arXiv subjects

Stephen Spurrier

Publications and source records attributed to Stephen Spurrier.

3 recordsLinked to original sources

arXiv2020

Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks

We establish an analytic low-energy theory describing higher-order topological insulator (HOTI) phases in quasicrystalline systems. We apply this to a model consisting of two stacked Haldane models with oppositely propagating edge modes, analogous to the Kane-Mele model, and with a $30^\circ$ twist. We show that the resulting localized modes at corners, characteristic of a HOTI, are not associated with conventional mass inversions but are instead associated with what we dub "fractional mass kinks". By generalizing the low-energy theory, we establish a classification for arbitrary $ n $-fold rotational symmetries. We also derive a relationship between corner modes in a bilayer and disclination modes in a single layer. By using numerics to go beyond the weak-coupling limit, we show that a hierarchy of additional gaps occurs due to the quasiperiodicity, which also harbor corner-localized modes.

cond-mat.mes-hall↗

arXiv2019

Theory of quantum oscillations in quasicrystals: Quantizing spiral Fermi surfaces

We show that electronic materials with disallowed rotational symmetries that enforce quasiperiodic order can exhibit quantum oscillations and that these are generically associated with exotic "spiral Fermi surfaces." These Fermi surfaces are self-intersecting, and characterized by a winding number of their surface tangent---a topological invariant---that is larger than one. We compute the nature of the quantum oscillations in two experimentally relevant settings which give rise to spiral Fermi surfaces: a "nearly-free-electron" quasicrystal, and \ang{30} twisted bilayer graphene.

cond-mat.mes-hall↗

arXiv2018

Semiclassical Dynamics, Berry Curvature and Spiral Holonomy in Optical Quasicrystals

We describe the theory of the dynamics of atoms in two-dimensional quasicrystalline optical lattices. We focus on a regime of shallow lattice depths under which the applied force can cause Landau-Zener tunneling past a dense hierarchy of gaps in the quasiperiodic energy spectrum. We derive conditions on the external force that allow for a "semiadiabatic" regime in which semiclassical equations of motion can apply, leading to Bloch oscillations between the edges of a pseudo-Brillouin-zone. We verify this semiclassical theory by comparing to the results of an exact numerical solution. Interesting features appear in the semiclassical dynamics for the quasicrystal for a particle driven in a cyclic trajectory around the corner of the pseudo-Brillouin-zone: The particle fails to return to its initial state, providing a realization of a "spiral holonomy" in the dynamics. We show that there can appear anomalous velocity contibutions, associated with nonzero Berry curvature. We relate these to the Berry phase associated with the spiral holonomy, and show how the Berry curvature can be accessed from the semiclassical dynamics. Finally, by identifying the pseudo-Brillouin-zone as a higher genus surface, we show that the Chern number classification for periodic systems can be extended to a quasicrystal, thereby determining a topological index for the system.

cond-mat.quant-gas↗