Na Diffusion in Hard Carbon Studied with Positive Muon Spin Rotation and Relaxation

The diffusive nature of Na⁺ in Na-inserted hard carbon (C _x Na), which is the most common anode material for a Na-ion battery, was studied with a positive muon spin rotation and relaxation (μ⁺SR) technique in transverse, zero, and longitudinal magnetic fields (TF, ZF, and LF) at temperatures between 50 and 375 K, where TF (LF) denotes the applied magnetic field perpendicular (parallel) to the initial muon spin polarization. At temperatures above 150 K, TF-μ⁺SR measurements showed a distinct motional narrowing behavior, implying that Na⁺ begins to diffuse above 150 K. The presence of two different muon sites in C _x Na was confirmed with ZF- and LF-μ⁺SR measurements; one is in the Na-inserted graphene layer, and the other is in the Na-vacant graphene layer adjacent to the Na-inserted graphene layer. A systematic increase in the field fluctuation rate (ν) with increasing temperature also evidenced a thermally activated Na diffusion, particularly above 150 K. Assuming the two-dimensional diffusion of Na⁺ in the graphene layers, the self-diffusion coefficient of Na⁺ (D _Na ^J) at 300 K was estimated to be 2.5 × 10^-11 cm²/s with a thermal activation energy of 39(7) meV.

Electron-phonon superconductivity in C-doped topological nodal-line semimetal Zr5Pt3: a muon spin rotation and relaxation (μSR) study

In the present work, we demonstrate that C-doped Zr₅Pt₃is an electron-phonon superconductor (with critical temperatureT_C= 3.8 K) with a nonsymmorphic topological Dirac nodal-line semimetal state, which we report here for the first time. The superconducting properties of Zr₅Pt₃C_0.5have been investigated by means of magnetization, resistivity, specific heat, and muon spin rotation and relaxation (μSR) measurements. We find that at low temperatures, the depolarization rate is almost constant and it can be well described by a single-bands-wave model with a superconducting gap of 2Δ(0)/k_BT_C= 3.84, somewhat higher than the value of BCS theory. From the transverse field μSR analysis, we estimate the London penetration depthλ_L= 469 nm, superconducting carrier densityn_s= 1.83 × 10²⁶ m^-3, and effective massm* = 1.428m_e. The zero field μSR confirms the absence of any spontaneous magnetic field in the superconducting ground state. In order to gain additional insights into the electronic ground state of C-doped Zr₅Pt₃, we also performed first-principles calculations within the framework of density functional theory (DFT). The observed homogenous electronic character of the Fermi surface as well as the mutual decrease ofT_Cand density of states at the Fermi level are consistent with the experimental findings of this study. However, the band structure reveals the presence of robust, gapless fourfold-degenerate nodal lines protected by 6₃screw rotations and glide mirror planes. Therefore, Zr₅Pt₃represents a novel, unprecedented condensed matter system to investigate the intricate interplay between superconductivity and topology.