, the electrodynamics become highly nonlinear. Josephson plasma solitons (JPSs) are breather excitations predicted in this regime, bound vortex–antivortex pairs that propagate coherently without dispersion. We experimentally demonstrate the excitation of a JPS in La 1.84 Sr 0.16 CuO 4 , using intense narrowband radiation from an infrared free-electron laser tuned to the 2-THz Josephson plasma resonance. The JPS becomes observable as it causes a transparency window in the opaque spectral region immediately below the plasma resonance. Optical control of magnetic-flux-carrying solitons may lead to new applications in terahertz-frequency plasmonics, in information storage and transport and in the manipulation of high- T c superconductivity. Josephson plasma solitons are a kind of excitation predicted to occur in cuprate superconductors subject to strong electromagnetic fields. By using intense radiation from a free-electron laser, these modes are now demonstrated experimentally in the copper oxide material La 1.84 Sr 0.16 CuO 4 .