42 research outputs found
Observation of a phononic quadrupole topological insulator
The modern theory of charge polarization in solids is based on a generalization of Berry’s phase. The possibility of the quantization of this phase arising from parallel transport in momentum space is essential to our understanding of systems with topological band structures. Although based on the concept of charge polarization, this same theory can also be used to characterize the Bloch bands of neutral bosonic systems such as photonic or phononic crystals. The theory of this quantized polarization has recently been extended from the dipole moment to higher multipole moments. In particular, a two-dimensional quantized quadrupole insulator is predicted to have gapped yet topological one-dimensional edge modes, which stabilize zero-dimensional in-gap corner states. However, such a state of matter has not previously been observed experimentally. Here we report measurements of a phononic quadrupole topological insulator. We experimentally characterize the bulk, edge and corner physics of a mechanical metamaterial (a material with tailored mechanical properties) and find the predicted gapped edge and in-gap corner states. We corroborate our findings by comparing the mechanical properties of a topologically non-trivial system to samples in other phases that are predicted by the quadrupole theory. These topological corner states are an important stepping stone to the experimental realization of topologically protected wave guides in higher dimensions, and thereby open up a new path for the design of metamaterials
Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
The discovery of topological states of matter has profoundly augmented our
understanding of phase transitions in physical systems. Instead of local order
parameters, topological phases are described by global topological invariants
and are therefore robust against perturbations. A prominent example thereof is
the two-dimensional integer quantum Hall effect. It is characterized by the
first Chern number which manifests in the quantized Hall response induced by an
external electric field. Generalizing the quantum Hall effect to
four-dimensional systems leads to the appearance of a novel non-linear Hall
response that is quantized as well, but described by a 4D topological invariant
- the second Chern number. Here, we report on the first observation of a bulk
response with intrinsic 4D topology and the measurement of the associated
second Chern number. By implementing a 2D topological charge pump with
ultracold bosonic atoms in an angled optical superlattice, we realize a
dynamical version of the 4D integer quantum Hall effect. Using a small atom
cloud as a local probe, we fully characterize the non-linear response of the
system by in-situ imaging and site-resolved band mapping. Our findings pave the
way to experimentally probe higher-dimensional quantum Hall systems, where new
topological phases with exotic excitations are predicted