The field of topological photonics emerged as one of the most promising areas for
applications in transformative technologies: possible applications are in topological lasers or …

Over the past two decades, following the early developments on maximally localized
Wannier functions, an ecosystem of electronic-structure simulation techniques and software …

We investigate disorder-driven topological phase transitions in quantized electric
quadrupole insulators in two dimensions. We show that chiral symmetry can protect the …

We report the theoretical discovery and characterization of higher-order Floquet topological
phases dynamically generated in a periodically driven system with mirror symmetries. We …

Flat-band superconductivity has theoretically demonstrated the importance of band topology
to correlated phases. In two dimensions, the superfluid weight, which determines the critical …

Topological materials can host edge and corner states that are protected from disorder and
material imperfections. In particular, the topological edge states of mechanical structures …

In this Tutorial, we pedagogically review recent developments in the field of non-interacting
fermionic phases of matter, focusing on the low-energy description of higher-order …

We characterize non-Hermitian band structures by symmetry indicator topological invariants.
Enabled by crystalline inversion symmetry, these indicators allow us to short-cut the …

We use multi-band SSH models to demonstrate a prescription for calculating the correct Zak
phase and winding number of multi-band systems. We verify our prescription by comparing …

Higher-order topological crystalline phases in low-dimensional interacting quantum systems
represent a challenging and largely unexplored research topic. Here, we derive a …