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We study a problem modelling segregation of an arbitrary number of competing species in planar domains. The solutions give rise to a well known free boundary problem with the domain partitioning itself into subdomains occupied by different species. In principle, several of them can coexist in a neighborhood of any point. However, we show that {\it generically} the domain partitions into subdomains with only triple junctions, meaning that at most three populations meet at the free boundary. Our main tools are the use of the formalism of harmonic maps into singular spaces and the introduction of a complex structure via the Hopf differential., Comment: 31 pages, 7 figures

Screening, a ubiquitous phenomenon associated with the shielding of electric fields by surrounding charges, has been widely adopted as a means to modify a material's properties. While so far most studies have relied on static changes of screening through doping or gating, here we demonstrate that screening can also drive the onset of distinct quantum states on the ultrafast timescale. By using time and angle-resolved photoemission spectroscopy we show that intense optical excitation can drive 1T-TiSe$_2$, a prototypical charge density wave material, almost instantly from a gapped into a semimetallic state. By systematically comparing changes in bandstructure over time and excitation strength with theoretical calculations we find that the appearance of this state is likely caused by a dramatic reduction of the screening length. In summary, this work showcases how optical excitation enables the screening driven design of a non-equilibrium semimetallic phase in TiSe$_2$, possibly providing a general pathway into highly screened phases in other strongly correlated materials.

Non-zero spin orbit coupling has been reported in several unconventional superconductors due to the absence of inversion symmetry breaking. This contrasts with cuprate superconductors, where such interaction has been neglected for a long time. The recent report of a non-trivial spin orbit coupling in overdoped Bi2212 cuprate superconductor, has re-opened an old debate on both the source and role of such interaction and its evolution throughout the superconducting dome. Using high-resolution spin- and angle-resolved photoemission spectroscopy, we reveal a momentum-dependent spin texture throughout the hole-doped side of the superconducting phase diagram for single- and double-layer bismuth-based cuprates. The universality of the reported effect among different dopings and the disappearance of spin polarization upon lead substitution, suggest a common source. We argue that local structural fluctuations of the CuO planes and the resulting charge imbalance may cause local inversion symmetry breaking and spin polarization, which might be crucial for understanding cuprates physics., Comment: 6 figures

PtTe$_2$ and PdTe$_2$ are among the first transition metal dichalcogenides that were predicted to host type-II Dirac fermions, exotic particles prohibited in free space. These materials are layered and air-stable, which makes them top candidates for technological applications that take advantage of their anisotropic magnetotransport properties. Here, we provide a detailed characterization of the electronic structure of PtTe$_2$ and PdTe$_2$ using Angle Resolved Photoemission Spectroscopy (ARPES) and Density Functional Theory (DFT) calculations, unveiling a new three-dimensional dispersion in these materials. Through the use of circularly polarized light, we report a different behavior of such dispersion in PdTe$_2$ compared to PtTe$_2$, that we relate to a symmetry analysis of the dipole matrix element. Such analysis reveals a link between the observed circular dichroism and the different momentum-dependent terms in the dispersion of these two compounds, despite their close similarity in crystal structure. Additionally, our data shows a clear difference in the circular dichroic signal for the type-II Dirac cones characteristic of these materials, compared to their topologically protected surface states. Our work provides a useful reference for the ARPES characterization of other transition metal dichalcogenides with topological properties and illustrates the use of circular dichroism as a guide to identify the topological character of two otherwise equivalent band dispersions, and to recognize different attributes in the band structure of similar materials., Comment: 14 pages, 9 figures

Molecular crystals are a flexible platform to induce novel electronic phases. Due to the weak forces between molecules, intermolecular distances can be varied over relatively larger ranges than interatomic distances in atomic crystals. On the other hand, the hopping terms are generally small, which results in narrow bands, strong correlations and heavy electrons. Here, by growing K$_x$C$_{60}$ fullerides on hexagonal layered Bi$_2$Se$_3$, we show that upon doping the series undergoes a Mott transition from a molecular insulator to a correlated metal, and an in-gap state evolves into highly dispersive Dirac-like fermions at half filling, where superconductivity occurs. This picture challenges the commonly accepted description of the low energy quasiparticles as appearing from a gradual electron doping of the conduction states, and suggests an intriguing parallel with the more famous family of the cuprate superconductors. More in general, it indicates that molecular crystals offer a viable route to engineer electron-electron interactions., Comment: 5 pages, 4 figures. Accepted at Physical Review Research

$\alpha$-RuCl$_3$ is considered to be the top candidate material for the experimental realization of the celebrated Kitaev model. It is however known that additional interactions beyond the Kitaev model trigger in $\alpha$-RuCl$_3$, a long-range zigzag antiferromagnetic ground state. In this work, we investigate a nanoflake of $\alpha$-RuCl$_3$ through guarded high impedance measurements aimed at reaching through electronic transport, the regime where the system turns into a zigzag antiferromagnet. We investigated a variety of temperatures (\SI{1.45}{\kelvin} - \SI{175}{\kelvin}) and out-of-plane magnetic fields ranging up to \SI{11}{\tesla}. We found a clear signature of a structural phase transition at $\approx 160$\,K as reported for thin crystals of $\alpha$-RuCl$_3$, as well as a thermally activated behavior at temperatures above $\approx 30$\,K with a characteristic activation energy significantly smaller than the energy gap that we observe for $\alpha$-RuCl$_3$ bulk crystals through our Angle Resolved Photoemission Spectroscopy (ARPES) experiments. Additionally we found that below $\approx 30$\,K, transport is ruled by Efros-Shklovskii (ES) VRH. These observations point to the presence of Coulomb impurities in our thin crystals. Most importantly, our data shows that below the magnetic ordering transition known for bulk $\alpha$-RuCl$_3$ ($\approx 7$\,K), there is a clear deviation from VRH or thermal activation transport mechanisms. Our work demonstrates the possibility of reaching through specialized high impedance measurements, the thrilling ground states predicted for $\alpha$-RuCl$_3$ at low temperatures in the frame of the Kitaev model, and informs about the transport mechanisms in this material in a wide temperature range as well as on important characteristic quantities such as the localization length of the impurities in a thin $\alpha$-RuCl$_3$ crystal., Comment: 8 pages, 6 figures, Supplementary Materials

Astroaccesible is an outreach project hosted by the Instituto de Astrof\'{\i}sica de Andaluc\'{\i}a - CSIC aimed at the teaching and popularisation of the astronomy among all publics independently of their capabilities and abilities, paying special attention to the collective of blind and visually impaired (BVI). Among the different strategies and resources using in our project, we have developed new 3D models representing in relief some of the stars, constellations and deep sky objects that can be observed during night from the Northern hemisphere in spring and summer. These models can be used by BVI to transmit to them the spatial configuration of the sky during night, but can be also used as an additional resource for all kind of publics to complement their sensorial experience. We also describe additional resources based on sounds that can also be employed to get deeper into this multisensorial experience. Finally, we summarize some of the activities and the context in which this new material has been used in the last 2 years., Comment: 6 pages, 2 figures. To appear as proceeding of the 15th Scientific Meeting of the Spanish Astronomical Society

Long viewed as passive elements, antiferromagnetic materials have emerged as promising candidates for spintronic devices due to their insensitivity to external fields and potential for high-speed switching. Recent work exploiting spin and orbital effects has identified ways to electrically control and probe the spins in metallic antiferromagnets, especially in noncollinear or noncentrosymmetric spin structures. The rare earth nickelate NdNiO3 is known to be a noncollinear antiferromagnet where the onset of antiferromagnetic ordering is concomitant with a transition to an insulating state. Here, we find that for low electron doping, the magnetic order on the nickel site is preserved while electronically a new metallic phase is induced. We show that this metallic phase has a Fermi surface that is mostly gapped by an electronic reconstruction driven by the bond disproportionation. Furthermore, we demonstrate the ability to write to and read from the spin structure via a large zero-field planar Hall effect. Our results expand the already rich phase diagram of the rare-earth nickelates and may enable spintronics applications in this family of correlated oxides., Comment: 25 pages, 4 figures

The formation of a charge density wave state is characterized by an order parameter. The way it is established provides unique information on both the role that correlation plays in driving the charge density wave formation and the mechanism behind its formation. Here we use time and angle resolved photoelectron spectroscopy to optically perturb the charge-density phase in 1T-TiSe$_2$ and follow the recovery of its order parameter as a function of energy, momentum and excitation density. Our results reveal that two distinct orders contribute to the gap formation, a CDW order and pseudogap-like order, manifested by an overall robustness to optical excitation. A detailed analysis of the magnitude of the the gap as a function of excitation density and delay time reveals the excitonic long-range nature of the CDW gap and the short-range Jahn-Teller character of the pseudogap order. In contrast to the gap, the intensity of the folded Se$_{4p}$* band can only give access to the excitonic order. These results provide new information into the the long standing debate on the origin of the gap in TiSe$_2$ and place it in the same context of other quantum materials where a pseudogap phase appears to be a precursor of long-range order., Comment: 6 pages, 4 figures

Layered ferromagnets are thrilling materials from both a fundamental and technological point of view. VI3 is an interesting example, with a complex magnetism that differentiates it from the first reported Cr based layered ferromagnets. Here, we show in an indirect way through Angle Resolved Photoemission Spectroscopy (ARPES) experiments, the importance of spin-orbit coupling setting the electronic properties of this material. Our light polarized photoemission measurements point to a ground state with a half-filled e'_+- doublet, where a gap opening is triggered by spin-orbit coupling enhanced by electronic correlations.

Optical excitation serves as a powerful approach to control the electronic structure of layered Van der Waals materials via many-body screening effects, induced by photoexcited free carriers, or via light-driven coherence, such as optical Stark and Bloch-Siegert effects. Although theoretical work has also pointed to an exotic mechanism of renormalizing band structure via excitonic correlations in bound electron-hole pairs (excitons), experimental observation of such exciton-driven band renormalization and the full extent of their implications is still lacking, largely due to the limitations of optical probes and the impact of screening effects. Here, by using extreme-ultraviolet time-resolved angle-resolved photoemission spectroscopy together with excitonic many-body theoretical calculations, we directly unmask the band renormalization effects driven by excitonic correlations in a monolayer semiconductor. We revealed a surprising bandgap opening, increased by 40 meV, and a simultaneous enhancement of band effective mass. Our findings unmask the novel exciton-driven mechanism towards the band engineering in photoexcited semiconducting materials, opening a new playground to manipulate the transient energy states in layered quantum materials via optical controls of excitonic many-body correlations.

Charge density waves (CDW) are states of broken symmetry with a periodic modulation of charge and lattice typically leading to the opening of a gap in the band structure. In the model CDW system 1T-TiSe$_2$ such a gap opens up between its Se$_{4p}$ valence and Ti$_{3d}$ conduction band, accompanied by a change of dispersion. These changes are crucial in understanding the CDW phase, as they provide a measure of the Se$_{4p}$-Ti$_{3d}$ hybridization strength and characteristic mechanistic features. Using time- and angle-resolved photoelectron spectroscopy (trARPES), the unoccupied band structure is populated with near-infrared (NIR) pump pulses which allows to to directly visualize the parabolically-shaped Ti$_{3d}$ conduction band. Furthermore, we observe a transient change of effective mass in the Se$_{4p}$ valence band following photoexcitation. This occurs alongside an overall reduction due to weakening of the CDW phase and is accompanied by an oscillating component with the frequency of the characteristic A$_{1g}$ phonon. These observations, enabled by trAPRES, highlight the importance of the lattice contributions in establishing the CDW order in 1T-TiSe$_2$., Comment: 4 figures

A topological flatband, also known as drumhead states, is an ideal platform to drive new exotic topological quantum phases. Using angle-resolved photoemission spectroscopy experiments, we reveal the emergence of a highly localized possible drumhead surface state in a topological semimetal BaAl4 and provide its full energy and momentum space topology. We find that the observed surface state is highly localized in momentum, inside a square-shaped bulk Dirac nodal loop, and in energy, leading to a flat band and a peak in the density of state. These results establish this class of materials as a possible experimental realization of drumhead surface states and provide an important reference for future studies of fundamental physics of topological quantum phase transition.

This paper proposes a spatial model with a realistic geography where a continuous distribution of agents (e.g., farmers) engages in economic interactions with one location from a finite set (e.g., cities). The spatial structure of the equilibrium consists of a tessellation, i.e., a partition of space into a collection of mutually exclusive market areas. After proving the existence of a unique equilibrium, we characterize how the location of borders and, in the case with mobile labor, the set of inhabited cities change in response to economic shocks. To deal with a two-dimensional space, we draw on tools from computational geometry and from the theory of shape optimization. Finally, we provide an empirical application to illustrate the usefulness of the framework for applied work., Comment: revised version, 64 pages

Electron-hole asymmetry is a fundamental property in solids that can determine the nature of quantum phase transitions and the regime of operation for devices. The observation of electron-hole asymmetry in graphene and recently in the phase diagram of bilayer graphene has spurred interest into whether it stems from disorder or from fundamental interactions such as correlations. Here, we report an effective new way to access electron-hole asymmetry in 2D materials by directly measuring the quasiparticle self-energy in graphene/Boron Nitride field effect devices. As the chemical potential moves from the hole to the electron doped side, we see an increased strength of electronic correlations manifested by an increase in the band velocity and inverse quasiparticle lifetime. These results suggest that electronic correlations play an intrinsic role in driving electron hole asymmetry in graphene and provide a new insight for asymmetries in more strongly correlated materials., Comment: 22 pages, 7 figures

Spatial segregation occurs in population dynamics when $k$ species interact in a highly competitive way. As a model for the study of this phenomenon, we consider the competition-diffusion system of $k$ differential equations \[ -\Delta u_i(x)=-\mu u_i (x)\displaystyle{\sum_{j\neq i}} u_j (x) \quad i=1,...,k \] in a domain $D$ with appropriate boundary conditions. Any $u_i$ represents a population density and the parameter $\mu$ determines the interaction strength between the populations. The purpose of this paper is to study the geometry of the limiting configuration as $\mu\longrightarrow+\infty$ on a planar domain for any number of species. If $k$ is even we show that some limiting configurations are strictly connected to the solution of a Dirichlet problem for the Laplace equation.

The BaAl$_4$ prototype crystal structure is the most populous of all structure types, and is the building block for a diverse set of sub-structures including the famous ThCr$_2$Si$_2$ family that hosts high-temperature superconductivity and numerous magnetic and strongly correlated electron systems. The MA$_4$ family of materials (M=Sr, Ba, Eu; A=Al, Ga, In) themselves present an intriguing set of ground states including charge and spin orders, but have largely been considered as uninteresting metals. Using electronic structure calculations, symmetry analysis and topological quantum chemistry techniques, we predict the exemplary compound BaAl$_4$ to harbor a three-dimensional Dirac spectrum with non-trivial topology and possible nodal lines crossing the Brillouin zone, wherein one pair of semi-Dirac points with linear dispersion along the $k_z$ direction and quadratic dispersion along the $k_x/k_y$ direction resides on the rotational axis with $C_{4v}$ point group symmetry. Electrical transport measurements reveal the presence of an extremely large, unsaturating positive magnetoresistance in BaAl$_4$ despite an uncompensated band structure, and quantum oscillations and angle-resolved photoemission spectroscopy measurements confirm the predicted multiband semimetal structure with pockets of Dirac holes and a Van Hove singularity (VHS) remarkably consistent with the theoretical prediction. We thus present BaAl$_4$ as a new topological semimetal, casting its prototype status into a new role as building block for a vast array of new topological materials., Comment: 11 pages, 5 figures

In the past decade, the advent of time-resolved spectroscopic tools has provided a new ground to explore fundamental interactions in solids and to disentangle degrees of freedom whose coupling leads to broad structures in the frequency domain. Time- and angle-resolved photoemission spectroscopy (tr-ARPES) has been utilized to directly study the relaxation dynamics of a metal in the presence of electron-phonon coupling. The effect of photo-excitations on the real and imaginary part of the self-energy as well as the time scale associated with different recombination processes are discussed. In contrast to a theoretical model, the phonon energy does not set a clear scale governing quasiparticle dynamics, which is also different from the results observed in a superconducting material. These results point to the need for a more complete theoretical framework to understand electron-phonon interaction in a photo-excited state., Comment: 4 figures

The discovery of Weyl semimetals (WSMs) has fueled tremendous interest in condensed matter physics. WSMs require breaking of either inversion symmetry (IS) or time-reversal symmetry (TRS); they can be categorized into type-I and type-II WSMs, characterized by un-tilted and strongly tilted Weyl cones respectively. Type-I WSMs with breaking of IS or TRS and type-II WSMs with IS breaking have been realized experimentally, but TRS-breaking type-II WSM still remains elusive. In this article, we report an ideal TRS-breaking type-II WSM with only one pair of Weyl nodes observed in the antiferromagnetic topological insulator Mn(Bi1-xSbx)2Te4 under magnetic fields. This state is manifested by a large intrinsic anomalous Hall effect, a non-trivial $\mathrm{{\pi}}$ Berry phase of the cyclotron orbit and a large positive magnetoresistance in the ferromagnetic phase at an optimal sample composition. Our results establish a promising platform for exploring the physics underlying the long-sought, ideal TRS breaking type-II WSM., Comment: 28 Pages, 5 Figures