There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Rechargeable metal–air batteries and water splitting are highly competitive options for a sustainable energy future, but their commercialization is hindered by the absence of cost-effective, highly efficient and stable catalysts for the oxygen evolution reaction. Here we report the rational design and synthesis of a double perovskite PrBa0.5Sr0.5Co1.5Fe0.5O5+δ nanofiber as a highly efficient and robust catalyst for the oxygen evolution reaction. Co-doping of strontium and iron into PrBaCo2O5+δ is found to be very effective in enhancing intrinsic activity (normalized by the geometrical surface area, ∼4.7 times), as validated by electrochemical measurements and first-principles calculations. Further, the nanofiber morphology enhances its mass activity remarkably (by ∼20 times) as the diameter is reduced to ∼20 nm, attributed to the increased surface area and an unexpected intrinsic activity enhancement due possibly to a favourable eg electron filling associated with partial surface reduction, as unravelled from chemical titration and electron energy-loss spectroscopy. The design of efficient and stable oxygen evolution catalysts has implications for water splitting and metal-air battery technology. Here, the authors fabricate double perovskite nanofibers and demonstrate the favourable effects of co-doping and nanostructuring on oxygen evolution performance.

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A tailored double perovskite nanofiber catalyst enables ultrafast oxygen evolution

We report discovery of collinear-magnetism-driven ferroelectricity in the Ising chain magnet Ca3Co2-xMn(x)O6 (x approximately 0.96). Neutron diffraction shows that Co2+ and Mn4+ ions alternating along the chains exhibit an up-up-down-down ( upward arrow upward arrow downward arrow downward arrow) magnetic order. The ferroelectricity results from the inversion symmetry breaking in the upward arrow upward arrow downward arrow downward arrow spin chain with an alternating charge order. Unlike in spiral magnetoelectrics where antisymmetric exchange coupling is active, the symmetry breaking in Ca3(Co,Mn)2O6 occurs through exchange striction associated with symmetric superexchange.

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Ferroelectricity in an Ising Chain Magnet

Angle-resolved photoemission spectroscopy (ARPES) has emerged as a leading experimental probe for studying the complex phenomena in quantum materials, a subject of increasing importance The power of this technique stems from the directness and the richness of the momentum-resolved information it can provide, such as band dispersion, Fermi surface topology, and electron self-energy Over the past decade, the significantly improved energy and momentum resolution and carefully matched experiments have turned this technique into a sophisticated tool in characterizing the electronic structure of complex materials This revolution is mostly evident in the study of cuprate high-temperature superconductors More recently, this technique has played a critical role in advancing our understanding of the newly discovered iron-based superconductors and topological insulators In this paper we review some of the recent ARPES results and discuss the future perspective in this rapidly developing field

Angle-Resolved Photoemission Studies of Quantum Materials

The perfectly linear temperature dependence of the electrical resistivity observed as T → 0 in a variety of metals close to a quantum critical point1–4 is a major puzzle of condensed-matter physics5. Here we show that T-linear resistivity as T → 0 is a generic property of cuprates, associated with a universal scattering rate. We measured the low-temperature resistivity of the bilayer cuprate Bi2Sr2CaCu2O8+δ and found that it exhibits a T-linear dependence with the same slope as in the single-layer cuprates Bi2Sr2CuO6+δ (ref. 6), La1.6−xNd0.4SrxCuO4 (ref. 7) and La2−xSrxCuO4 (ref. 8), despite their very different Fermi surfaces and structural, superconducting and magnetic properties. We then show that the T-linear coefficient (per CuO2 plane), A1□, is given by the universal relation A1□TF = h/2e2, where e is the electron charge, h is the Planck constant and TF is the Fermi temperature. This relation, obtained by assuming that the scattering rate 1/τ of charge carriers reaches the Planckian limit9,10, whereby ħ/τ = kBT, works not only for hole-doped cuprates6–8,11,12 but also for electron-doped cuprates13,14, despite the different nature of their quantum critical point and strength of their electron correlations. A transport study of overdoped cuprates reveals a resistivity that is linear as the temperature approaches 0 K, and is associated with a universal scattering rate.

Universal T -linear resistivity and Planckian dissipation in overdoped cuprates

An understanding of the high-temperature copper oxide (cuprate) superconductors has eluded the physics community for over thirty years and represents one of the greatest unsolved problems in conden...

The Strange Metal State of the Electron-Doped Cuprates

Frequency and temperature dependence of dielectric and electrical properties of TFe2O4 (T = Ni, Zn, Zn0.5Ni0.5) ferrite nanocrystals

Oxygen-vacancy and charge hopping related dielectric relaxation and conduction process in orthorhombic Gd doped YFe0.6Mn0.4O3 multiferroics

An understanding of the normal state in the high-temperature superconducting cuprates is crucial to the ultimate understanding of the long-standing problem of the origin of the superconductivity itself. This so-called “strange metal” state is thought to be associated with a quantum critical point (QCP) hidden beneath the superconductivity. In electron-doped cuprates—in contrast to hole-doped cuprates—it is possible to access the normal state at very low temperatures and low magnetic fields to study this putative QCP and to probe the T ➔ 0 K state of these materials. We report measurements of the low-temperature normal-state magnetoresistance (MR) of the n-type cuprate system La 2− x Ce x CuO 4 and find that it is characterized by a linear-in-field behavior, which follows a scaling relation with applied field and temperature, for doping ( x ) above the putative QCP ( x = 0.14). The magnitude of the unconventional linear MR decreases as T c decreases and goes to zero at the end of the superconducting dome ( x ~ 0.175) above which a conventional quadratic MR is found. These results show that there is a strong correlation between the quantum critical excitations of the strange metal state and the high- T c superconductivity.

https://advances.sciencemag.org/content/advances/5/5/eaav6753.full.pdf

Correlation between scale-invariant normal-state resistivity and superconductivity in an electron-doped cuprate.

We report $ab$-plane Hall-effect and magnetoresistivity measurements on $\mathrm{L}{\mathrm{a}}_{2\ensuremath{-}x}\mathrm{C}{\mathrm{e}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ thin films as a function of doping for magnetic fields up to 14 T and temperatures down to 1.8 K. A dramatic change in the low-temperature (1.8 K) normal-state Hall coefficient is found near a doping $\mathrm{Ce}=0.14$. This, along with a nonlinear Hall resistance as a function of magnetic field, suggests that the Fermi surface reconstructs at a critical doping of $\mathrm{Ce}=0.14$. A competing antiferromagnetic phase is the likely cause of this Fermi surface reconstruction. Low-temperature linear-in-$T$ resistivity is found at $\mathrm{Ce}=0.14$, but anomalously, also at higher doping. We compare our data with similar behavior found in hole-doped cuprates at a doping where the pseudogap ends.

P. R. Mandal

Papers

The Strange Metal State of the Electron-Doped Cuprates

Frequency and temperature dependence of dielectric and electrical properties of TFe2O4 (T = Ni, Zn, Zn0.5Ni0.5) ferrite nanocrystals

Oxygen-vacancy and charge hopping related dielectric relaxation and conduction process in orthorhombic Gd doped YFe0.6Mn0.4O3 multiferroics

Correlation between scale-invariant normal-state resistivity and superconductivity in an electron-doped cuprate.

Fermi surface reconstruction and anomalous low-temperature resistivity in electron-doped L a 2 − x C e x Cu O 4