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Theory of statistical topological insulators

Project description

A theoretical framework to characterise a novel class of topological insulators

Topology, a branch of mathematics with its origins in the late 1800s, is concerned with properties that are preserved or invariant under deformations. Over the past 15 years, an increasing number of unique and exotic topological materials have been discovered, such as topological insulators whose surfaces are conducting while the underlying bulk is insulating. The surface conduction is protected by the topological properties of the bulk if a fundamental symmetry is present. The European Research Council-funded STATOPINS project will investigate to what degree the protection holds when the protecting symmetry is only present in a statistical sense (on average) and develop a general theory of such ‘statistical topological insulators’.


Topological insulators (TI) are a novel class of materials with insulating bulk and conducting surface. The conduction of the surface is protected by the topological properties of the bulk, as long as a fundamental symmetry is present (for instance time-reversal symmetry). My goal is to investigate to what limits does the protection hold in cases where the protecting symmetry is broken, and only present in statistical sense, after averaging over the disordered ensemble. In a pilot study I showed that materials that are protected by such average symmetry, which I have called “statistical topological insulators” (STI) significantly extend the classification of topological phases of matter and promise new methods to robustly control the conducting surface properties. I plan to develop a general theory of STI for physically relevant symmetries, describe the observable properties of their protected surface states, invent ways to predict whether materials are expected to be STI, and explore the generalization of STIs to strongly interacting topological phases of matter. I expect that the outcome of my research will significantly extend our understanding of topological phases of matter, and provide new ways to design materials with robust properties.



Net EU contribution
€ 1 355 103,00
Stevinweg 1
2628 CN Delft

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West-Nederland Zuid-Holland Delft en Westland
Activity type
Higher or Secondary Education Establishments
Other funding
€ 0,00

Beneficiaries (1)