Significance The physics responsible for most of the interannual geomagnetic field changes, continually recorded by satellites for 20 years, is a long-standing open issue. By analyzing magnetic data, we detect Magneto–Coriolis waves in the Earth’s outer core that account for a significant part of this signal. We further propose theoretical advances in the physical characterization of these waves, enabling a deeper understanding of the dynamics behind the geomagnetic signal. It should allow one to better sketch the heterogeneous magnetic field deep within the core, shedding further light on the mechanisms that sustain the geodynamo. Our interpretation does not require the presence of a stratified layer at the top of the core, with potent consequences regarding the Earth’s thermal history.

We propose a robust and efficient algorithm for computing bound states of infinite tightbinding systems that are made up of a finite scattering region connected to semi-infinite leads. Our method uses wave matching in close analogy to the approaches used to obtain propagating states and scattering matrices. We show that our algorithm is robust in presence of slowly decaying bound states where a diagonalization of a finite system would fail. It also allows to calculate the bound states that can be present in the middle of a continuous spectrum. We apply our technique to quantum billiards and the following topological materials: Majorana states in 1D superconducting nanowires, edge states in the 2D quantum spin Hall phase, and Fermi arcs in 3D Weyl semimetals.

Simulations of quantum transport in coherent conductors have evolved into mature techniques that are used in fields of physics ranging from electrical engineering to quantum nanoelectronics and material science. The most efficient general-purpose algorithms have a computational cost that scales as L 6...7 in 3D, which on the one hand is a substantial improvement over older algorithms, but on the other hand still severely restricts the size of the simulation domain, limiting the usefulness of simulations through strong finite-size effects. Here, we present a novel class of algorithms that, for certain systems, allows to directly access the thermodynamic limit. Our approach, based on the Green's function formalism for discrete models, targets systems which are mostly invariant by translation, i.e. invariant by translation up to a finite number of orbitals and/or quasi-1D electrodes and/or the presence of edges or surfaces. Our approach is based on an automatic calculation of the poles and residues of series expansions of the Green's function in momentum space. This expansion allows to integrate analytically in one momentum variable. We illustrate our algorithms with several applications: devices with graphene electrodes that consist of half an infinite sheet; Friedel oscillation calculations of infinite 2D systems in presence of an impurity; quantum spin Hall physics in presence of an edge; the surface of a Weyl semi-metal in presence of impurities and electrodes connected to the surface. In this last example, we study the conduction through the Fermi arcs of the topological material and its resilience to the presence of disorder. Our approach provides a practical route for simulating 3D bulk systems or surfaces as well as other setups that have so far remained elusive.

Summary We present an update of the geomagnetic data assimilation tool pygeodyn, use it to analyze ground and satellite-based geomagnetic datasets, and report new findings on the dynamics of the Earth’s outer core on interannual to decadal time-scales. Our results support the idea that quasi-geostrophic Magneto-Coriolis waves, recently discovered at a period of 7 years, also operate on both shorter and longer time-scales, specifically in period bands centered around 3.5 and 15 years. We revisit the source of interannual variations in the length of day and argue that both geostrophic torsional Alfvén waves and quasi-geostrophic Magneto-Coriolis waves can possibly contribute to spectral lines that have been isolated around 8.5 and 6 years. A significant improvement to our ensemble Kalman filter algorithm comes from accounting for cross-correlations between variables of the state vector forecast, using the ‘Graphical lasso’ method to help stabilize the correlation matrices. This allows us to avoid spurious shrinkage of the model uncertainties while (i) conserving important information contained in off-diagonal elements of the forecast covariance matrix, and (ii) considering a limited number of realizations, thus reducing the computational cost. Our updated scheme also permits us to use observations either in the form of Gauss coefficient data or more directly as ground-based and satellite-based virtual observatory series. It is thanks to these advances that we are able to place global constraints on core dynamics even at short periods.