Origin of High-Temperature Superconductivity in Compressed LaH10_{10}

Room-temperature superconductivity has been one of the most challenging subjects in modern physics. Recent experiments reported that lanthanum hydride LaH$_{10{\pm}x}$ ($x$$<$1) raises a superconducting transition temperature $T_{\rm c}$ up to ${\sim}$260 (or 215) K at high pressures around 190 (150) GPa. Here, based on first-principles calculations, we reveal the existence of topological Dirac-nodal-line (DNL) states in compressed LaH$_{10}$. Remarkably, the DNLs protected by the combined inversion and time-reversal symmetry and the rotation symmetry create a van Hove singularity (vHs) near the Fermi energy, giving rise to large electronic density of states. Contrasting with other La hydrides containing cationic La and anionic H atoms, LaH$_{10}$ shows a peculiar characteristic of electrical charges with anionic La and both cationic and anionic H species, caused by a strong hybridization of the La $f$ and H $s$ orbitals. We find that a large number of electronic states at the vHs are strongly coupled to the H-derived high-frequency phonon modes that are induced via the unusual, intricate bonding network of LaH$_{10}$, thereby yielding a high $T_{\rm c}$. Our findings not only elucidate the microscopic origin of the observed high-$T_{\rm c}$ BCS-type superconductivity in LaH$_{10}$, but also pave the route for achieving room-temperature topological superconductors in compressed hydrogen-rich compounds.Comment: 9 pages, 11 figure

Towards Optimal Decoding for Polar Codes

In the conventional successive cancellation (SC) decoder for polar codes, all the future bits to be estimated later are treated as random variables. However, polar codes inevitably involve frozen bits, and their concatenated coding schemes also include parity bits causally generated from the past bits estimated earlier. We refer to the frozen and parity bits located behind a target decoding bit as its future constraints (FCs). Although the values of FCs are deterministic given the past estimates, they have not been exploited in the conventional SC-based decoders, not leading to optimality. In this paper, we propose SC-check (SCC) and belief-propagation SCC (BP-SCC) decoding algorithms in order to leverage FCs in decoding.We further devise a tree search technique based on stack-based backjumping (SBJ) to solve dynamic constraint satisfaction problems (CSPs) formulated by FCs. Over the binary erasure channel (BEC), numerical results show that a combination of the BP-SCC algorithm and the SBJ tree search technique achieves the erasure recovery performance close to the dependence testing (DT) bound, a bound of achievable finite-length performance

Combining Non-probability and Probability Survey Samples Through Mass Imputation

This paper presents theoretical results on combining non-probability and probability survey samples through mass imputation, an approach originally proposed by Rivers (2007) as sample matching without rigorous theoretical justification. Under suitable regularity conditions, we establish the consistency of the mass imputation estimator and derive its asymptotic variance formula. Variance estimators are developed using either linearization or bootstrap. Finite sample performances of the mass imputation estimator are investigated through simulation studies and an application to analyzing a non-probability sample collected by the Pew Research Centre.Comment: Submitted to Journal of the Royal Statistical Society: Series

Competing edge structures of Sb and Bi bilayers by trivial and nontrivial band topologies

One-dimensional (1D) edge states formed at the boundaries of 2D normal and topological insulators have shown intriguing quantum phases such as charge density wave and quantum spin Hall effect. Based on first-principles density-functional theory calculations including spin-orbit coupling (SOC), we show that the edge states of zigzag Sb(111) and Bi(111) nanoribbons drastically change the stability of their edge structures. For zigzag Sb(111) nanoribbon, the Peierls-distorted or reconstructed edge structure is stabilized by a band-gap opening. However, for zigzag Bi(111) nanoribbon, such two insulating structures are destabilized due to the presence of topologically protected gapless edge states, resulting in the stabilization of a metallic, shear-distorted edge structure. We also show that the edge states of the Bi(111) nanoribbon exhibit a larger Rashba-type spin splitting at the boundary of Brillouin zone, compared to those of the Sb(111) nanoribbon. Interestingly, the spin textures of edge states in the Peierls-distorted Sb edge structure and the shear-distorted Bi edge structure have all three spin components perpendicular and parallel to the edges, due to their broken mirror-plane symmetry. The present findings demonstrate that the topologically trivial and nontrivial edge states play crucial roles in determining the edge structures of normal and topological insulators.Comment: 7 pages, 8 figure