Metamaterials (MMs), which include phononic crystals (PCs) as a particular type, exhibit
anomalous wave propagation properties through artificial design of topologies or lattice …

Topological materials, whether in solid state, photonic or acoustic systems, or other
domains, are characterized by bulk topological invariants that remain unchanged as long as …

While Hermiticity lies at the heart of quantum mechanics, recent experimental advances in
controlling dissipation have brought about unprecedented flexibility in engineering non …

The realization of controllable fermionic quantum systems via quantum simulation is
instrumental for exploring many of the most intriguing effects in condensed-matter physics …

INTRODUCTION Physical systems that exhibit topological invariants are naturally endowed
with robustness against perturbations, as was recently demonstrated in many settings in …

There have been significant recent advances in realizing band structures with geometrical
and topological features in experiments on cold atomic gases. This review summarizes …

We extend the theory of dipole moments in crystalline insulators to higher multipole
moments. As first formulated in Benalcazar et al.[Science 357, 61 (2017) SCIEAS 0036-8075 …

The concept of topological phases is a powerful framework for characterizing ground states
of quantum many-body systems that goes beyond the paradigm of symmetry breaking …

The topological phases of matter are characterized using the Berry phase, a geometrical
phase associated with the energy-momentum band structure. The quantization of the Berry …

Originating from the studies of two-dimensional condensed-matter states, the concept of
topological order has recently been expanded to other fields of physics and engineering …