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Motivated by recent progress in the superconductivity nonreciprocal phenomena, we study the general theory of Josephson diodes. The central ingredient for Josephson diodes is the asymmetric proximity process inside the tunneling barrier. From the symmetry breaking point of view, there are two types of Josephson diodes: inversion breaking and time-reversal breaking. For the inversion breaking case, applying voltage bias could effectively tune the proximity process like the voltage-dependent Rashba coupling or electric polarization giving rise to I_{c}(V)≠I_{c}(-V) and I_{r+}≠I_{r-}. For the time-reversal breaking case, the current flow could adjust the internal time-reversal breaking field like magnetism or time-reversal breaking electron-electron pairing, which leads to I_{c+}≠I_{c-}. All these results provide a complete understanding and the general principles of realizing Josephson diodes, especially the recently found NbSe_{2}/Nb_{3}Br_{8}/NbSe_{2} Josephson diodes.

Parity is a fundamental quantum number used to classify a state of matter. Materials rarely possess ground states with odd parity. We show that the superconducting state in iron-based superconductors is classified as an odd-parity s -wave spin-singlet pairing state in a single trilayer FeAs/Se , the building block of the materials. In a low-energy effective model constructed on the Fe square bipartite lattice, the superconducting order parameter in this state is a combination of an s -wave normal pairing between two sublattices and an s -wave η pairing within the sublattices. The state has a fingerprint with a real-space sign inversion between the top and bottom As/Se layers. The results suggest that iron-based superconductors are a new quantum state of matter, and the measurement of the odd parity can help to establish high-temperature superconducting mechanisms.

High-temperature superconductivity in the iron-based materials emerges from, or sometimes coexists with, their metallic or insulating parent compound states. This is surprising, as these undoped states exhibit dramatically different antiferromagnetic spin arrangements and Néel temperatures. Although there is a general consensus that magnetic interactions are important for superconductivity, much remains unknown concerning the microscopic origin of the magnetic states. In this review, we summarize the progress in this area, focusing on recent experimental and theoretical results, and their microscopic implications. We conclude that the parent compounds are in a state that is more complex than that implied by a simple Fermi surface nesting scenario, and a dual description including both itinerant and localized degrees of freedom is needed to properly describe these fascinating materials. The magnetic states found in iron-based superconductors are more complex than originally thought. This Review argues that the magnetism arises from both itinerant and localized electrons.

A distinct electronic structure was observed in the single-layer FeSe which shows surprisingly high-temperature superconductivity over 65 K. Here, we demonstrate that the electronic structure can be explained by the effective strain effect due to substrates. More importantly, we find that this electronic structure can be tuned into robust topological phases from a topologically trivial metallic phase by the spin-orbital interaction and couplings to substrates. The topological phase is robust against any perturbations that preserve the time-reversal symmetry. Our study suggests that nontrivial topology and high-Tc superconductivity can be intertwined in the single FeSe layer to search novel physics.

High-temperature superconductivity was discovered in the pressurized nickelate La 3 Ni 2 O 7 which has a unique bilayer structure and mixed valence state of nickel. The properties at ambient pressure contain crucial information of the fundamental interactions and bosons mediating superconducting pairing. Here, using X-ray absorption spectroscopy and resonant inelastic X-ray scattering, we identified that Ni 3 d x 2 − y 2 , Ni 3 d z 2 , and ligand oxygen 2 p orbitals dominate the low-energy physics with a small charge-transfer energy. Well-defined optical-like magnetic excitations soften into quasi-static spin-density-wave ordering, evidencing the strong electronic correlation and rich magnetic properties. Based on an effective Heisenberg spin model, we extract a much stronger inter-layer effective magnetic superexchange than the intra-layer ones and propose two viable magnetic structures. Our findings emphasize that the Ni 3 d z 2 orbital bonding within the bilayer induces novel electronic and magnetic excitations, setting the stage for further exploration of La 3 Ni 2 O 7 superconductor. It was recently found that a certain nickelate compound, La 3 Ni 2 O 7 , at moderately high pressures has a superconducting phase that persists to above liquid nitrogen temperatures. Here, by studying the parent phase at ambient pressure, Chen et al uncover rich magnetic properties and show the vital role of the strong bonding of the inter-layer Ni orbitals in the magnetic and electronic excitations.

The Kagome superconductors AV 3 Sb 5 (A = K, Rb, Cs) have received enormous attention due to their nontrivial topological electronic structure, anomalous physical properties and superconductivity. Unconventional charge density wave (CDW) has been detected in AV 3 Sb 5 . High-precision electronic structure determination is essential to understand its origin. Here we unveil electronic nature of the CDW phase in our high-resolution angle-resolved photoemission measurements on KV 3 Sb 5 . We have observed CDW-induced Fermi surface reconstruction and the associated band folding. The CDW-induced band splitting and the associated gap opening have been revealed at the boundary of the pristine and reconstructed Brillouin zones. The Fermi surface- and momentum-dependent CDW gap is measured and the strongly anisotropic CDW gap is observed for all the V-derived Fermi surface. In particular, we have observed signatures of the electron-phonon coupling in KV 3 Sb 5 . These results provide key insights in understanding the nature of the CDW state and its interplay with superconductivity in AV 3 Sb 5 superconductors. The impact of the charge density wave (CDW) state to the electronic structure in the Kagome superconductors A V 3 Sb 5 remains unclear. Here, the authors observe CDW-induced Fermi surface reconstruction with a strongly anisotropic CDW gap and signatures of the electron-phonon coupling for all V-derived bands.

Cuprates, ferropnictides and ferrochalcogenides are three classes of unconventional high temperature superconductors, who share similar phase diagrams in which superconductivity develops after a magnetic order is suppressed, suggesting a strong interplay between superconductivity and magnetism, although the exact picture of this interplay remains elusive. Here we show that there is a direct bridge connecting antiferromagnetic exchange interactions determined in the parent compounds of these materials to the superconducting gap functions observed in the corresponding superconducting materials: in all high temperature superconductors, the Fermi surface topology matches the form factor of the pairing symmetry favored by local magnetic exchange interactions. We suggest that this match offers a principle guide to search for new high temperature superconductors.

The discovery of unconventional superconductivity in hole doped NdNiO 2 , similar to CaCuO 2 , has received enormous attention. However, different from CaCuO 2 , R NiO 2 ( R  = Nd, La) has itinerant electrons in the rare-earth spacer layer. Previous studies show that the hybridization between Ni- d x 2 − y 2 and rare-earth- d orbitals is very weak and thus R NiO 2 is still a promising analog of CaCuO 2 . Here, we perform first-principles calculations to show that the hybridization between Ni- d x 2 − y 2 orbital and itinerant electrons in R NiO 2 is substantially stronger than previously thought. The dominant hybridization comes from an interstitial- s orbital rather than rare-earth- d orbitals, due to a large inter-cell hopping. Because of the hybridization, Ni local moment is screened by itinerant electrons and the critical U Ni for long-range magnetic ordering is increased. Our work shows that the electronic structure of R NiO 2 is distinct from CaCuO 2 , implying that the observed superconductivity in infinite-layer nickelates does not emerge from a doped Mott insulator. The discovery of superconductivity in doped NdNiO 2 has generated excitement due to similarities with cuprates. Here, the authors use first-principles calculations to show that different from cuprates, a hybridization between Ni d -orbitals and itinerant electrons in NdNiO 2 disfavours magnetism by screening Ni moment, as in Kondo systems.

In the presence of both space and time reversal symmetries, ans-waveA1gsuperconducting state is usually topologically trivial. Here, we demonstrate that an exception can take place in a type of nonsymmorphic lattice structure. We specify the demonstration in a time reversal invariant system with a centrosymmetric space groupP4/nmm, the symmetry that governs iron-based superconductors, by showing the existence of a second-order topological state protected by a mirror symmetry. The topological superconductivity is featured by2Zdegenerate Dirac cones on the (10) edge andZpairs of Majorana modes at the intersection between the (11) and(11¯)edges. The topological invariance and Fermi surface criterion for the topological state are provided. Moreover, we point out that the previously proposeds-wave state in iron-based superconductors, which features a sign-changed superconducting order parameter between two electron pockets, is such a topological state. Thus, these results not only open a new route to pursue topological superconductivity, but also establish a measurable quantity to settle one long-lasting debate on the pairing nature of iron-based superconductors.

The recently discovered kagome metals AV 3 Sb 5 (A = Cs, Rb, K) exhibit a variety of intriguing phenomena, such as a charge density wave (CDW) with time-reversal symmetry breaking and possible unconventional superconductivity. Here, we report a rare non-monotonic evolution of the CDW temperature ( T CDW ) with the reduction of flake thickness approaching the atomic limit, and the superconducting transition temperature ( T c ) features an inverse variation with T CDW . T CDW initially decreases to a minimum value of 72 K at 27 layers and then increases abruptly, reaching a record-high value of 120 K at 5 layers. Raman scattering measurements reveal a weakened electron-phonon coupling with the reduction of sample thickness, suggesting that a crossover from electron-phonon coupling to dominantly electronic interactions could account for the non-monotonic thickness dependence of T CDW . Our work demonstrates the novel effects of dimension reduction and carrier doping on quantum states in thin flakes and provides crucial insights into the complex mechanism of the CDW order in the family of AV 3 Sb 5 kagome metals. The kagome superconductor CsV 3 Sb 5 exhibits a charge density wave (CDW) as well as superconductivity (SC). Here, the authors find that the CDW transition temperature decreases with decreasing sample thickness to 72 K at 27 atomic layers, but then unexpectedly increases to 120 K at 5 layers, an opposite trend to SC.