Spectacular ongoing developments in fabricating high-precision multilayer transition metal oxide
structures, in the engineering of optical meta materials and optical lattices loaded with cold atoms,
provide intriguing new platforms for the study, design and ultimately control of the properties of
novel forms of light and matter. At the same time, the discovery of topological materials is
transforming the way we think of, and search for, collective physical phenomena.
The present proposal embraces this ongoing paradigm shift: instead of mainly aiming to explain
earlier experiments and existing materials, we theoretically explore new possibilities for sculptured
topological phenomena in novel multi-component setups. We ask what there can be rather than
what there already is. In particular, we target effects of incommensurability and dissipation that
have traditionally been seen as detrimental. In fact, there is strong emerging evidence that they lead
to qualitatively new phenomena that are both of fundamental interest and technological relevance.
This leads us to consider two complementary frontiers and their cross-fertilisation:
(i) Strongly correlated phenomena in moiré heterostructures, with focus on systems with
fractional band filling in highly tuneable twisted multilayer systems.
(ii) Dissipative topological phenomena.
(iii) Higher-order topological phases possessing topological corner and hinge states. These very recently discovered systems feature a novel interplay between bulk and crystalline boundary symmetries that is still not fully understood even at the single particle level. We will analyse these systems starting from the viewpoint of a class of exactly solvable lattice models, whereby we make the effect of symmetries and
symmetry breaking explicit and thus pave the way towards classifying these systems as well as exploring their experimental signatures. We will also take first steps toward understanding the role of interactions in these systems.
(iv) Interfaces and extended defects in topologically ordered systems, especially microscopic models of dislocations and interfaces between superconductors and fractional quantum Hall states, with the goal of identifying and simulating non-Abelian parafermions. While being highly sophisticated theoretically, the study of these exotic hybrid systems is exceedingly well motivated by the fundamental physics they entail as well as the potential future harnessing of parafermions that can be—in sharp contrast to the more conventional Majorana fermions—used to perform universal quantum computation. Albeit being distinct in detail, the parallel theoretical study of these setups is expected to bring about several synergy effects, especially conceptually but also regarding the development of numerical techniques. Notably, recurring themes include proximity and commensurability effects and non-equilibrium responses to external probes (i.e. measurements). Moreover, project (i) provides the very basis for the studies in projects (ii) and (iv) while strong interactions and novel forms of topological order naturally links projects (iii) and (iv). Further inspiration will come from the experimental side where I have contact with leading experimentalists in Princeton regarding projects (i) and (ii) and in Stockholm regarding (iii).
It is conceivable that these investigations may in the future lead to profound technological advances in terms of computing, information storage and energy efficient electronics—such applications of topological materials will ultimately require their integration in actual circuits and heterostrusctures as studied here. Yet our focus is firmly on the fundamental physics of these systems, ranging from novel non-equilibrium
phenomena and transport signatures resulting from quantum anomalies, to unusual proximity effects and topological bound states at corners and hinges, and parafermions emerging at defects and interfaces.