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Berry's random wave conjecture posits that high energy eigenfunctions of chaotic systems resemble random monochromatic waves at the Planck scale. One important consequence is that, at the Planck scale around "many" points in the manifold, any solution to the Helmholtz equation $\Delta\varphi+\varphi =0$ can be approximated by high energy eigenfunctions. This property, sometimes called inverse localization, has useful applications to the study of the nodal sets of eigenfunctions. Alas, the only manifold for which the local limits of a sequence of high energy eigenfunctions are rigorously known to be given by random waves is the flat torus $(\mathbf{R}/\mathbf{Z})^2$, which is certainly not chaotic. Our objective in this paper is to study the validity of this "inverse localization" property in the class of integrable billiards, exploiting the fact that integrable polygonal billiards are classified and that Birkhoff conjectured that ellipses are the only smooth integrable billiards. Our main results show that, while there are infinitely many integrable polygons exhibiting good inverse localization properties, for "most" integrable polygons and ellipses, this property fails dramatically. We thus conclude that, in a generic integrable billiard, the local limits of Dirichlet and Neumann eigenfunctions do not match random waves, as one might expect in view of Berry's conjecture. Extensions to higher dimensions and nearly integrable polygons are discussed too.

Polytypes of tetralayer graphene (TLG: Bernal, rhombohedral and mixed stacking) are crystalline structures with different symmetries. Among those, mixed-stacking tetralayers lack inversion symmetry, which allows for intrinsic spontaneous out-of-plane electrical polarisation, inverted in the mirror-image pair, ABCB and ABAC stackings. Here, we compare the intrinsic polarisation of such TLGs with the symmetry-breaking effect of a substrate, which can also generate out-of-plane electric dipole moments with different sizes in all four polytypes, including ABCB and ABAC twins. We analyse their temperature and magnetic field dependence, in view of understanding the origin of the recently measured Kelvin probe force microscopy maps of tetralayer flakes, and notice that the intrinsic contribution could be singled out based on magnetic field dependence of polarisation measured at low temperatures., Comment: 11 pages, 8 figures

Graphene-based van der Waals heterostructures take advantage of tailoring spin-orbit coupling (SOC) in the graphene layer by proximity effect. At long-wavelength -- saddled by the electronic states near the Dirac points -- the proximitized features can be effectively modelled by the Hamiltonian involving novel SOC terms and allow for an admixture of the tangential and radial spin textures -- by the so-called Rashba angle $\theta_{\text{R}}$. Taking such effective models we perform realistic large-scale magneto-transport calculations -- transverse magnetic focusing and Dyakonov-Perel spin relaxation -- and show that there are unique qualitative and quantitative features allowing for an unbiased experimental disentanglement of the conventional Rashba SOC from its novel radial counterpart, called here the radial Rashba SOC. Along with that, we propose a scheme for a direct estimation of the Rashba angle by exploring the magneto-response symmetries when swapping an in-plane magnetic field. To complete the story, we analyze the magneto-transport signatures in the presence of an emergent Dresselhaus SOC and also provide some generic ramifications about possible scenarios of the radial superconducting diode effect., Comment: 6 pages, 4 figures, comments are welcome

Electron doping is an excellent tuning knob to explore different phases of matter in two-dimensional (2D) materials. For example, tuning the Fermi level at a van Hove singularity in twisted bilayer graphene can enhance electron-electron interactions and induce a diverse range of correlated phases. Here, using a single-particle picture, we study the electronic reconstruction of the band edges of a 2D semiconductor, monolayer MoS2, on a hexagonal moire potential induced by another MoS2 monolayer. We find that such system transitions from a honeycomb to a hexagonal symmetry when the Fermi level is tuned from the conduction to the valence side. We also study the system under magnetic fields, and construct the Hofstadter's butterfly in the electron- and hole-doped side. Our findings are confirmed by simulating the conductance across a large-scale two-terminal device. We conclude that this duality is a general property that MoS2 and other transition-metal-dichalcogenides exhibit under non-symmetric superlattice potentials., Comment: 13 pages, 6 figures

We present ensemblQueryR, a package providing an R interface to the Ensembl REST API that facilitates flexible, fast, user-friendly and R workflow integrable querying of Ensembl REST API linkage disequilibrium (LD) endpoints, optimised for high-throughput querying. ensemblQueryR achieves this through functions that are intuitive and amenable to custom code integration, use of familiar R object types as inputs and outputs, code optimisation and optional parallelisation functionality. For each LD endpoint, ensemblQueryR provides two functions, permitting both single-query and multi-query modes of operation. The multi-query functions are optimised for large query sizes and provide optional parallelisation to leverage available computational resources and minimise processing time. We demonstrate that ensemblQueryR has improved performance in terms of random access memory (RAM) usage and speed, delivering a 10-fold speed increase over analogous software whilst using a third of the RAM. Finally, ensemblQueryR is near-agnostic to operating system and computational architecture through availability of Docker and singularity images, making this tool widely accessible to the scientific community.

The Random Wave Conjecture of M. V. Berry is the heuristic that eigenfunctions of a classically chaotic system should behave like Gaussian random fields, in the large eigenvalue limit. In this work we collect some definitions and properties of Gaussian random fields, and show that the formulation of the Berry's conjecture proposed using local weak limits is equivalent to the one that is based on the Benjamini-Schramm convergence. Finally, we see that both these formulations of the Berry's property imply another property known as inverse localization that relates high energy eigenfunctions and solutions to the Euclidean Helmholtz equation., Comment: 19 pages

Ferroelectricity (Valasek, J. Phys. Rev. 1921, 17, 475) - a spontaneous formation of electric polarisation - is a solid state phenomenon, usually, associated with ionic compounds or complex materials. Here we show that, atypically for elemental solids, few-layer graphenes can host an equilibrium out-of-plane electric polarisation, switchable by sliding the constituent graphene sheets. The systems hosting such effect include mixed-stacking tetralayers and thicker (5-9 layers) rhombohedral graphitic films with a twin boundary in the middle of a flake. The predicted electric polarisation would also appear in marginally (small-angle) twisted few-layer flakes, where lattice reconstruction would give rise to networks of mesoscale domains with alternating value and sign of out-of-plane polarisation., Comment: 25 pages, 7 figures

Diverse emergent correlated electron phenomena have been observed in twisted graphene layers due to electronic interactions with the moir\'e superlattice potential. Many electronic structure predictions have been reported exploring this new field, but with few momentum-resolved electronic structure measurements to test them. Here we use angle-resolved photoemission spectroscopy (ARPES) to study the twist-dependent ($1^\circ < \theta < 8^\circ$) electronic band structure of few-layer graphenes, including twisted bilayer, monolayer-on-bilayer, and double-bilayer graphene (tDBG). Direct comparison is made between experiment and theory, using a hybrid $\textbf{k}\cdot\textbf{p}$ model for interlayer coupling and implementing photon-energy-dependent phase shifts for photo-electrons from consecutive layers to simulate ARPES spectra. Quantitative agreement between experiment and theory is found across twist angles, stacking geometries, and back-gate voltages, validating the models and revealing displacement field induced gap openings in twisted graphenes. However, for tDBG at $\theta=1.5\pm0.2^\circ$, close to the predicted magic-angle of $\theta=1.3^\circ$, a flat band is found near the Fermi-level with measured bandwidth of $E_w = 31\pm5$ meV. Analysis of the gap between the flat band and the next valence band shows significant deviations between experiment ($\Delta_h=46\pm5$meV) and the theoretical model ($\Delta_h=5$meV), indicative of the importance of lattice relaxation in this regime.

Periodic systems feature the Hofstadter butterfly spectrum produced by Brown--Zak minibands of electrons formed when magnetic field flux through the lattice unit cell is commensurate with flux quantum and manifested by magneto-transport oscillations. Quantum oscillations, such as Shubnikov -- de Haas effect and Aharonov--Bohm effect, are also characteristic for electronic systems with closed orbits in real space and reciprocal space. Here we show the intricate relation between these two phenomena by tracing quantum magneto-oscillations to Lifshitz transitions in graphene superlattices, where they persist even at relatively low fields and very much above liquid-helium temperatures. The oscillations originate from Aharonov--Bohm interference on cyclotron trajectories that form a kagom\'e-shaped network characteristic for Lifshitz transitions. In contrast to Shubnikov - de Haas oscillations, the kagom\'e oscillations are robust against thermal smearing and they can be detected even when the Hofstadter butterfly spectrum is undermined by electron's scattering. We expect that kagom\'e quantum oscillations are generic to rotationally-symmetric two-dimensional crystals close to Lifshitz transitions., Comment: 7+7 pages

Tetralayer graphene has recently become a new addition to the family of few-layer graphene with versatile electronic properties. This material can be realised in three distinctive stacking configurations, for which we determine spectroscopic signatures in angle-resolved photoemission spectroscopy (ARPES), dynamical optical conductivity, and Raman spectra of inter-band excitations. The reported library of spectral features of tetralayer graphenes can be used for the non-invasive identification of the stacking order realised in a particular film., Comment: Pages 11, figures 7

Topologically protected flat surface bands make thin films of rhombohedral graphite an appealing platform for searching for strongly correlated states of 2D electrons. In this work, we study rhombohedral graphite with a twin boundary stacking fault and analyse the semimetallic and topological properties of low-energy bands localised at the surfaces and at the twinned interface. We derive an effective 4-band low energy model, where we implement the full set of Slonczewski-Weiss-McClure (SWMcC) parameters, and find the conditions for the bands to be localised at the twin boundary, protected from the environment-induced disorder. This protection together with a high density of states at the charge neutrality point, in some cases -- due to a Lifshitz transition, makes this system a promising candidate for hosting strongly-correlated effects., Comment: 8 pages, 5 figures

We report experimental investigations of transport through bilayer graphene (BLG)/chromium trihalide (CrX$_3$; X=Cl, Br, I) van der Waals interfaces. In all cases, a large charge transfer from BLG to CrX$_3$ takes place (reaching densities in excess of $10^{13}$ cm$^{-2}$), and generates an electric field perpendicular to the interface that opens a band gap in BLG. We determine the gap from the activation energy of the conductivity and find excellent agreement with the latest theory accounting for the contribution of the $\sigma$ bands to the BLG dielectric susceptibility. We further show that for BLG/CrCl$_3$ and BLG/CrBr$_3$ the band gap can be extracted from the gate voltage dependence of the low-temperature conductivity, and use this finding to refine the gap dependence on the magnetic field. Our results allow a quantitative comparison of the electronic properties of BLG with theoretical predictions and indicate that electrons occupying the CrX$_3$ conduction band are correlated.

We consider the question of whether the high-energy eigenfunctions of certain Schr\"odinger operators on the $d$-dimensional hyperbolic space of constant curvature $-\kappa^2$ are flexible enough to approximate an arbitrary solution of the Helmholtz equation $\Delta h+h=0$ on $\mathbf{R}^d$, over the natural length scale $O(\lambda^{-1/2})$ determined by the eigenvalue $\lambda \gg 1$. This problem is motivated by the fact that, by the asymptotics of the local Weyl law, approximate Laplace eigenfunctions do have this approximation property on any compact Riemannian manifold. In this paper we are specifically interested in the Coulomb and harmonic oscillator operators on the hyperbolic spaces $\mathbf{H}^d(\kappa)$. As the dimension of the space of bound states of these operators tends to infinity as $\kappa$ tends to 0, one can hope to approximate solutions to the Helmholtz equation by eigenfunctions for some $\kappa > 0$ that is not fixed a priori. Our main result shows that this is indeed the case, under suitable hypotheses. We also prove a global approximation theorem with decay for the Helmholtz equation on manifolds that are isometric to the hyperbolic space outside a compact set, and consider an application to the study of the heat equation on $\mathbf{H}^d(\kappa)$. Although global approximation and inverse approximation results are heuristically related in that both theorems explore flexibility properties of solutions to elliptic equations on hyperbolic spaces, we will see that the underlying ideas behind these theorems are very different.

We consider the question of when the Laplace eigenfunctions on an arbitrary flat torus $\mathbf{T}_\Gamma:=\mathbf{R}^d/\Gamma$ are flexible enough to approximate, over the natural length scale of order $1/\sqrt\lambda$, where $\lambda\gg1$ is the eigenvalue, an arbitary solution of the Helmholtz equation $\Delta h + h=0$ on $\mathbf{R}^d$. This problem is motivated by the fact that, by the asymptotics for the local Weyl law, "approximate Laplace eigenfunctions" do have this approximation property on any compact Riemannian manifold. What we find is that the answer depends solely on the arithmetic properties of the spectrum. Specifically, recall that the eigenvalues of $\mathbf{T}_\Gamma$ are of the form $\lambda_k=Q_\Gamma(k)$, where $Q_\Gamma$ is a quadratic form and $k \in \mathbf{Z}^d$. Our main result is that the eigenfunctions of $\mathbf{T}_\Gamma$ have the desired approximation property if and only $Q_\Gamma$ is a multiple of a quadratic form with integer coefficients. In particular, the set of lattices $\Gamma$ for which this approximation property holds has measure zero but includes all rational lattices. A consequence of this fact is that when $Q_\Gamma$ is a multiple of a quadratic form with integer coefficients, Laplace eigenfunctions exhibit an extremely flexible behavior over scales of order $1/\sqrt\lambda$. In particular, there are eigenfunctions of arbitrarily high energy that exhibit nodal components diffeomorphic to any compact hypersurface of diameter $O(1/\sqrt\lambda)$.

A unique feature of the complex band structures of moir\'e materials is the presence of minivalleys, their hybridization, and scattering between them. Here we investigate magneto-transport oscillations caused by scattering between minivalleys - a phenomenon analogous to magneto-intersubband oscillations - in a twisted double bilayer graphene sample with a twist angle of 1.94{\deg}. We study and discuss the potential scattering mechanisms and find an electron-phonon mechanism and valley conserving scattering to be likely. Finally, we discuss the relevance of our findings for different materials and twist angles., Comment: 4 figures

We use a hybrid k dot p theory - tight binding (HkpTB) model to describe interlayer coupling simultaneously in both Bernal and twisted graphene structures. For Bernal-aligned interfaces, HkpTB is parametrized using the full Slonczewski-Weiss-McClure (SWMcC) Hamiltonian of graphite, which is then used to refine the commonly used minimal model for twisted interfaces, by deriving additional terms that reflect all details of the full SWMcC model of graphite. We find that these terms introduce some electron-hole asymmetry in the band structure of twisted bilayers, but in twistronic multilayer graphene, they produce only a subtle change of moire miniband spectra, confirming the broad applicability of the minimal model for implementing the twisted interface coupling in such systems.

Graphene has evolved as a platform for quantum transport that can compete with the best and cleanest semiconductor systems. Recently, many interesting local properties of carrier transport in graphene have been investigated by various scanning probe techniques. Here, we report on the observation of distinct electronic jets emanating from a narrow split-gate defined channel in bilayer graphene. We find that these jets, which are visible via their interference patterns, occur predominantly with an angle of 60{\deg} between each other. This observation is related to the specific bandstructure of bilayer graphene, in particular trigonal warping, which leads to a valley-dependent selection of momenta for low-energy conduction channels. This experimental observation of electron jetting has consequences for carrier transport in graphene in general as well as for devices relying on ballistic and valley selective transport.

We study electronic contribution to the Raman scattering signals of two-, three- and four-layer graphene with layers at one of the interfaces twisted by a small angle with respect to each other. We find that the Raman spectra of these systems feature two peaks produced by van Hove singularities in moir\'{e} minibands of twistronic graphene, one related to direct hybridization of Dirac states, and the other resulting from band folding caused by moir\'{e} superlattice. The positions of both peaks strongly depend on the twist angle, so that their detection can be used for non-invasive characterization of the twist, even in hBN-encapsulated structures., Comment: 7 pages (including 4 figures) + 10 pages (3 figures) supplement

Understanding and tuning correlated states is of great interest and significance to modern condensed matter physics. The recent discovery of unconventional superconductivity and Mott-like insulating states in magic-angle twisted bilayer graphene (tBLG) presents a unique platform to study correlation phenomena, in which the Coulomb energy dominates over the quenched kinetic energy as a result of hybridized flat bands. Extending this approach to the case of twisted multilayer graphene would allow even higher control over the band structure because of the reduced symmetry of the system. Here, we study electronic transport properties in twisted trilayer graphene (tTLG, bilayer on top of monolayer graphene heterostructure). We observed the formation of van Hove singularities which are highly tunable by twist angle and displacement field and can cause strong correlation effects under optimum conditions, including superconducting states. We provide basic theoretical interpretation of the observed electronic structure., Comment: 16 pages, 9 figures

We describe how the out-of-plane dielectric polarizability of monolayer graphene influences the electrostatics of bilayer graphene -- both Bernal (BLG) and twisted (tBLG). We compare the polarizability value computed using density functional theory with the output from previously published experimental data on the electrostatically controlled interlayer asymmetry potential in BLG and data on the on-layer density distribution in tBLG. We show that monolayers in tBLG are described well by polarizability $\alpha_{exp} = 10.8 \unicode{x212B}^3$ and effective out-of-plane dielectric susceptibility $\epsilon_z = 2.5$, including their on-layer electron density distribution at zero magnetic field and the inter-layer Landau level pinning at quantizing magnetic fields., Comment: 4 pages

Rhombohedral graphite features peculiar electronic properties, including persistence of low-energy surface bands of a topological nature. Here, we study the contribution of electron-hole excitations towards inelastic light scattering in thin films of rhombohedral graphite. We show that, in contrast to the featureless electron-hole contribution towards Raman spectrum of graphitic films with Bernal stacking, the inelastic light scattering accompanied by electron-hole excitations in crystals with rhombohedral stacking produces distinct features in the Raman signal which can be used both to identify the stacking and to determine the number of layers in the film., Comment: 15 pages in preprint format, 4 figures, accepted version

Using the continuum model, we investigate theoretically contribution of the low-energy electronic excitations to the Raman spectrum of superconducting monolayer graphene. We consider superconducting phases characterised by an isotropic order parameter in a single valley and find a Raman peak at a shift set by the size of the superconducting gap. The height of this peak is proportional to the square root of the gap and the third power of the Fermi level, and we estimate its quantum efficiency as $I\sim10^{-14}$., Comment: 7 pages, 2 figures

Direct reaction techniques are powerful tools to study the single-particle nature of nuclei. Performing direct reactions on short-lived nuclei requires radioactive ion beams produced either via fragmentation or the Isotope Separation OnLine (ISOL) method. Some of the most interesting regions to study with direct reactions are close to the magic numbers where changes in shell structure can be tracked. These changes can impact the final abundances of explosive nucleosynthesis. The structure of the chain of tin isotopes is strongly influenced by the Z=50 proton shell closure, as well as the neutron shell closures lying in the neutron-rich, N=82, and neutron-deficient, N=50, regions. Here we present two examples of direct reactions on exotic tin isotopes. The first uses a one-neutron transfer reaction and a low-energy reaccelerated ISOL beam to study states in 131Sn from across the N=82 shell closure. The second example utilizes a one-neutron knockout reaction on fragmentation beams of neutron-deficient 106,108Sn. In both cases, measurements of gamma rays in coincidence with charged particles proved to be invaluable., Comment: 11 pages, 5 figures, Zakopane Conference on Nuclear Physics "Extremes of the Nuclear Landscape", Zakopane, Poland, August 31 - September 7, 2014

We present 21-cm HI line and optical R-band observations for a sample of 26 edge-on galaxies. The HI observations were obtained with the Westerbork Synthesis Radio Telescope, and are part of the WHISP database (Westerbork HI Survey of Spiral and Irregular Galaxies). We present HI maps, optical images, and radial HI density profiles. We have also derived the rotation curves and studied the warping and lopsidedness of the HI disks. 20 out of the 26 galaxies of our sample are warped, confirming that warping of the HI disks is a very common phenomenon in disk galaxies. Indeed, we find that all galaxies that have an extended HI disk with respect to the optical are warped. The warping usually starts around the edge of the optical disk. The degree of warping varies considerably from galaxy to galaxy. Furthermore, many warps are asymmetric, as they show up in only one side of the disk or exhibit large differences in amplitude in the approaching and receding sides of the galaxy. These asymmetries are more pronounced in rich environments, which may indicate that tidal interactions are a source of warp asymmetry. A rich environment tends to produce larger warps as well. The presence of lopsidedness seems to be related to the presence of nearby companions., Comment: To appear in Astronomy & Astrophysics

After studying the orientation of a warp generated by a companion satellite, we show that the Galactic Warp would be oriented in a different way if the Magellanic Clouds were its cause. We have treated the problem analytically, and complemented it with numerical N-Body simulations., Comment: 5 pages, 5 figures, submitted to MNRAS

Secondary infall in galaxies could cause the angular momentum of the outer halo to change its orientation. The generation of warps due to this effect is studied using N-body simulations., Comment: 3 pages, with 3 figures. Proceedings of the Halo Workshop, UC Santa Cruz, (Aug, 1997). LaTeX, using PASP macro paspconf.sty

We provide a new tool to interpret the large scale structure of the Universe. As suggested in Paper II, energy density filaments could have been produced by subjacent magnetic flux tubes when the Universe was dominated by radiation. In more recent time epochs, small scale filaments have evolved in a complicated way, but large scale filaments have probably survived and should be identified with present observed matter filaments of clusters. A primordial magnetic field lattice made up of magnetic flux tubes would then have originated a matter lattice made up of cluster filaments. Taking into account some restrictions in the magnetic field configuration we speculate what type of matter network this would have generated. The simplest lattice is made up of octohedra connected at their vertexes, reminding us of a structure of superimposed egg cartons. The vertexes would correspond to large superclusters, which would therefore have eight filaments emerging from them. Some observational evidence is found in the Local Supercluster, which is spider-like, with eight legs., Comment: 4 pages, latex using A&A macros v 3, figures available upon request. Full version with figures available as gzipped ps at http://deneb.ugr.es/papers/bmf3.ps.gz