Proofs that the Gerber Statistic is Positive Semidefinite
In this brief note, we prove that both forms of the Gerber statistic introduced in Gerber et al. (2022) are positive semi-definite.
q-fin.PM↗
arXiv subjects
Y. Miao
Publications and source records attributed to Y. Miao.
Tuning the Parity Mixing of Singlet-Septet Pairing in a Half-Heusler Superconductor
In superconductors, electrons with spin ${s=1/2}$ form Cooper pairs whose spin structure is usually singlet (${S=0}$) or triplet (${S=1}$). When the electronic structure near the Fermi level is characterized by fermions with angular momentum ${j=3/2}$ due to strong spin-orbit interactions, novel pairing states such as even-parity quintet (${J=2}$) and odd-parity septet (${J=3}$) states become allowed. Prime candidates for such exotic states are half-Heusler superconductors, which exhibit unconventional superconducting properties, but their pairing nature remains unsettled. Here we show that the superconductivity in the noncentrosymmetric half-Heusler LuPdBi can be consistently described by the admixture of isotropic even-parity singlet and anisotropic odd-parity septet pairing, whose ratio can be tuned by electron irradiation. From magnetotransport and penetration depth measurements, we find that carrier concentrations and impurity scattering both increase with irradiation, resulting in a nonmonotonic change of the superconducting gap structure. Our findings shed new light on our fundamental understanding of unconventional superconducting states in topological materials.
cond-mat.supr-con↗
Strongly correlated superconductivity in a copper-based metal-organic framework with a perfect kagome lattice
Metal-organic frameworks (MOFs), which are self-assemblies of metal ions and organic ligands, provide a tunable platform to search a new state of matter. A two-dimensional (2D) perfect kagome lattice, whose geometrical frustration is a key to realizing quantum spin liquids, has been formed in the $π$-${d}$ conjugated 2D MOF [Cu$_{3}$(C$_{6}$S$_{6}$)]$_{n}$ (Cu-BHT). The recent discovery of its superconductivity with a critical temperature $T_{\rm c}$ of 0.25\,kelvin raises fundamental questions about the nature of electron pairing. Here, we show that Cu-BHT is a strongly correlated unconventional superconductor with extremely low superfluid density. A nonexponential temperature dependence of superfluid density is observed, indicating the possible presence of superconducting gap nodes. The magnitude of superfluid density is much smaller than those in conventional superconductors, and follows the Uemura's relation of strongly correlated superconductors. These results imply that the unconventional superconductivity in Cu-BHT originates from electron correlations related to spin fluctuations of kagome lattice.
cond-mat.str-el↗
Signature of Unconventional Superconductivity in a Copper-based Metal-Organic Framework with Perfect Kagome Structure
Recently, the superconductivity in a metal-organic framework (MOF) has been discovered for the first time in copper(II) benzenehexathiolate ([Cu$_3$(C$_6$S$_6$)]$_n$, Cu-BHT). The Cu atoms form a two-dimensional perfect Kagome lattice, which has the potential to host a metallic quantum spin liquid state. Here we present high-precision measurements of in-plane magnetic penetration depth $λ$ in Cu-BHT films down to 40\,mK. The temperature dependence of $λ$ shows a non-exponential, quasi-linear behavior at low temperatures, suggesting that unconventional superconductivity with low-energy quasiparticle excitations is realized in this system. With the reported non-Fermi liquid behavior, this finding implies that MOFs can provide a flexible platform to investigate the superconducting pairing mechanisms in the presence of spin frustration and strong quantum fluctuations.
cond-mat.supr-con↗
Evidence for s-wave Pairing with Atomic Scale Disorder in the van der Waals Superconductor NaSn2As2
The recent discovery of superconductivity in NaSn$_2$As$_2$ with a van der Waals layered structure raises immediate questions on its pairing mechanism and underlying electronic structure. Here, we present measurements of the temperature-dependent magnetic penetration depth $λ(T)$ in single crystals of NaSn$_2$As$_2$ down to $\sim40$ mK. We find a very long penetration depth $λ(0) = 960$ nm, which is strongly enhanced from the estimate of first-principles calculations. This enhancement comes from a short mean free path $\ell \approx 1.7$ nm, indicating atomic scale disorder possibly associated with the valence-skipping states of Sn. The temperature dependence of superfluid density is fully consistent with the conventional fully gapped s-wave state in the dirty limit. These results suggest that NaSn$_2$As$_2$ is an ideal material to study quantum phase fluctuations in strongly disordered superconductors with its controllable dimensionality.
cond-mat.supr-con↗