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Micro X-ray diffraction imaging of the spatial distribution of charge-density-wave puddles and quenched disorder in HgBa 2 CuO 4 + y reveals a complex, inhomogeneous spatial landscape due to the interplay between charge and dopant order. The geometry of high- T c superconductors The geometry favouring the high-transition-temperature superconducting state ( T c ) emerges from the coexistence of charge-density-wave order and quenched disorder. Gaetano Campi et al . have used micro X-ray diffraction imaging to study the spatial distribution of charge-density-wave 'puddles' and quenched disorder in HgBa 2 CuO 4+ y . They describe a complex, inhomogeneous spatial landscape resulting from the interplay between charge and dopant order. The charge-density-wave puddles, like the steam bubbles in boiling water, show a size distribution typical of self-organization near a critical point. The quenched disorder shows a distribution contrary to the usual assumed random uncorrelated distribution. It has recently been established that the high-transition-temperature (high- T c ) superconducting state coexists with short-range charge-density-wave order 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 and quenched disorder 12 , 13 arising from dopants and strain 14 , 15 , 16 , 17 . This complex, multiscale phase separation 18 , 19 , 20 , 21 invites the development of theories of high-temperature superconductivity that include complexity 22 , 23 , 24 , 25 . The nature of the spatial interplay between charge and dopant order that provides a basis for nanoscale phase separation remains a key open question, because experiments have yet to probe the unknown spatial distribution at both the nanoscale and mesoscale (between atomic and macroscopic scale). Here we report micro X-ray diffraction imaging of the spatial distribution of both short-range charge-density-wave ‘puddles’ (domains with only a few wavelengths) and quenched disorder in HgBa 2 CuO 4 + y , the single-layer cuprate with the highest T c , 95 kelvin (refs 26 , 27 , 28 ). We found that the charge-density-wave puddles, like the steam bubbles in boiling water, have a fat-tailed size distribution that is typical of self-organization near a critical point 19 . However, the quenched disorder, which arises from oxygen interstitials, has a distribution that is contrary to the usually assumed random, uncorrelated distribution 12 , 13 . The interstitial-oxygen-rich domains are spatially anticorrelated with the charge-density-wave domains, because higher doping does not favour the stripy charge-density-wave puddles, leading to a complex emergent geometry of the spatial landscape for superconductivity.

By exciting high-temperature K 3 C 60 with mid-infrared pulses, a large increase in carrier mobility is obtained, accompanied by the opening of a gap in the optical conductivity; these same signatures are observed at equilibrium when cooling K 3 C 60 below the superconducting transition temperature of 20 kelvin, which could be an indication of light-induced high-temperature superconductivity. Light-stimulated superconductivity The use of light to control the properties of condensed-matter materials is a promising area of research, with the long-term prospect that it might lead to the development of quantum devices driven by light. In particular, it was shown recently that nonlinear excitation of certain phonons in bilayer copper oxides induces superconducting-like optical properties at temperatures far above the material's superconducting transition temperature ( T c ). This effect was accompanied by the disruption of competing charge-density-wave correlations, explaining some, but not all, of the experimental results. Andrea Cavalleri and colleagues now report that by exciting metallic K 3 C 60 with mid-infrared optical pulses, they can induce a large increase in carrier mobility, accompanied by the opening of a gap in the optical conductivity. Strikingly, these same signatures are observed at equilibrium when K 3 C 60 cools below its T c of 20 K. The non-equilibrium control of emergent phenomena in solids is an important research frontier, encompassing effects such as the optical enhancement of superconductivity 1 . Nonlinear excitation 2 , 3 of certain phonons in bilayer copper oxides was recently shown to induce superconducting-like optical properties at temperatures far greater than the superconducting transition temperature, T c (refs 4 , 5 , 6 ). This effect was accompanied by the disruption of competing charge-density-wave correlations 7 , 8 , which explained some but not all of the experimental results. Here we report a similar phenomenon in a very different compound, K 3 C 60 . By exciting metallic K 3 C 60 with mid-infrared optical pulses, we induce a large increase in carrier mobility, accompanied by the opening of a gap in the optical conductivity. These same signatures are observed at equilibrium when cooling metallic K 3 C 60 below T c (20 kelvin). Although optical techniques alone cannot unequivocally identify non-equilibrium high-temperature superconductivity, we propose this as a possible explanation of our results.

Although high-transition-temperature (high- T c ) superconductivity in cuprates has been known for more than three decades, the underlying mechanism remains unknown 1 – 4 . Cuprates are the only unconventional superconductors that exhibit bulk superconductivity with T c above the liquid-nitrogen boiling temperature of 77 K. Here we observe that high-pressure resistance and mutual inductive magnetic susceptibility measurements showed signatures of superconductivity in single crystals of La 3 Ni 2 O 7 with maximum T c of 80 K at pressures between 14.0 GPa and 43.5 GPa. The superconducting phase under high pressure has an orthorhombic structure of Fmmm space group with the 3 d x 2 − y 2 and 3 d z 2 orbitals of Ni cations strongly mixing with oxygen 2 p orbitals. Our density functional theory calculations indicate that the superconductivity emerges coincidently with the metallization of the σ-bonding bands under the Fermi level, consisting of the 3 d z 2 orbitals with the apical oxygen ions connecting the Ni–O bilayers. Thus, our discoveries provide not only important clues for the high- T c superconductivity in this Ruddlesden–Popper double-layered perovskite nickelates but also a previously unknown family of compounds to investigate the high- T c superconductivity mechanism. Signatures of superconductivity in single crystals of La 3 Ni 2 O 7 were observed at a maximum transition temperature of 80  K at pressures between 14.0  GPa and 43.5  GPa.

High-resolution angle-resolved photoemission spectroscopy reveals bosonic modes in a SrTiO 3 substrate coupling to electrons in an FeSe overlayer to facilitate high-temperature superconductivity. Strontium titanate boosts supereconductivity Bulk iron selenide (FeSe) is a superconductor with a critical temperature T c = 8 K, but superconductivity is substantially enhanced in single-unit cell films of FeSe grown on strontium titanate (SrTiO 3 or STO) substrates, where superconducting energy gaps open at temperatures close to the boiling point of liquid nitrogen (77 K). This raises the question of whether the substrate has a contributory role in this enhancement. Zhi-Xun Shen and colleagues report high-resolution angle-resolved photoemission spectroscopy (ARPES) results that reveal bosonic modes (thought to be oxygen optical phonons) in the SrTiO 3 substrate coupling to electrons in the FeSe overlayer to facilitate high-temperature superconductivity. Such coupling helps superconductivity in most channels, so the pairing enhancement described here may well work for other superconducting materials, as well as for FeSe. Films of iron selenide (FeSe) one unit cell thick grown on strontium titanate (SrTiO 3 or STO) substrates have recently shown 1 , 2 , 3 , 4 superconducting energy gaps opening at temperatures close to the boiling point of liquid nitrogen (77 kelvin), which is a record for the iron-based superconductors. The gap opening temperature usually sets the superconducting transition temperature T c , as the gap signals the formation of Cooper pairs, the bound electron states responsible for superconductivity. To understand why Cooper pairs form at such high temperatures, we examine the role of the SrTiO 3 substrate. Here we report high-resolution angle-resolved photoemission spectroscopy results that reveal an unexpected characteristic of the single-unit-cell FeSe/SrTiO 3 system: shake-off bands suggesting the presence of bosonic modes, most probably oxygen optical phonons in SrTiO 3 (refs 5 , 6 , 7 ), which couple to the FeSe electrons with only a small momentum transfer. Such interfacial coupling assists superconductivity in most channels, including those mediated by spin fluctuations 8 , 9 , 10 , 11 , 12 , 13 , 14 . Our calculations suggest that this coupling is responsible for raising the superconducting gap opening temperature in single-unit-cell FeSe/SrTiO 3 .

The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology 1 – 18 , which continues to bear surprises. Here, using spectroscopic imaging scanning tunnelling microscopy, we discover a temperature-dependent cascade of different symmetry-broken electronic states in a new kagome superconductor, CsV 3 Sb 5 . We reveal, at a temperature far above the superconducting transition temperature T c  ~ 2.5 K, a tri-directional charge order with a 2 a 0 period that breaks the translation symmetry of the lattice. As the system is cooled down towards T c , we observe a prominent V-shaped spectral gap opening at the Fermi level and an additional breaking of the six-fold rotational symmetry, which persists through the superconducting transition. This rotational symmetry breaking is observed as the emergence of an additional 4 a 0 unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the vanadium kagome bands. Our experiments reveal a complex landscape of electronic states that can coexist on a kagome lattice, and highlight intriguing parallels to high- T c superconductors and twisted bilayer graphene. A study reveals a temperature-dependent cascade of different symmetry-broken electronic states in the kagome superconductor CsV 3 Sb 5 , and highlights intriguing parallels between vanadium-based kagome metals and materials exhibiting similar electronic phases.

The transition metal kagome lattice materials host frustrated, correlated and topological quantum states of matter 1 – 9 . Recently, a new family of vanadium-based kagome metals, AV 3 Sb 5 (A = K, Rb or Cs), with topological band structures has been discovered 10 , 11 . These layered compounds are nonmagnetic and undergo charge density wave transitions before developing superconductivity at low temperatures 11 – 19 . Here we report the observation of unconventional superconductivity and a pair density wave (PDW) in CsV 3 Sb 5 using scanning tunnelling microscope/spectroscopy and Josephson scanning tunnelling spectroscopy. We find that CsV 3 Sb 5 exhibits a V-shaped pairing gap Δ  ~ 0.5 meV and is a strong-coupling superconductor (2 Δ / k B T c  ~ 5) that coexists with 4 a 0 unidirectional and 2 a 0  × 2 a 0 charge order. Remarkably, we discover a 3Q PDW accompanied by bidirectional 4 a 0 /3 spatial modulations of the superconducting gap, coherence peak and gap depth in the tunnelling conductance. We term this novel quantum state a roton PDW associated with an underlying vortex–antivortex lattice that can account for the observed conductance modulations. Probing the electronic states in the vortex halo in an applied magnetic field, in strong field that suppresses superconductivity and in zero field above T c , reveals that the PDW is a primary state responsible for an emergent pseudogap and intertwined electronic order. Our findings show striking analogies and distinctions to the phenomenology of high- T c cuprate superconductors, and provide groundwork for understanding the microscopic origin of correlated electronic states and superconductivity in vanadium-based kagome metals. A study reports unconventional superconductivity and a pair density wave in the kagome superconductor CsV 3 Sb 5 , and provides a basis for understanding the microscopic origin of correlated electronic states and superconductivity in vanadium-based kagome metals.

Majorana bound states constitute one of the simplest examples of emergent non-Abelian excitations in condensed matter physics. A toy model proposed by Kitaev shows that such states can arise at the ends of a spinless p -wave superconducting chain 1 . Practical proposals for its realization 2 , 3 require coupling neighbouring quantum dots (QDs) in a chain through both electron tunnelling and crossed Andreev reflection 4 . Although both processes have been observed in semiconducting nanowires and carbon nanotubes 5 – 8 , crossed-Andreev interaction was neither easily tunable nor strong enough to induce coherent hybridization of dot states. Here we demonstrate the simultaneous presence of all necessary ingredients for an artificial Kitaev chain: two spin-polarized QDs in an InSb nanowire strongly coupled by both elastic co-tunnelling (ECT) and crossed Andreev reflection (CAR). We fine-tune this system to a sweet spot where a pair of poor man’s Majorana states is predicted to appear. At this sweet spot, the transport characteristics satisfy the theoretical predictions for such a system, including pairwise correlation, zero charge and stability against local perturbations. Although the simple system presented here can be scaled to simulate a full Kitaev chain with an emergent topological order, it can also be used imminently to explore relevant physics related to non-Abelian anyons. A minimal artificial Kitaev chain can be realized by using two spin-polarized quantum dots in an InSb nanowire strongly coupled by both elastic co-tunnelling and crossed Andreev reflection.

Superconductivity can occur under conditions approaching broken-symmetry parent states 1 . In bilayer graphene, the twisting of one layer with respect to the other at ‘magic’ twist angles of around 1 degree leads to the emergence of ultra-flat moiré superlattice minibands. Such bands are a rich and highly tunable source of strong-correlation physics 2 – 5 , notably superconductivity, which emerges close to interaction-induced insulating states 6 , 7 . Here we report the fabrication of magic-angle twisted bilayer graphene devices with highly uniform twist angles. The reduction in twist-angle disorder reveals the presence of insulating states at all integer occupancies of the fourfold spin–valley degenerate flat conduction and valence bands—that is, at moiré band filling factors ν  = 0, ±1, ±2, ±3. At ν  ≈ −2, superconductivity is observed below critical temperatures of up to 3 kelvin. We also observe three new superconducting domes at much lower temperatures, close to the ν  = 0 and ν  = ±1 insulating states. Notably, at ν  = ± 1 we find states with non-zero Chern numbers. For ν  = −1 the insulating state exhibits a sharp hysteretic resistance enhancement when a perpendicular magnetic field greater than 3.6 tesla is applied, which is consistent with a field-driven phase transition. Our study shows that broken-symmetry states, interaction-driven insulators, orbital magnets, states with non-zero Chern numbers and superconducting domes occur frequently across a wide range of moiré flat band fillings, including close to charge neutrality. This study provides a more detailed view of the phenomenology of magic-angle twisted bilayer graphene, adding to our evolving understanding of its emergent properties. The fabrication of magic-angle twisted bilayer graphene devices with highly uniform twist angles enables the observation of new superconducting domes, orbital magnets and Chern insulating states.

Recent experimental observations have showed some signatures of superconductivity close to 80 K in La 3 Ni 2 O 7 under pressure and have raised the hope of achieving high-temperature superconductivity in bulk nickelates. However, a zero-resistance state—a key characteristic of a superconductor—was not observed. Here we show that the zero-resistance state does exist in single crystals of La 3 Ni 2 O 7− δ using a liquid pressure medium at up to 30 GPa. We also find that the system remains metallic under applied pressures, suggesting the absence of a metal–insulator transition proximate to the superconductivity. Moreover, analysis of the normal state T -linear resistance reveals a link between this strange-metal behaviour and superconductivity. The association between strange-metal behaviour and high-temperature superconductivity is very much in line with other classes of unconventional superconductors, including the cuprates and Fe-based superconductors. Further investigations exploring the interplay of strange-metal behaviour and superconductivity, as well as possible competing electronic or structural phases, are essential to understand the mechanism of superconductivity in this system. Some features resembling superconductivity at high temperature have been seen under pressure in La 3 Ni 2 O 7 , but a transition to a zero-resistance state has not been observed. Now transport studies demonstrate this transition, along with strange metallicity.

The recent discovery of superconductivity in La 3 Ni 2 O 7− δ under high pressure with a transition temperature around 80 K (ref. 1 ) has sparked extensive experimental 2 – 6 and theoretical efforts 7 – 12 . Several key questions regarding the pairing mechanism remain to be answered, such as the most relevant atomic orbitals and the role of atomic deficiencies. Here we develop a new, energy-filtered, multislice electron ptychography technique, assisted by electron energy-loss spectroscopy, to address these critical issues. Oxygen vacancies are directly visualized and are found to primarily occupy the inner apical sites, which have been proposed to be crucial to superconductivity 13 , 14 . We precisely determine the nanoscale stoichiometry and its correlation to the oxygen K-edge spectra, which reveals a significant inhomogeneity in the oxygen content and electronic structure within the sample. The spectroscopic results also reveal that stoichiometric La 3 Ni 2 O 7 has strong charge-transfer characteristics, with holes that are self-doped from Ni sites into O sites. The ligand holes mainly reside on the inner apical O and the planar O, whereas the density on the outer apical O is negligible. As the concentration of O vacancies increases, ligand holes on both sites are simultaneously annihilated. These observations will assist in further development and understanding of superconducting nickelate materials. Our imaging technique for quantifying atomic deficiencies can also be widely applied in materials science and condensed-matter physics. Direct visualization of oxygen vacancies and self-doped ligand holes reveals the role of ligand oxygen in La 3 Ni 2 O 7− δ and provides further understanding of superconducting nickelate materials.