Assuming some regularity of the dynamical zeta function, we establish an explicit formula with an error term for the prime orbit counting function of a suspended flow. We define the subclass of self-similar flows, for which we give an extensive analysis of the error term in the corresponding prime orbit theorem.

Michel Lapidus Machiel van Frankenhuysen

The recently discovered $C_4$ tetragonal magnetic phase in hole-doped members of the iron-based superconductors provides new insights into the origin of unconventional superconductivity. Previously observed in Ba$_{1-x}A_x$Fe$_2$As$_2$ (with $A =$ K, Na), the $C_4$ magnetic phase exists within the well studied $C_2$ spin-density wave (SDW) dome, arising just before the complete suppression of antiferromagnetic (AFM) order but after the onset of superconductivity. Here, we present detailed x-ray and neutron diffraction studies of Sr$_{1-x}$Na$_x$Fe$_2$As$_2$ ($0.10 \leq\ x \leq\ 0.60$) to determine their structural evolution and the extent of the $C_4$ phase. Spanning $\Delta x\sim 0.14$ in composition, the $C_4$ phase is found to extend over a larger range of compositions, and to exhibit a significantly higher transition temperature, $T_r \sim 65$K, than in either of the other systems in which it has been observed. The onset of this phase is seen near a composition ($x \sim 0.30$) where the bonding angles of the Fe$_2$As$_2$ layers approach the perfect $109.46^\circ$ tetrahedral angle. We discuss the possible role of this return to a higher symmetry environment for the magnetic iron site in triggering the magnetic reorientation and the coupled re-entrance to the tetragonal structure. Finally, we present a new phase diagram, complete with the $C_4$ phase, and use its observation in a third hole-doped 122 system to suggest the universality of this phase.

K. M. Taddei J. M. Allred D. E. Bugaris S. H. Lapidus M. J. Krogstad R. Stadel H. Claus D. Y. Chung M. G. Kanatzidis S. Rosenkranz R. Osborn O. Chmaissem

3D Dirac semi-metals (DSMs) are materials that have massless Dirac electrons and exhibit exotic physical properties It has been suggested that structurally distorting a DSM can create a Topological Insulator (TI), but this has not yet been experimentally verified. Furthermore, quasiparticle excitations known as Majorana Fermions have been theoretically proposed to exist in materials that exhibit superconductivity and topological surface states. Here we show that the cubic Laves phase Au$_2$Pb has a bulk Dirac cone above 100 K that gaps out upon cooling at a structural phase transition to create a topologically non trivial phase that superconducts below 1.2 K. The nontrivial Z$_2$ = -1 invariant in the low temperature phase indicates that Au$_2$Pb in its superconducting state must have topological surface states. These characteristics make Au$_2$Pb a unique platform for studying the transition between bulk Dirac electrons and topological surface states as well as studying the interaction of superconductivity with topological surface states.

Leslie M. Schoop Lilia S. Xie Ru Chen Quinn D. Gibson Saul H. Lapidus Itamar Kimchi Max Hirschberger Neel Haldolaarachchige Mazhar N. Ali Carina A. Belvin Tian Liang Jeffrey B. Neaton N. P. Ong Ashvin Vishwanath R. J. Cava

The magnetic properties of the quasi-two-dimensional van der Waals magnet Fe$_{5-\delta}$GeTe$_2$ (F5GT), which has a high ferromagnetic ordering temperature $T_{\text{C}}$ $\sim$ 315 K, remains to be better understood. It has been demonstrated that the magnetization of F5GT is sensitive to both the Fe deficiency ${\delta}$ and the thermal cycling history. Here, we investigate the structural and magnetic properties of F5GT with a minimal Fe deficiency ($|{\delta}|$ $\le$ 0.1), utilizing combined x-ray and neutron scattering techniques. Our study reveals that the quenched F5GT single crystals experience an irreversible, first-order transition at $T_{\text{S}}$ $\sim$ 110 K upon first cooling, where the stacking order partly or entirely converts from ABC-stacking to AA-stacking order. Importantly, the magnetic properties, including the magnetic moment direction and the enhanced $T_{\text{C}}$ after the thermal cycling, are intimately related to the alteration of the stacking order. Our work highlights the significant influence of the lattice symmetry to the magnetism in F5GT.

Xiang Chen Wei Tian Yu He Hongrui Zhang Tyler L. Werner Saul Lapidus Jacob P. C. Ruff Ramamoorthy Ramesh Robert J. Birgeneau

${\lambda}$-RhO$_2$, a prototype 4d transition metal oxide, has been prepared by oxidative delithiation of spinel LiRh$_2$O$_4$ using ceric ammonium nitrate. Average-structure studies of this RhO$_2$ polytype, including synchrotron powder X-ray diffraction and electron diffraction, indicate the room temperature structure to be tetragonal, in the space group I41/amd, with a first-order structural transition to cubic Fd-3m at T = 345 K on warming. Synchrotron X-ray pair distribution function analysis and $^7$Li solid state nuclear magnetic resonance measurements suggest that the room temperature structure displays local Rh-Rh bonding. The formation of these local dimers appears to be associated with a metal-to insulator transition with a non-magnetic ground state, as also supported by density functional theory-based electronic structure calculations. This contribution demonstrates the power of soft chemistry to kinetically stabilize a surprisingly simple binary oxide compound.

Juan R. Chamorro Julia L. Zuo Euan N. Bassey Aurland K. Watkins Guomin Zhu Arava Zohar Kira E. Wyckoff Tiffany L. Kinnibrugh Saul H. Lapidus Susanne Stemmer Raphaële J. Clément Stephen D. Wilson Ram Seshadri

We present the analysis of the inclusive $K^{0}$ production in p+p and p+Nb collisions measured with the HADES detector at a beam kinetic energy of 3.5 GeV. Data are compared to the GiBUU transport model. The data suggest the presence of a repulsive momentum-dependent kaon potential as predicted by the Chiral Perturbation Theory (ChPT). For the kaon at rest and at normal nuclear density, the ChPT potential amounts to $\approx 35$ MeV. A detailed tuning of the kaon production cross sections implemented in the model has been carried out to reproduce the experimental data measured in p+p collisions. The uncertainties in the parameters of the model were examined with respect to the sensitivity of the experimental results from p+Nb collisions to the in-medium kaon potential.

G. Agakishiev O. Arnold D. Belver A. Belyaev J. C. Berger-Chen A. Blanco M. Böhmer J. L. Boyard P. Cabanelas S. Chernenko A. Dybczak E. Epple L. Fabbietti O. Fateev P. Finocchiaro P. Fonte J. Friese I. Fröhlich T. Galatyuk J. A. Garzón R. Gernhäuser K. Göbel M. Golubeva D. González-Díaz F. Guber M. Gumberidze T. Heinz T. Hennino R. Holzmann A. Ierusalimov I. Iori A. Ivashkin M. Jurkovic B. Kämpfer T. Karavicheva I. Koenig W. Koenig B. W. Kolb G. Korcyl G. Kornakov R. Kotte A. Krása F. Krizek R. Krücken H. Kuc W. Kühn A. Kugler T. Kunz A. Kurepin V. Ladygin R. Lalik K. Lapidus A. Lebedev L. Lopes M. Lorenz L. Maier A. Mangiarotti J. Markert V. Metag J. Michel C. Müntz R. Münzer L. Naumann Y. C. Pachmayer M. Palka Y. Parpottas V. Pechenov O. Pechenova J. Pietraszko W. Przygoda B. Ramstein A. Reshetin A. Rustamov A. Sadovsky P. Salabura A. Schmah E. Schwab J. Siebenson Yu. G. Sobolev B. Spruck H. Ströbele J. Stroth C. Sturm A. Tarantola K. Teilab P. Tlusty M. Traxler H. Tsertos T. Vasiliev V. Wagner M. Weber C. Wendisch J. Wüstenfeld S. Yurevich Y. Zanevsky . T. Gaitanos J. Weil

We use the self-similar tilings constructed by the second author in "Canonical self-affine tilings by iterated function systems" to define a generating function for the geometry of a self-similar set in Euclidean space. This tubular zeta function encodes scaling and curvature properties related to the complement of the fractal set, and the associated system of mappings. This allows one to obtain the complex dimensions of the self-similar tiling as the poles of the tubular zeta function and hence develop a tube formula for self-similar tilings in \$\mathbb{R}^d$. The resulting power series in $\epsilon$ is a fractal extension of Steiner's classical tube formula for convex bodies $K \ci \bRd$. Our sum has coefficients related to the curvatures of the tiling, and contains terms for each integer $i=0,1,...,d-1$, just as Steiner's does. However, our formula also contains terms for each complex dimension. This provides further justification for the term "complex dimension". It also extends several aspects of the theory of fractal strings to higher dimensions and sheds new light on the tube formula for fractals strings obtained in "Fractal Geometry and Complex Dimensions" by the first author and Machiel van Frankenhuijsen.

Michel L. Lapidus Erin P. J. Pearse

Elucidating the nature of the magnetic ground state of iron-based superconductors is of paramount importance in unveiling the mechanism behind their high temperature superconductivity. Until recently, it was thought that superconductivity emerges only from an orthorhombic antiferromagnetic stripe phase, which can in principle be described in terms of either localized or itinerant spins. However, we recently reported that tetragonal symmetry is restored inside the magnetically ordered state of a hole-doped BaFe2As2. This observation was interpreted as indirect evidence of a new double-Q magnetic structure, but alternative models of orbital order could not be ruled out. Here, we present Mossbauer data that show unambiguously that half of the iron sites in this tetragonal phase are non-magnetic, establishing conclusively the existence of a novel magnetic ground state with a non-uniform magnetization that is inconsistent with localized spins. We show that this state is naturally explained as the interference between two spin-density waves, demonstrating the itinerant character of the magnetism of these materials and the primary role played by magnetic over orbital degrees of freedom.

J. M. Allred K. M. Taddei D. E. Bugaris M. J. Krogstad S. H. Lapidus D. Y. Chung H. Claus M. G. Kanatzidis D. E. Brown J. Kang R. M. Fernandes I. Eremin S. Rosenkranz O. Chmaissem R. Osborn

We present a systematic study on the heavily Cr doped iron pnictides BaFe$_{1.9-x}$Ni$_{0.1}$Cr$_{x}$As$_{2}$ by using elastic neutron scattering, high-resolution synchrotron X-ray diffraction (XRD), resistivity and Hall transport measurements. When the Cr concentration increases from $x=$ 0 to 0.8, neutron diffraction experiments suggest that the collinear antiferromagnetism persists in the whole doping range, where the N\'{e}el temperature $T_N$ coincides with the tetragonal-to-orthorhombic structural transition temperature $T_s$, and both of them keeps around 35 K. The magnetic ordered moment, on the other hand, increases within increasing $x$ until $x=$ 0.5, and then decreases with further increasing $x$. Detailed refinement of the powder XRD patterns reveals that the Cr substitutions actually stretch the FeAs$_4$ tetrahedron along the $c-$axis and lift the arsenic height away Fe-Fe plane. Transport results indicate that the charge carriers become more localized upon Cr doping, then changes from electron-type to hole-type around $x=$ 0.5. Our results suggest that the ordered moment and the ordered temperature of static magnetism in iron pnictides can be decoupled and tuned separately by chemical doping.

Dongliang Gong Tao Xie Rui Zhang Jonas Birk Christof Niedermayer Fei Han S. H. Lapidus Pengcheng Dai Shiliang Li Huiqian Luo

The crystal structures of Ni$X_2$(pyz)$_2$ ($X$ = Cl (\textbf{1}), Br (\textbf{2}), I (\textbf{3}) and NCS (\textbf{4})) were determined at 298~K by synchrotron X-ray powder diffraction. All four compounds consist of two-dimensional (2D) square arrays self-assembled from octahedral NiN$_4$$X_2$ units that are bridged by pyz ligands. The 2D layered motifs displayed by \textbf{1}-\textbf{4} are relevant to bifluoride-bridged [Ni(HF$_2$)(pyz)$_2$]$Z$F$_6$ ($Z$ = P, Sb) which also possess the same 2D layers. In contrast, terminal $X$ ligands occupy axial positions in \textbf{1}-\textbf{4} and cause a staggering of adjacent layers. Long-range antiferromagnetic order occurs below 1.5 (Cl), 1.9 (Br and NCS) and 2.5~K (I) as determined by heat capacity and muon-spin relaxation. The single-ion anisotropy and $g$ factor of \textbf{2}, \textbf{3} and \textbf{4} are measured by electron spin resonance where no zero--field splitting was found. The magnetism of \textbf{1}-\textbf{4} crosses a spectrum from quasi-two-dimensional to three-dimensional antiferromagnetism. An excellent agreement was found between the pulsed-field magnetization, magnetic susceptibility and $T_\textrm{N}$ of \textbf{2} and \textbf{4}. Magnetization curves for \textbf{2} and \textbf{4} calculated by quantum Monte Carlo simulation also show excellent agreement with the pulsed-field data. \textbf{3} is characterized as a three-dimensional antiferromagnet with the interlayer interaction ($J_\perp$) slightly stronger than the interaction within the two-dimensional [Ni(pyz)$_2$]$^{2+}$ square planes ($J_\textrm{pyz}$).

J. Liu P. A. Goddard J. Singleton J. Brambleby F. Foronda J. S. Möller Y. Kohama S. Ghannadzadeh A. Ardavan S. J. Blundell T. Lancaster F. Xiao R. C. Williams F. L. Pratt P. J. Baker K. Wierschem S. H. Lapidus K. H. Stone P. W. Stephens J. Bendix M. R. Lees T. J. Woods K. E. Carreiro H. E. Tran C. J. Villa J. L. Manson