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In this paper, we examine how soccer players can use their spatial relationships to control parts of the field and safely move play up the field via chains of ``safe configurations,'' i.e. configurations of players on a team ensuring the possessor of the ball has a collection of open passing options all connected by open passing lanes. An underlying philosophy behind our work is that it is most difficult to disrupt an attacking team's progression forward (with the ball) when this attacking team has multiple ``good'' options of how to proceed at each moment in time. We provide some evidence of this. Our main construction is a directed weighted graph where the nodes encode the configurations of players, the directed edges encode transformations between these configurations, and the weights encode the relative frequencies of the transformations. We conclude with a few applications and proposed further investigations. We believe that our work can serve as a launching platform for significant further investigation into how teams can ``safely progress'' the ball up the field, strategy development, and sophisticated decision making metrics. For coaches and players, we aim to streamline the process of moving safely up the field. In particular, we aim to construct a framework for creating new successful patterns of movement and aim that our framework allows for the development of new strategy. At the same time, our work could help identify configurations on the field which often result in turnovers or that allow for a lot of strategic flexibility (also impeding defensive containment of the attacking team). *Because the contributions of the female authors to this paper were by no means less than those of the male authors, we have chosen to reverse convention and to list the authors in reverse alphabetical order to ensure that the female authors were not listed only after the male authors., Comment: correction to bug in code (leading to new figures and example) and to a few references

Metallic iridium oxides (iridates) provide a fertile playground to explore new phenomena resulting from the interplay between topological protection, spin-orbit and electron-electron interactions. To date, however, few studies of the low energy electronic excitations exist due to the difficulty in synthesising crystals with sufficiently large carrier mean-free-paths. Here, we report the observation of Shubnikov-de Haas quantum oscillations in high-quality single crystals of monoclinic SrIrO$_3$ in magnetic fields up to 35~T. Analysis of the oscillations reveals a Fermi surface comprising multiple small pockets with effective masses up to 4.5 times larger than the calculated band mass. \textit{Ab-initio} calculations reveal robust linear band-crossings at the Brillouin zone boundary, due to its non-symmorphic symmetry, and overall we find good agreement between the angular dependence of the oscillations and the theoretical expectations. Further evidence of strong electron correlations is realized through the observation of signatures of non-Fermi liquid transport as well as a large Kadowaki-Woods ratio. These collective findings, coupled with knowledge of the evolution of the electronic state across the Ruddlesden-Popper iridate series, establishes monoclinic SrIrO$_3$ as a topological semimetal on the boundary of the Mott metal-insulator transition.

Resonant inelastic x-ray scattering (RIXS) is an extremely valuable tool for the study of elementary, including magnetic, excitations in matter. Latest developments of this technique mostly aimed at improving the energy resolution and performing polarization analysis of the scattered radiation, with a great impact on the interpretation and applicability of RIXS. Instead, this article focuses on the sample environment and presents a setup for high-pressure low-temperature RIXS measurements of low-energy excitations. The feasibility of these experiments is proved by probing the magnetic excitations of the bilayer iridate Sr$_3$Ir$_2$O$_7$ at pressures up to 12 GPa., Comment: 9 pages, 7 figures

(Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$ undergoes a bulk insulator-to-metal transition (IMT) at $x \approx \mathrm{0.04}$. Through careful analysis of previously published data ($x=\mathrm{0.053, 0.061, 0.076}$), we find an extended region below the Debye temperature in which the resistivity appears to scale linearly with temperature. Meanwhile resonant (in)elastic x-ray scattering data ($x=\mathrm{0.065}$) suggest a possible crossover from quantum paramagnetic to quantum critical phenomenology between 100 and 200~K. We put this into context with other results, and propose a possible phase diagram as a function of doping., Comment: Submitted to Physical Review B

The collective magnetic excitations in the spin-orbit Mott insulator (Sr$_{1-x}$La$_x$)$_2$IrO$_4$ ($x=0,\,0.01,\,0.04,\, 0.1$) were investigated by means of resonant inelastic x-ray scattering. We report significant magnon energy gaps at both the crystallographic and antiferromagnetic zone centers at all doping levels, along with a remarkably pronounced momentum-dependent lifetime broadening. The spin-wave gap is accounted for by a significant anisotropy in the interactions between $J_\text{eff}=1/2$ isospins, thus marking the departure of Sr$_2$IrO$_4$ from the essentially isotropic Heisenberg model appropriate for the superconducting cuprates., Comment: 6 pages, 4 figures

It is widely believed that high-temperature superconductivity in the cuprates emerges from doped Mott insulators. The physics of the parent state seems deceivingly simple: The hopping of the electrons from site to site is prohibited because their on-site Coulomb repulsion U is larger than the kinetic energy gain t. When doping these materials by inserting a small percentage of extra carriers, the electrons become mobile but the strong correlations from the Mott state are thought to survive; inhomogeneous electronic order, a mysterious pseudogap and, eventually, superconductivity appear. How the insertion of dopant atoms drives this evolution is not known, nor whether these phenomena are mere distractions specific to hole-doped cuprates or represent the genuine physics of doped Mott insulators. Here, we visualize the evolution of the electronic states of (Sr1-xLax)2IrO4, which is an effective spin-1/2 Mott insulator like the cuprates, but is chemically radically different. Using spectroscopic-imaging STM, we find that for doping concentration of x=5%, an inhomogeneous, phase separated state emerges, with the nucleation of pseudogap puddles around clusters of dopant atoms. Within these puddles, we observe the same glassy electronic order that is so iconic for the underdoped cuprates. Further, we illuminate the genesis of this state using the unique possibility to localize dopant atoms on topographs in these samples. At low doping, we find evidence for much deeper trapping of carriers compared to the cuprates. This leads to fully gapped spectra with the chemical potential at mid-gap, which abruptly collapse at a threshold of around 4%. Our results clarify the melting of the Mott state, and establish phase separation and electronic order as generic features of doped Mott insulators., Comment: This version contains the supplementary information and small updates on figures and text

We characterize the electron doping evolution of (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$ by means of angle-resolved photoemission. Concomitant with the metal insulator transition around $x\approx0.05$ we find the emergence of coherent quasiparticle states forming a closed small Fermi surface of volume $3x/2$, where $x$ is the independently measured La concentration. The quasiparticle weight $Z$ remains large along the entire Fermi surface, consistent with the moderate renormalization of the low-energy dispersion. This indicates a conventional, weakly correlated Fermi liquid state with a momentum independent residue $Z\approx0.5$ in lightly doped Sr$_3$Ir$_2$O$_7&., Comment: 5 pages, 4 figures