The topological aspects of electrons in solids can emerge in real materials, as represented by topological insulators. In theory, they show a variety of new magneto-electric phenomena, and especially the ones hosting superconductivity are strongly desired as candidates for topological superconductors. While efforts have been made to develop possible topological superconductors by introducing carriers into topological insulators, those exhibiting indisputable superconductivity free from inhomogeneity are very few. Here we report on the observation of topologically protected surface states in a centrosymmetric layered superconductor, β-PdBi2, by utilizing spin- and angle-resolved photoemission spectroscopy. Besides the bulk bands, several surface bands are clearly observed with symmetrically allowed in-plane spin polarizations, some of which crossing the Fermi level. These surface states are precisely evaluated to be topological, based on the Z2 invariant analysis in analogy to three-dimensional strong topological insulators. β-PdBi2 may offer a solid stage to investigate the topological aspect in the superconducting condensate.

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Topologically protected surface states in a centrosymmetric superconductor β-PdBi2.

The occurrence of polyanions in a group of liquid ionic alloys, viz. alloys of the alkali metals with 13, 14, 15 and 16 elements (post-transition-metal groups 3, 4, 5 and 6), is discussed. It is shown that there are strong parallels with the corrresponding crystalline phases, in which polyanions such as .Pb4/4 , .Sb /1 and .Te2/2 exist, known for a long time as 'Zintl ions'. Little evidence exists for remnants of the diamond-lattice-type Zintl ion in liquid alkali-group-13 alloys, but in the alloys of Tl with K, Rb and Cs very long-range superstructures have been found, which are related to the occurrence of large, compact, polyhedral clusters in many crystalline phases. A stability rule, first proposed by Geertsma, relating the stability of the polyanions to the size of the cations, is universally observed. Furthermore it is shown that the range of the superstructure in the liquid is with remarkable precision proportional to the intercluster distance in the corresponding solids. The interpretation of the experimental data in terms of polyanion formation is discussed critically. There remains a paradox. Some sharp experimental features (superstructure peaks and maxima in the resistivities and stability functions) seem to indicate that the Zintl ions in the liquid are near perfect whereas specific heat results and ab initio computer simulations clearly show that the structure of the liquid is seriously blurred.

https://iopscience.iop.org/article/10.1088/0953-8984/8/34/003/pdf

Polyanions in liquid ionic alloys: a decade of research

The synthesis, structure and bonding of two types of metal clusters are described. A large family of zirconium cluster halides of the general type AIxZr6(Z)X12 +n are obtained with A = Na to Cs, X = Cl, Br or I, 0 < x, n⩽ 6, and the required interstitial Z atom as variables. Extension to the rare-earth elements (Sc, Y, lanthanides) gives some new, hypostoichiometric cluster variations as well as condensed oligomeric and infinite-chain compounds. Zintl-phase concepts and the alkali-metal compounds that contain anionic ‘naked’ clusters or cluster networks of the triel elements Ga, In and Tl are also covered. The clusters include empty hypoelectronic examples as well as those that are centred by a heterometal or a triel element. The last compounds are remarkable parallels of the interstitial halides described.

Diverse solid-state clusters with strong metal–metal bonding. In praise of synthesis

The title compounds, which are synthesized from be elements, are shown to be isostructural with K8In11 (R3¯c Z=6) and to contain pentacapped trigonal prismatic clusters that have been compressed along the three-fold axes so as to bring the two types of capping atoms within bonding distances. These are arranged in double-ccp layers separated by double alkali--metal layers. Extended Huckel calculations show a substantial energy gap and the end of significant intracluster bonding for the hypoelectronic (by Wade's rules) 18-electron Tl11
7−. Correspondingly, all three compounds are metallic (ρ298 ≈ 400 μΩ · cm) and Pauli-paramagnetic (χM ≈ 4 x 10−4 emu. mol−1, consistent with their formulation as metallic (A
+)8Tl11
7− e− phases. Factors thought to be responsible for the cluster distortion, the metallic salt characteristics, and the unusual chemistry of thallium am noted.

A 8 Tl 11 ( A = K, Rb, or Cs) phases with hypoelectronic Tl 11 7− cluster anions: Syntheses, structure, bonding, and properties

We investigate bulk superconductivity in a high-quality single crystal of Bi 2 Pd (β-Bi 2 Pd; space group: I 4/ m m m ) with a superconducting transition temperature of 5.4 K, by exploring its electrical resistivity, magnetic susceptibility, and specific heat. The temperature dependence of the electrical resistivity shows convex-upward behavior at temperatures greater than 40–50 K, which can be explained using a parallel-resistor model. In addition, the temperature dependences of the upper critical magnetic field and the specific heat suggest that β-Bi 2 Pd is a multiple-band/multiple-gap superconductor.

Superconductivity at 5.4 K in β-Bi 2Pd

The electrical resistivities p of liquid Na-Bi and Rb-Bi alloys have been measured as functions of composition and temperature. Plotted as a function of composition the resistivity of Na-Bi exhibits a maximum at the composition corresponding to Na3Bi while for Rb-Bi two maxima, at 25 and 40 at.% Bi, can be discerned. In both alloys, the maximum value of rho is far beyond the metallic range. In the composition ranges around the maxima the temperature dependence d rho /dT of the resistivity is negative and -d rho /dT attains extraordinarily large values. The results can be explained by assuming that for Na-Bi a strong octet compound is formed whereas for Rb-Bi both an octet and a clustered compound are formed. Comparison with the other alkali-Bi alloys shows that in the sequence from Li-Bi to Cs-Bi a transition from a simple octet configuration to a clustered configuration occurs.

Electrical resistivities of liquid Na-Bi and Rb-Bi alloys

Structure factors obtained from neutron diffraction measurements on liquid K-Tl and Cs-Tl alloys exhibit large prepeaks at approximately 0.77 AA-1 and 0.70 AA-1. respectively. It is concluded that the liquid contains large units of thallium atoms, possibly bearing some resemblance to those found in crystalline K8Tl11.

https://iopscience.iop.org/article/10.1088/0953-8984/5/50/007/pdf

Nanometre superstructure in liquid alkali-thallium alloys

Measurements of the electrical resistivity rho of liquid Pd-Bi alloys as a function of temperature have been performed in the concentration range from pure bismuth to 60 at.% Pd. Plotted as a function of composition, the resistivity of Pd-Bi exhibits a maximum near 30 at.% Pd. At this maximum the resistivity reaches a value of 187.6 mu Omega cm while the temperature dependence of the resistivity d rho /dT has a sharp minimum and is almost zero at the same composition. For comparison, calculations of the electronic structure of the crystalline compounds PdBi2 and PdBi have been carried out using the augmented spherical wave (ASW) method.

https://iopscience.iop.org/article/10.1088/0953-8984/4/10/005/pdf

The electrical resistivities of liquid Pd-Bi alloys and the band structure of crystalline beta -PdBi2 and PdBi

The structure factors of several liquid K-Tl and Cs-Tl alloys have been measured by means of neutron time-of-flight diffraction at the spallation neutron source ISIS. A large first sharp diffraction peak (FSDP) or prepeak is observed in all measurements at relatively short wave vector, indicating long-range correlations or larger molecular units. So far, we have analysed the data for equiatomic KTl. We arrive at the conclusion that the liquid contains large clusters of thallium atoms, possibly bearing some resemblance to those found in crystalline KTl or K8Tl11.

Clusters in liquid k-tl and cs-tl alloys

Resistivity measurement on liquid RbIn and CsIn alloys provide evidence for compound formation at a composition of 50% In. The discussion is based on existing electronic structure calculations for solid alloys of Li and Na with Ga, In and Tl. Several possible models for describing liquid equiatomic RbIn and CsIn are discussed. In particular the NaTl-type and CsCl-type local structures are compared.

R. Xu

Papers

Electrical resistivities of liquid Na-Bi and Rb-Bi alloys

Nanometre superstructure in liquid alkali-thallium alloys

The electrical resistivities of liquid Pd-Bi alloys and the band structure of crystalline beta -PdBi2 and PdBi

Clusters in liquid k-tl and cs-tl alloys

Compound formation in liquid alkali indium alloys