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The symbiosis of strong interactions, flat bands, topology and symmetry has led to the discovery of exotic phases of matter, including fractional Chern insulators, correlated moir\'e topological superconductors, and Dirac and Weyl semimetals. Correlated metals, such as those present in Kondo lattices, rely on the screening of local moments by a sea of non-magnetic conduction electrons. Here, we report on a unique topological Kondo lattice compound, CeCo2P2, where the Kondo effect - whose existence under the magnetic Co phase is protected by PT symmetry - coexists with antiferromagnetic order emerging from the flat bands associated with the Co atoms. Remarkably, this is the only known Kondo lattice compound where magnetic order occurs in non-heavy electrons, and puzzlingly, at a temperature significantly higher than that of the Kondo effect. Furthermore, at low temperatures, the emergence of the Kondo effect, in conjunction with a glide-mirror-z symmetry, results in a nodal line protected by bulk topology near the Fermi energy. These unusual properties, arising from the interplay between itinerant and correlated electrons from different constituent elements, lead to novel quantum phases beyond the celebrated topological Kondo insulators and Weyl Kondo semimetals. CeCo2P2 thus provides an ideal platform for investigating narrow bands, topology, magnetism, and the Kondo effect in strongly correlated electron systems., Comment: 17pages,4 figures

We explore both experimental and theoretical aspects of the superconducting properties in the distinctive layered caged compound, Ba$_{3}$Ir$_{4}$Ge$_{16}$. Our approach integrates muon spin rotation and relaxation ($\mu$SR) measurements with magnetization and heat capacity experiments, accompanied by first-principle calculations. The compound's bulk superconductivity is unequivocally established through DC magnetization measurements, revealing a critical temperature ($T_\mathrm{C}$) of 5.7 K. A noteworthy characteristic observed in the low-temperature superfluid density is its saturating behavior, aligning with the features typical of conventional Bardeen-Cooper-Schrieffer (BCS) superconductors. The assessment of moderate electron-phonon coupling superconductivity is conducted through transverse field $\mu$SR measurements, yielding a superconducting gap to $T_\mathrm{C}$ ratio ($2\Delta(0)/k_\mathrm{B}T_\mathrm{C}$) of 4.04, a value corroborated by heat capacity measurements. Crucially, zero field $\mu$SR measurements dismiss the possibility of any spontaneous magnetic field emergence below $T_\mathrm{C}$, highlighting the preservation of time-reversal symmetry. Our experimental results are reinforced by first-principles density functional calculations, underscoring the intricate interplay between crystal structure and superconducting order parameter symmetry in polyhedral caged compounds. This comprehensive investigation enhances our understanding of the nuanced relationship between crystal structure and superconductivity in such unique compounds.

We report on a microscopic study of the noncentrosymmetric superconductor W$_3$Al$_2$C (with $T_c$ = 7.6 K), mostly by means of $^{27}$Al- and $^{13}$C nuclear magnetic resonance (NMR). Since in this material the density of states at the Fermi level is dominated by the tungsten's 5$d$ orbitals, we expect a sizeable spin-orbit coupling (SOC) effect. The normal-state electronic properties of W$_3$Al$_2$C resemble those of a standard metal, but with a Korringa product $1/(T_{1}T)$ significantly smaller than that of metallic Al, reflecting the marginal role played by $s$-electrons. In the superconducting state, we observe a reduction of the Knight shift and an exponential decrease of the NMR relaxation rate $1/T_1$, typical of $s$-wave superconductivity. This is further supported by the observation of a small but distinct coherence peak just below $T_c$ in the $^{13}$C NMR relaxation-rate, in agreement with the fully-gapped superconducting state inferred from the electronic specific-heat data well below $T_c$. The above features are compared to those of members of the same family, in particular, Mo$_3$Al$_2$C, often claimed to exhibit unconventional superconductivity. We discuss why, despite the enhanced SOC, W$_3$Al$_2$C does not show spin-triplet features in its superconducting state and consider the broader consequences of our results for noncentrosymmetric superconductors in general., Comment: 8 pages, 6 figures, accepted by J. Phys.: Condens. Matter

In this paper we prove a new version of Kransoselskii's fixed-point theorem under a ($\psi, \theta, \varphi$)-weak contraction condition. The theoretical result is applied to prove the existence of a solution of the following fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators orders of $0<\alpha<1$ and $\beta>0:$ \begin{equation}\nonumber \left\{\begin{array}{ll} D^{\alpha}[x(t)-f(t, x(t))]=g(t, x(t), I^{\beta}(x(t))), \,\,\, \text{a.e.} \,\,\, t\in J,\,\, \beta>0,\\ x(t_{0})=x_{0}, \end{array} \right. \end{equation} where $D^{\alpha}$ is the Riemann-Liouville fractional derivative order of $\alpha,$ $I^{\beta}$ is Riemann-Liouville fractional integral operator order of $\beta>0,$ $J=[t_{0}, t_{0}+a],$ for some fixed $t_{0}\in \mathbb{R},$ $a>0$ and the functions $f:J\times \mathbb{R}\rightarrow \mathbb{R}$ and $g:J\times \mathbb{R}\times \mathbb{R}\rightarrow \mathbb{R}$ satisfy certain conditions. An example is also furnished to illustrate the hypotheses and the abstract result of this paper.

The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a solution of a nonlinear Hammerstein integral equation. Moreover, we provide an example to illustrate the hypotheses and the abstract result of this paper.

A detailed zero-field and transverse-field muon spin relaxation/rotation ($\mu$SR) experiemnts have been carried out on the recently discovered non-centrosymmetric superconductor W$_3$Al$_2$C to speculate about its superconducting ground state. Bulk nature of superconductivity below 7.6 K is confirmed through magnetization measurements. No change in the $\mu$SR spectra collected above and below $T_c$ is visible, ruling out the possibility of spontaneous magnetic field below $T_c$. This confirms that time-reversal symmetry is preserved for W$_3$Al$_2$C upon entering in the superconducting ground state. Temperature dependent superfluid density [$\rho_s(T)$], which directly reflects the superconducting gap symmetry is obtained by the analysis of spectra obtained from the transverse-field $\mu$SR experiments. Despite a non-centrosymmetric structure, W$_3$Al$_2$C adopts a fully gaped spin-singlet superconducting ground state with a zero temperature value of gap $\Delta_0$ = 1.158(8) meV with gap-to-$T_c$ ratio 2$\Delta_0/k_BT_c\approx$3.54, classifying this material as a weakly-coupled superconductors., Comment: 6 pages, 5 figures

We grew the single crystals of the SnAs-based van der Waals (vdW)-type superconductor NaSn$_2$As$_2$ and systematically measured its resistivity, specific heat, and ultralow-temperature thermal conductivity. The superconducting transition temperature $T_c$ = 1.60 K of our single crystal is 0.3 K higher than that previously reported. A weak but intrinsic anomaly situated at 193 K is observed in both resistivity and specific heat, which likely arises from a charge-density-wave (CDW) instability. Ultralow-temperature thermal conductivity measurements reveal a fully-gapped superconducting state with a negligible residual linear term in zero magnetic field, and the field dependence of $\kappa_0 / T$ further suggests NaSn$_2$As$_2$ is an $s$-wave superconductor., Comment: 6 pages, 4 figures, submitted on 28 May

A general feature of unconventional superconductors is the existence of a superconducting dome in the phase diagram as a function of carrier concentration. For the simplest iron-based superconductor FeSe (with transition temperature Tc ~ 8 K), its Tc can be greatly enhanced by doping electrons via many routes, even up to 65 K in monolayer FeSe/SiTiO3. However, a clear phase diagram with carrier concentration for FeSe-derived superconductors is still lacking. Here, we report the observation of a series of discrete superconducting phases in FeSe thin flakes by continuously tuning carrier concentration through the intercalation of Li and Na ions with a solid ionic gating technique. Such discrete superconducting phases are robust against the substitution of Se by 20% S, but are vulnerable to the substitution of Fe by 2% Cu, highlighting the importance of the iron site being intact. A complete superconducting phase diagram for FeSe-derivatives is given, which is distinct from other unconventional superconductors., Comment: 24 pages, 5 figures

Here we report the electronic structure of FeS, a recently identified iron-based superconductor. Our high-resolution angle-resolved photoemission spectroscopy studies show two hole-like ($\alpha$ and $\beta$) and two electron-like ($\eta$ and $\delta$) Fermi pockets around the Brillouin zone center and corner, respectively, all of which exhibit moderate dispersion along $k_z$. However, a third hole-like band ($\gamma$) is not observed, which is expected around the zone center from band calculations and is common in iron-based superconductors. Since this band has the highest renormalization factor and is known to be the most vulnerable to defects, its absence in our data is likely due to defect scattering --- and yet superconductivity can exist without coherent quasiparticles in the $\gamma$ band. This may help resolve the current controversy on the superconducting gap structure of FeS. Moreover, by comparing the $\beta$ bandwidths of various iron chalcogenides, including FeS, FeSe$_{1-x}$S$_x$, FeSe, and FeSe$_{1-x}$ Te$_x$, we find that the $\beta$ bandwidth of FeS is the broadest. However, the band renormalization factor of FeS is still quite large, when compared with the band calculations, which indicates sizable electron correlations. This explains why the unconventional superconductivity can persist over such a broad range of isovalent substitution in FeSe$_{1-x}$Te$_{x}$ and FeSe$_{1-x}$S$_{x}$., Comment: 10 pages, 5 figures

We measured the ultra-low-temperature specific heat and thermal conductivity of Au$_2$Pb single crystal, a possible three-dimensional Dirac semimetal with a superconducting transition temperature $T_c \approx$ 1.05 K. The electronic specific heat can be fitted by a two-band s-wave model, which gives the gap amplitudes $\Delta_1$(0)/$k_BT_c$ = 1.38 and $\Delta_2$(0)/$k_BT_c$ = 5.25. From the thermal conductivity measurements, a negligible residual linear term $\kappa_0/T$ in zero field and a slow field dependence of $\kappa_0/T$ at low field are obtained. These results suggest that Au$_2$Pb has a fully gapped superconducting state in the bulk, which is a necessary condition for topological superconductor if Au$_2$Pb is indeed one., Comment: 6 pages, 4 figures

As the simplest iron-based superconductor, FeSe forms a tetragonal structure with transition temperature Tc ~ 8 K. With assistance of pressure, or other techniques, Tc can be greatly enhanced, even to above liquid nitrogen temperature. The newly discovered superconducting tetragonal FeS (Tc ~ 4.5 K), a sulfide counterpart of FeSe, promotes us on its high pressure investigation. The transport and structure evolution of FeS with pressure have been studied. A rapid suppression of Tc and vanishing of superconductivity at 4.0 GPa are observed, followed by a second superconducting dome with a 30% enhancement in maximum Tc. An onsite tetragonal to hexagonal phase transition occurs around 7.0 GPa, followed by a broad pressure range of phase coexistence. The residual deformed tetragonal phase is considered as the source of second superconducting dome. The observation of two superconducting domes in iron-based superconductors poses great challenges for understanding their pairing mechanism., Comment: 20 pages, 5 figures

We report low-temperature heat transport measurements on superconducting iron sulfide FeS with $T_c \approx$ 5 K, which has the same crystal structure and similar electronic band structure to the superconducting iron selenide FeSe. In zero magnetic field, a significant residual linear term $\kappa_0/T$ is observed. At low field, $\kappa_0/T$ increases rapidly with the increase of field. These results provide strong evidence for nodal superconducting gap in FeS. We compare it with the sister compound FeSe, and other iron-based superconductors with nodal gap., Comment: 7 pages, 4 figures

The Bose-Hubbard Hamiltonian describes the competition between superfluidity and Mott insulating behavior at zero temperature and commensurate filling as the strength of the on-site repulsion is varied. Gapped insulating phases also occur at non-integer densities as a consequence of longer ranged repulsive interactions. In this paper we explore the formation of gapped phases in coupled chains due instead to anisotropies $t_x \neq t_y$ in the bosonic hopping, extending the work of Crepin {\it et al.} [Phys. Rev. B 84, 054517 (2011)] on two coupled chains, where a gap was shown to occur at half filling for arbitrarily small interchain hopping $t_y$. Our main result is that, unlike the two-leg chains, for three- and four-leg chains, a charge gap requires a finite nonzero critical $t_y$ to open. However, these finite values are surprisingly small, well below the analogous values required for a fermionic band gap to open., Comment: 8 pages, 15 figures

Determinant Quantum Monte Carlo (DQMC) is used to determine the pairing and magnetic response for a Hubbard model built up from four-site clusters -a two-dimensional square lattice consisting of elemental 2x2 plaquettes with hopping $t$ and on-site repulsion $U$ coupled by an inter-plaquette hopping $t' \leq t$. Superconductivity in this geometry has previously been studied by a variety of analytic and numeric methods, with differing conclusions concerning whether the pairing correlations and transition temperature are raised near half-filling by the inhomogeneous hopping or not. For $U/t=4$, DQMC indicates an optimal $t'/t \approx 0.4$ at which the pairing vertex is most attractive. The optimal $t'/t$ increases with $U/t$. We then contrast our results for this plaquette model with a Hamiltonian which instead involves a regular pattern of site energies whose large site energy limit is the three band CuO$_2$ model; we show that there the inhomogeneity rapidly, and monotonically, suppresses pairing., Comment: 13 pages, 19 figures

The two dimensional square lattice hard-core boson Hubbard model with near neighbor interactions has a `checkerboard' charge density wave insulating phase at half-filling and sufficiently large intersite repulsion. When doped, rather than forming a supersolid phase in which long range charge density wave correlations coexist with a condensation of superfluid defects, the system instead phase separates. However, it is known that there are other lattice geometries and interaction patterns for which such coexistence takes place. In this paper we explore the possibility that anisotropic hopping or anisotropic near neighbor repulsion might similarly stabilize the square lattice supersolid. By considering the charge density wave structure factor and superfluid density for different ratios of interaction strength and hybridization in the $\hat x$ and $\hat y$ directions, we conclude that phase separation still occurs., Comment: 8 pages, 11 figures

Striped phases, in which spin, charge, and pairing correlations vary inhomogeneously in the CuO_2 planes, are a known experimental feature of cuprate superconductors, and are also found in a variety of numerical treatments of the two dimensional Hubbard Hamiltonian. In this paper we use determinant Quantum Monte Carlo to show that if a stripe density pattern is imposed on the model, the d-wave pairing vertex is significantly enhanced. We attribute this enhancement to an increase in antiferromagnetic order which is caused by the appearence of more nearly half-filled regions when the doped holes are confined to the stripes. We also observe a \pi-phase shift in the magnetic order., Comment: 10 pages, 16 figures To appear in Phys. Rev. B

New iron selenide superconductors by intercalating smaller-sized alkali metals (Li, Na) and alkaline earths using high-temperature routes have been pursued ever since the discovery of superconductivity at about 30 K in KFe2Se2, but all have failed so far. Here we demonstrate that a series of superconductors with enhanced Tc=30~46 K can be obtained by intercalating metals, Li, Na, Ba, Sr, Ca, Yb, and Eu in between FeSe layers by the ammonothermal method at room temperature. Analysis on their powder X-ray diffraction patterns reveals that all the main phases can be indexed based on body-centered tetragonal lattices with a~3.755-3.831 {\AA} while c~15.99-20.54 {\AA}. Resistivities show the corresponding sharp transitions at 45 K and 39 K for NaFe2Se2 and Ba0.8Fe2Se2, respectively, confirming their bulk superconductivity. These findings provide a new starting point for studying the properties of these superconductors and an effective synthetic route for the exploration of new superconductors as well., Comment: 22 pages, 5 figures