The purpose of this proposal is to explore the combination and “sculpturing” of topological materials in novel heterostructure setups. In particular we will consider:
(i) Conventional sandwich structures with novel components including topological superconductors and Weyl semimetals. Such setups are experimentally realisable using current technology, and promises ample new phenomena, yet it is still a largely unexplored topic. Here we willinvestigate proximity and (in)commensurability effects as well as non- equilibrium and transport phenomena in these heterostructures.
(ii) Interfaces with curvature that trigger unusual quantum anomalies and responses. At the next level of sophistication I envisage the design of topological systems that feature an effective curvature, e.g. in terms of curved interfaces between materials with a different effective
description. In particular, two Weyl semimetals with different tilt parameters may be used to create a curved interface that activates a gravitational anomaly which is fundamentally distinct from the well-studied chiral anomaly that occurs in external electric and magnetic fields.
The present project targets the so-far elusive condensed matter realisation of this anomaly and measurable transport signatures thereof. Moreover, these setups have a natural definition of a Hawking temperature, whose implications for the non-equilibrium properties will be explored in this project.
(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.