Phasons and superconductivity in a quasiperiodic material

A new Science Advances paper by Malte's group, with collaborators in TCM and at Materials Science, establishes strong-coupling superconductivity in the quasiperiodic structure adopted by high pressure Bi-III as a consequence of exotic vibrational excitations of a quasiperiodic lattice,

Electrical resistivity in aperiodic high-pressure bismuth-III [Strong coupling superconductivity in a quasiperiodic host-guest structure, Science Advances 4, eaao4793 (2018)]

Most condensed matter physics research is based on the periodicity of crystalline lattices. The existence of repeat units enables advanced concepts such as Bloch's theorem, the reciprocal lattice, the Brillouin zone and the Fermi surface, which have become fundamental to our understanding of solids. However, it has long been known that there are many ordered materials that lack discrete translational symmetry and thereby fall outside the standard paradigm of condensed matter physics. Among them are quasicrystals, but also other quasiperiodic structures such as incommensurately modulated lattices or incommensurate host-guest structures. Intensely investigated by crystallographers, these materials tend to linger outside main-stream condensed matter research, and in particular their electronic and vibrational excitations remain largely unexplored. This paper describes the first detailed investigation of the superconducting and normal state properties of bismuth at high pressure, when it assumes the incommensurate host-guest structure Bi-III. The paper reports an unusually high superconducting upper critical field, the highest in any elemental superconductor to date, and an anomalously strong, linear temperature dependence of the electrical resistivity above the superconducting transition temperature. These findings are interpreted in terms of substantial phonon spectral weight at very low energies, attributed to the sliding or phason mode that can arise only in quasiperiodic systems. The sliding motion in Bi-III involves the movement of chains of bismuth atoms with a certain lattice constant inside tubes of bismuth atoms with a different lattice constant. Because the two lattice constants are incommensurate there is an equal energy manifold of spatial arrangements of the two sub-lattices, and their relative sliding motion can occur without energy barriers, pulling this mode down effectively to zero frequency. This is akin to the phenomenon of superlubricity observed, for instance, between slightly misaligned graphite surfaces. Quasiperiodic structures form an intermediate step between conventional crystalline lattices and full disorder. They present fundamentally new challenges to theory, because Bloch's theorem, one of the cornerstones of condensed matter physics, does not apply to them. Very little is known experimentally about their electronic and vibrational excitations, and this work raises further questions: where do we find instances of similar behaviour in compounds, at ambient pressure? Can we turn the structural frustration of quasiperiodic materials into magnetic frustration of an entirely new variety, by including magnetic elements in the structure, producing novel types of quantum magnets and spin liquids? What are the consequences of lacking discrete translational symmetry for the electronic structure? Will it be possible to detect signatures of the Fermi surface of Bi-III, for instance by quantum oscillation measurements? Can the additional low-lying phonon spectral weight inherent to incommensurate host-guest structures be harnessed to produce strong-coupling superconductors with technologically attractive high critical fields or enhanced transition temperatures, and could the peculiarities of electronic and vibrational states be exploited to produce superior thermoelectrics? It looks like there is a lot of work still to do. (20/4/18)