Multiferroic Quantum Criticality

The zero-temperature limit of a continuous phase transition is marked by a quantum critical point, which can generate exotic physics that extends to elevated temperatures. Magnetic quantum criticality is now well known, and has been explored in systems ranging from heavy fermion metals to quantum Ising materials. Ferroelectric quantum critical behaviour has also been recently established, motivating a flurry of research investigating its consequences. Here, we introduce the concept of multiferroic quantum criticality, in which both magnetic and ferroelectric quantum criticality occur in the same system. We develop the phenomenology of multiferroic quantum critical behaviour, describe the associated experimental signatures, and propose material systems and schemes to realize it.Comment: 8 pages, 4 figure

Direct evidence for superconductivity in the organic charge density-wave compound alpha-(BEDT-TTF)_2KHg(SCN)_4 under hydrostatic pressure

We present direct evidence of a superconducting state existing in the title compound below 300 mK under quasi-hydrostatic pressure. The superconducing transition is observed in the whole pressure range studied, 0 < P < 4 kbar. However, the character of the transition drastically changes with suppressing the charge-density wave state.Comment: 2 pages, 2 figure

Critical connectedness of thin arithmetical discrete planes

An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its $2$-connectedness. This infimum thickness can be computed thanks to the fully subtractive algorithm. This multidimensional continued fraction algorithm consists, in its linear form, in subtracting the smallest entry to the other ones. We provide a characterization of the discrete planes with critical thickness that have zero intercept and that are $2$-connected. Our tools rely on the notion of dual substitution which is a geometric version of the usual notion of substitution acting on words. We associate with the fully subtractive algorithm a set of substitutions whose incidence matrix is provided by the matrices of the algorithm, and prove that their geometric counterparts generate arithmetic discrete planes.Comment: 18 pages, v2 includes several corrections and is a long version of the DGCI extended abstrac