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Fluctuating superconductivity - vestigial Cooper pairing in the resistive state of a material - is usually associated with low dimensionality, strong disorder or low carrier density. Here, we report single particle spectroscopic, thermodynamic and magnetic evidence for persistent superconducting fluctuations in heavily hole-doped cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\\delta}$ ($T_c$ = 66~K) despite the high carrier density. With a sign-problem free quantum Monte Carlo calculation, we show how a partially flat band at ($\\pi$,0) can help enhance superconducting phase fluctuations. Finally, we discuss the implications of an anisotropic band structure on the phase-coherence-limited superconductivity in overdoped cuprates and other superconductors.

The layered vanadium antimonides AV 3 Sb 5 (A = K, Rb, Cs) are a recently discovered family of topological kagome metals that exhibit a range of strongly correlated electronic phases including charge order and superconductivity. However, it is not yet understood how the distinctive electronic structure of the kagome lattice is linked to the observed many-body phenomena. Here we combine angle-resolved photoemission spectroscopy and density functional theory to reveal multiple kagome-derived van Hove singularities (vHS) coexisting near the Fermi level of CsV 3 Sb 5 and analyse their contribution to electronic symmetry breaking. The vHS are characterized by two distinct sublattice flavours (p-type and m-type), which originate, respectively, from their pure and mixed sublattice characters. These twofold vHS flavours of the kagome lattice critically determine the pairing symmetry and unconventional ground states emerging in the AV 3 Sb 5 series. We establish that, among the multiple vHS in CsV 3 Sb 5 , the m-type vHS of the d xz / d yz kagome band and the p-type vHS of the d xy / d x 2– y 2 kagome band are located very close to the Fermi level, setting the stage for electronic symmetry breaking. The former band is characterized by pronounced Fermi surface nesting, while the latter exhibits a higher-order vHS. Our work reveals the essential role of kagome-derived vHS for the collective phenomena realized in the AV 3 Sb 5 family. Spectroscopic measurements show how the features of the band structure related to the kagome lattice in CsV 3 Sb 5 contribute to the observed strongly correlated phases.

Anyons are quasiparticles that, unlike fermions and bosons, show fractional statistics when two of them are exchanged. Here, we report the experimental observation of anyonic braiding statistics for the ν = 1/3 fractional quantum Hall state by using an electronic Fabry–Perot interferometer. Strong Aharonov–Bohm interference of the edge mode is punctuated by discrete phase slips that indicate an anyonic phase θ anyon = 2π/3. Our results are consistent with a recent theory that describes an interferometer operated in a regime in which device charging energy is small compared to the energy of formation of charged quasiparticles, which indicates that we have observed anyonic braiding. An interferometer device is used to detect the quantum-mechanical phase that is gained when two anyons are braided around each other. The fractional value of the phase proves that these quasiparticles are neither bosons nor fermions.

Applied magnetic fields underlie exotic quantum states, such as the fractional quantum Hall effect1 and Bose–Einstein condensation of spin excitations2. Superconductivity, however, is inherently antagonistic towards magnetic fields. Only in rare cases3–5 can these effects be mitigated over limited fields, leading to re-entrant superconductivity. Here, we report the coexistence of multiple high-field re-entrant superconducting phases in the spin-triplet superconductor UTe2 (ref. 6). We observe superconductivity in the highest magnetic field range identified for any re-entrant superconductor, beyond 65 T. Although the stability of superconductivity in these high magnetic fields challenges current theoretical models, these extreme properties seem to reflect a new kind of exotic superconductivity rooted in magnetic fluctuations7 and boosted by a quantum dimensional crossover8.

The mathematical field of topology has become a framework in which to describe the low-energy electronic structure of crystalline solids. Typical of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk–boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk–boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principles calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunnelling spectroscopy, we probe the signatures of the rotational symmetry of the one-dimensional states located at the step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.The study of the band structure and crystal symmetry of the semimetal bismuth indicates that this material is a higher-order topological insulator hosting robust one-dimensional metallic states on the hinges of the crystal.

Since the discovery of high-temperature superconductivity in copper oxide materials 1 , there have been sustained efforts to both understand the origins of this phase and discover new cuprate-like superconducting materials 2 . One prime materials platform has been the rare-earth nickelates and, indeed, superconductivity was recently discovered in the doped compound Nd 0.8 Sr 0.2 NiO 2 (ref. 3 ). Undoped NdNiO 2 belongs to a series of layered square-planar nickelates with chemical formula Nd n +1 Ni n O 2 n +2 and is known as the ‘infinite-layer’ ( n  =  ∞ ) nickelate. Here we report the synthesis of the quintuple-layer ( n  = 5) member of this series, Nd 6 Ni 5 O 12 , in which optimal cuprate-like electron filling ( d 8.8 ) is achieved without chemical doping. We observe a superconducting transition beginning at ~13 K. Electronic structure calculations, in tandem with magnetoresistive and spectroscopic measurements, suggest that Nd 6 Ni 5 O 12 interpolates between cuprate-like and infinite-layer nickelate-like behaviour. In engineering a distinct superconducting nickelate, we identify the square-planar nickelates as a new family of superconductors that can be tuned via both doping and dimensionality. The authors report a superconducting transition beginning at 13 K in films of the quintuple-layer nickelate Nd 6 Ni 5 O 12 .

Topological materials and unconventional iron-based superconductors are both important areas of study but, to date, relatively little overlap has been identified between these two fields. However, the combination of topological bands and superconductivity promises the manifestation of exotic superconducting states, including Majorana fermions, the central component of topological quantum computation. Here, using laser-based, spin-resolved and angle-resolved photoemission spectroscopy and density functional theory calculations, we have identified both topological insulator and Dirac semimetal states near the Fermi energy in different iron-based superconducting compounds. Carrier doping can tune these topologically non-trivial bands to the Fermi energy, potentially allowing access to several different superconducting topological states in the same material. These results reveal the generic coexistence of superconductivity and multiple topological states in iron-based superconductors, indicating that this broad class of materials is a promising platform for high-temperature topological superconductivity.

When electrons in a solid are excited by light, they can alter the free energy landscape and access phases of matter that are out of reach in thermal equilibrium. This accessibility becomes important in the presence of phase competition, when one state of matter is preferred over another by only a small energy scale that, in principle, is surmountable by the excitation. Here, we study a layered compound, LaTe 3 , where a small lattice anisotropy in the a – c plane results in a unidirectional charge density wave (CDW) along the c axis 1 , 2 . Using ultrafast electron diffraction, we find that, after photoexcitation, the CDW along the c axis is weakened and a different competing CDW along the a axis subsequently emerges. The timescales characterizing the relaxation of this new CDW and the reestablishment of the original CDW are nearly identical, which points towards a strong competition between the two orders. The new density wave represents a transient non-equilibrium phase of matter with no equilibrium counterpart, and this study thus provides a framework for discovering similar states of matter that are ‘trapped’ under equilibrium conditions. Short pulses of light shift the balance between two competing charge density wave phases, allowing the weaker one to manifest transiently while suppressing the stronger one. This shows that competing phases can be tuned in a non-equilibrium setting.

In the kagome metals AV3Sb5 (A = K, Rb, Cs), three-dimensional charge order is the primary instability that sets the stage for other collective orders to emerge, including unidirectional stripe order, orbital flux order, electronic nematicity and superconductivity. Here, we use high-resolution angle-resolved photoemission spectroscopy to determine the microscopic structure of three-dimensional charge order in AV3Sb5 and its interplay with superconductivity. Our approach is based on identifying an unusual splitting of kagome bands induced by three-dimensional charge order, which provides a sensitive way to refine the spatial charge patterns in neighbouring kagome planes. We found a marked dependence of the three-dimensional charge order structure on composition and doping. The observed difference between CsV3Sb5 and the other compounds potentially underpins the double-dome superconductivity in CsV3(Sb,Sn)5 and the suppression of Tc in KV3Sb5 and RbV3Sb5. Our results provide fresh insights into the rich phase diagram of AV3Sb5.The authors use high-resolution angle-resolved photoemission spectroscopy to determine the microscopic structure of three-dimensional charge order in AV3Sb5 (A = K, Rb, Cs) and its interplay with superconductivity.

We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite ratepfor each degree of freedom, we show that the system has two dynamical phases: “entangling” and “disentangling.” The former occurs forpsmaller than a critical ratepcand is characterized by volume-law entanglement in the steady state and “ballistic” entanglement growth after a quench. By contrast, forp>pcthe system can sustain only area-law entanglement. Atp=pcthe steady state is scale invariant, and in1+1D, the entanglement grows logarithmically after a quench. To obtain a simple heuristic picture for the entangling-disentangling transition, we first construct a toy model that describes the zeroth Rényi entropy in discrete time. We solve this model exactly by mapping it to an optimization problem in classical percolation. The generic entangling-disentangling transition can be diagnosed using the von Neumann entropy and higher Rényi entropies, and it shares many qualitative features with the toy problem. We study the generic transition numerically in quantum spin chains and show that the phenomenology of the two phases is similar to that of the toy model but with distinct “quantum” critical exponents, which we calculate numerically in1+1D. We examine two different cases for the unitary dynamics: Floquet dynamics for a nonintegrable Ising model, and random circuit dynamics. We obtain compatible universal properties in each case, indicating that the entangling-disentangling phase transition is generic for projectively measured many-body systems. We discuss the significance of this transition for numerical calculations of quantum observables in many-body systems.