Multiband superconductivity with unexpected deficiency of nodal quasiparticles in CeCu2Si2

Superconductivity in the heavy-fermion compound CeCu2Si2 is a prototypical example of Cooper pairs formed by strongly correlated electrons. For more than 30 years, it has been believed to arise from nodal d-wave pairing mediated by a magnetic glue. Here, we report a detailed study of the specific heat and magnetization at low temperatures for a high-quality single crystal. Unexpectedly, the specific-heat measurements exhibit exponential decay with a two-gap feature in its temperature dependence, along with a linear dependence as a function of magnetic field and the absence of oscillations in the field angle, reminiscent of multiband full-gap superconductivity. In addition, we find anomalous behavior at high fields, attributed to a strong Pauli paramagnetic effect. A low quasiparticle density of states at low energies with a multiband Fermi-surface topology would open a new door into electron pairing in CeCu2Si2.Comment: 5 pages, 4 figures (main text) + 5 pages, 6 figures (supplemental material), published in Phys. Rev. Let

Fans and polytopes in tilting theory II: gg-fans of rank 2

The $g$-fan of a finite dimensional algebra is a fan in its real Grothendieck group defined by tilting theory. We give a classification of complete $g$-fans of rank 2. More explicitly, our first main result asserts that every complete sign-coherent fan of rank 2 is a $g$-fan of some finite dimensional algebra. Our proof is based on three fundamental results, Gluing Theorem, Rotation Theorem and Subdivision Theorem, which realize basic operations on fans in the level of finite dimensional algebras. For each of 16 convex sign-coherent fans $\Sigma$ of rank 2, our second main result gives a characterization of algebras $A$ of rank 2 satisfying $\Sigma(A)=\Sigma$. As a by-product of our method, we prove that for each positive integer $N$, there exists a finite dimensional algebra $A$ of rank 2 such that the Hasse quiver of the poset of 2-term silting complexes of $A$ has precisely $N$ connected components.Comment: 37 pages, v2: Fixed typos, updated references and added section

Fans and polytopes in tilting theory

For a finite dimensional algebra $A$ over a field $k$, the 2-term silting complexes of $A$ gives a simplicial complex $\Delta(A)$ called the $g$-simplicial complex. We give tilting theoretic interpretations of the $h$-vectors and Dehn-Sommerville equations of $\Delta(A)$. Using $g$-vectors of 2-term silting complexes, $\Delta(A)$ gives a nonsingular fan $\Sigma(A)$ in the real Grothendieck group $K_0(\mathrm{proj } A)_\mathbb{R}$ called the $g$-fan. For example, the fan of $g$-vectors of a cluster algebra is given by the $g$-fan of a Jacobian algebra of a non-degenerate quiver with potential. We give several properties of $\Sigma(A)$ including idempotent reductions, sign-coherence, Jasso reductions and a connection with Newton polytopes of $A$-modules. Moreover, $\Sigma(A)$ gives a (possibly infinite and non-convex) polytope $P(A)$ in $K_0(\mathrm{proj } A)_\mathbb{R}$ called the $g$-polytope of $A$. We call $A$ $g$-convex if $P(A)$ is convex. In this case, we show that it is a reflexive polytope, and that the dual polytope is given by the 2-term simple minded collections of $A$. We give an explicit classification of $g$-convex algebras of rank $2$. We classify algebras whose $g$-polytopes are smooth Fano. We classify classical and generalized preprojective algebras which are $g$-convex, and also describe their $g$-polytope as the dual polytopes of short root polytopes of type $A$ and $B$. We also classify Brauer graph algebras which are $g$-convex, and describe their $g$-polytopes as root polytopes of type $A$ and $C$.Comment: 70 page

Thermodynamic study of gap structure and pair-breaking effect by magnetic field in the heavy-fermion superconductor CeCu2Si2

This paper presents the results of specific-heat and magnetization measurements, in particular their field-orientation dependence, on the first discovered heavy-fermion superconductor CeCu$_2$Si$_2$ ($T_{\rm c} \sim 0.6$ K). We discuss the superconducting gap structure and the origin of the anomalous pair-breaking phenomena, leading e.g., to the suppression of the upper critical field $H_{\rm c2}$, found in the high-field region. The data show that the anomalous pair breaking becomes prominent below about 0.15 K in any field direction, but occurs closer to $H_{\rm c2}$ for $H \parallel c$. The presence of this anomaly is confirmed by the fact that the specific-heat and magnetization data satisfy standard thermodynamic relations. Concerning the gap structure, field-angle dependences of the low-temperature specific heat within the $ab$ and $ac$ planes do not show any evidence for gap nodes. From microscopic calculations in the framework of a two-band full-gap model, the power-law-like temperature dependences of $C$ and $1/T_1$, reminiscent of nodal superconductivity, have been reproduced reasonably. These facts further support multiband full-gap superconductivity in CeCu$_2$Si$_2$.Comment: 10 pages, 8 figures, published in Phys. Rev.

High-performance, adiabatically nanotapered fibre-chip couplers in silicon at 2 microns wavelength

Fibre optic technology connects the world through the Internet, enables remote sensing, and connects disparate functional optical devices. Highly confined silicon photonics promises extreme scale and functional integration. However, the optical modes of silicon nanowire waveguides and optical fibres are very different, making efficient fibre-chip coupling a challenge. Vertical grating couplers, the dominant coupling method today, have limited optical bandwidth and are naturally out-of-plane. Here we demonstrate a new method that is low-loss, broadband, easily manufacturable, and naturally planar. We adiabatically couple a tapering silicon nanowire waveguide to a conic nanotapered optical fibre, measuring transmission between 2.0 and 2.2 micron wavelength. The silicon chip is fabricated at a commercial foundry and then post-processed to release the tapering nanowires. We estimate an optimal per-coupler transmission of -0.48 dB (maximum; 95% confidence interval [+0.46, -1.68] dB) and a 1-dB bandwidth of 295 nm . With automated measurements, we quantify the device tolerance to lateral misalignment, measuring a flat response within +/- 0.968 micron. This design can enable low-loss modular systems of integrated photonics irrespective of material and waveband.Comment: 6 pages, 3 figure