Type I superconductivity in the Dirac semimetal PdTe2

The superconductor PdTe$_2$ was recently classified as a Type II Dirac semimetal, and advocated to be an improved platform for topological superconductivity. Here we report magnetic and transport measurements conducted to determine the nature of the superconducting phase. Surprisingly, we find that PdTe$_2$ is a Type I superconductor with $T_c = 1.64$ K and a critical field $\mu_0 H_c (0) = 13.6$ mT. Our crystals also exhibit the intermediate state as demonstrated by the differential paramagnetic effect. For $H > H_c$ we observe superconductivity of the surface sheath. This calls for a close examination of superconductivity in PdTe$_2$ in view of the presence of topological surface states.Comment: 5 page

An automated and versatile ultra-low temperature SQUID magnetometer

We present the design and construction of a SQUID-based magnetometer for operation down to temperatures T = 10 mK, while retaining the compatibility with the sample holders typically used in commercial SQUID magnetometers. The system is based on a dc-SQUID coupled to a second-order gradiometer. The sample is placed inside the plastic mixing chamber of a dilution refrigerator and is thermalized directly by the 3He flow. The movement though the pickup coils is obtained by lifting the whole dilution refrigerator insert. A home-developed software provides full automation and an easy user interface.Comment: RevTex, 10 pages, 10 eps figures. High-resolution figures available upon reques

Low-temperature magnetization in geometrically frustrated Tb2Ti2O7

The nature of the low temperature ground state of the pyrochlore compound Tb2Ti2O7 remains a puzzling issue. Dynamic fluctuations and short-range correlations persist down to 50 mK, as evidenced by microscopic probes. In parallel, magnetization measurements show irreversibilities and glassy behavior below 200 mK. We have performed magnetization and AC susceptibility measurements on four single crystals down to 57 mK. We did not observe a clear plateau in the magnetization as a function of field along the [111] direction, as suggested by the quantum spin ice model. In addition to a freezing around 200 mK, slow dynamics are observed in the AC susceptibility up to 4 K. The overall frequency dependence cannot be described by a canonical spin-glass behavior.Comment: 5 pages, 4 figures + Supp. Mat (3 pages, 5 figures

Single-shot discrimination of quantum unitary processes

We formulate minimum-error and unambiguous discrimination problems for quantum processes in the language of process positive operator valued measures (PPOVM). In this framework we present the known solution for minimum-error discrimination of unitary channels. We derive a "fidelity-like" lower bound on the failure probability of the unambiguous discrimination of arbitrary quantum processes. This bound is saturated (in a certain range of apriori probabilities) in the case of unambiguous discrimination of unitary channels. Surprisingly, the optimal solution for both tasks is based on the optimization of the same quantity called completely bounded process fidelity.Comment: 11 pages, 1 figur

The construction problem for Hodge numbers modulo an integer in positive characteristic

Let k be an algebraically closed field of positive characteristic. For any integer 5 ≥ 2, we show that the Hodge numbers of a smooth projective k-variety can take on any combination of values modulo m, subject only to Serre duality. In particular, there are no non-trivial polynomial relations between the Hodge numbers

Superconductivity and magnetic order in the non-centrosymmetric Half Heusler compound ErPdBi

We report superconductivity at $T_c = 1.22$ K and magnetic order at $T_N = 1.06$ K in the semi-metallic noncentrosymmetric Half Heusler compound ErPdBi. The upper critical field, $B_{c2}$, has an unusual quasi-linear temperature variation and reaches a value of 1.6 T for $T \rightarrow 0$. Magnetic order is found below $T_c$ and is suppressed at $B{_M} \sim 2.5$ T for $T \rightarrow 0$. Since $T_c \simeq T_N$, the interaction of superconductivity and magnetism is expected to give rise to a complex ground state. Moreover, electronic structure calculations show ErPdBi has a topologically nontrivial band inversion and thus may serve as a new platform to study the interplay of topological states, superconductivity and magnetic order.Comment: 6 pages, 5 figures; accepted for publication in Europhysics Letter

Strict weak mixing of some C*-dynamical systems based on free shifts

We define a stronger property than unique ergodicity with respect to the fixed-point subalgebra previously investigated by Abadie and Dykema. Such a property is denoted as F-strict weak mixing (F stands for the Markov projection onto the fixed-point operator system). Then we show that the free shifts on the reduced C*-algebras of RD-groups, including the free group on infinitely many generators, and amalgamated free product C*-algebras, considered by Abadie and Dykema, are all strictly weak mixing and not merely uniquely ergodic.Comment: 10 page

Towards the understanding of vertical-axis wind turbines in double-rotor configuration

Vertical-axis wind turbines (VAWTs) in double-rotor configuration, meaning two rotors in close proximity, have the ability to enhance the power performance. In this study, we work towards the understanding of vertical-axis wind turbines in double-rotor configuration. Numerical simulations are performed to gain insight in the physics behind the double-rotor concept. Furthermore, a parametric study is performed to explore the effect of the double-rotor lay-out, rotor loading, rotor spacing and wind direction on the flow characteristics and the power generation.</p