Excitable media are ubiquitous in nature, and in such systems the local excitation tends to self-organize in traveling waves, or in rotating spiral-shaped patterns in two or three spatial... Show moreExcitable media are ubiquitous in nature, and in such systems the local excitation tends to self-organize in traveling waves, or in rotating spiral-shaped patterns in two or three spatial dimensions. Examples include waves during a pandemic or electrical scroll waves in the heart. Here we show that such phenomena can be extended to a space of four or more dimensions and propose that connections of excitable elements in a network setting can be regarded as additional spatial dimensions. Numerical simulations are performed in four dimensions using the FitzHugh-Nagumo model, showing that the vortices rotate around a twodimensional surface which we define as the superfilament. Evolution equations are derived for general superfilaments of codimension two in an N-dimensional space, and their equilibrium configurations are proven to be minimal surfaces. We suggest that biological excitable systems, such as the heart or brain which have nonlocal connections can be regarded, at least partially, as multidimensional excitable media and discuss further possible studies in this direction. Show less
Materials with an irreversible response to cyclic driving exhibit an evolving internal state which, in principle, encodes information on the driving history. Here we realize irreversible... Show moreMaterials with an irreversible response to cyclic driving exhibit an evolving internal state which, in principle, encodes information on the driving history. Here we realize irreversible metamaterials that count mechanical driving cycles and store the result into easily interpretable internal states. We extend these designs to aperiodic metamaterials that are sensitive to the order of different driving magnitudes, and realize “lock and key” metamaterials that only reach a specific state for a given target driving sequence. Our metamaterials are robust, scalable, and extendable, give insight into the transient memories of complex media, and open new routes towards smart sensing, soft robotics, and mechanical information processing. Show less
Mechanisms-collections of rigid elements coupled by perfect hinges which exhibit a zero-energy motion-motivate the design of a variety of mechanical metamaterials. We enlarge this design space by... Show moreMechanisms-collections of rigid elements coupled by perfect hinges which exhibit a zero-energy motion-motivate the design of a variety of mechanical metamaterials. We enlarge this design space by considering pseudo-mechanisms, collections of elastically coupled elements that exhibit motions with very low energy costs. We show that their geometric design generally is distinct from those of true mechanisms, thus opening up a large and virtually unexplored design space. We further extend this space by designing building blocks with bistable and tristable energy landscapes, realize these by 3D printing, and show how these form unit cells for multistable metamaterials. Show less
A spatially oscillating pair potential Delta(r) = Delta(0)e(2iK center dot r) with momentum K > Delta(0)/hv drives a deconfinement transition of the Majorana bound states in the vortex cores of... Show moreA spatially oscillating pair potential Delta(r) = Delta(0)e(2iK center dot r) with momentum K > Delta(0)/hv drives a deconfinement transition of the Majorana bound states in the vortex cores of a Fu-Kane heterostructure (a 3D topological insulator with Fermi velocity v, on a superconducting substrate with gap Delta(0), in a perpendicular magnetic field). In the deconfined phase at zero chemical potential the Majorana fermions form a dispersionless Landau level, protected by chiral symmetry against broadening due to vortex scattering. The coherent superposition of electrons and holes in the Majorana Landau level is detectable as a local density of states oscillation with wave vector root K-2 - (Delta(0)/hv)(2). The striped pattern also provides a means to measure the chirality of the Majorana fermions. Show less
In LaAlO3/SrTiO3 heterostructures, a still poorly understood phenomenon is that of electron trapping in back-gating experiments. Here, by combining magnetotransport measurements and self-consistent... Show moreIn LaAlO3/SrTiO3 heterostructures, a still poorly understood phenomenon is that of electron trapping in back-gating experiments. Here, by combining magnetotransport measurements and self-consistent Schrödinger-Poisson calculations, we obtain an empirical relation between the amount of trapped electrons and the gate voltage. The amount of trapped electrons decays exponentially away from the interface. However, contrary to earlier observations, we find that the Fermi level remains well within the quantum well. The enhanced trapping of electrons induced by the gate voltage can therefore not be explained by a thermal escape mechanism. Further gate sweeping experiments strengthen that conclusion. We propose a new mechanism which involves the electromigration and clustering of oxygen vacancies in SrTiO3 and argue that such electron trapping is a universal phenomenon in SrTiO3-based two-dimensional electron systems. Show less
