Abstract
Bloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to a force. Observed in a wide range of synthetic systems, BOs are intrinsically related to geometric and topological properties of the underlying band structure. This has established BOs as a prominent tool for the detection of Berry-phase effects, including those described by non-Abelian gauge fields. In this work, we unveil a unique topological effect that manifests in the BOs of higher-order topological insulators through the interplay of non-Abelian Berry curvature and quantized Wilson loops. It is characterized by an oscillating Hall drift synchronized with a topologically-protected inter-band beating and a multiplied Bloch period. We elucidate that the origin of this synchronization mechanism relies on the periodic quantum dynamics of Wannier centers. Our work paves the way to the experimental detection of non-Abelian topological properties through the measurement of Berry phases and center-of-mass displacements.
Highlights
Bloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to a force
The Wilson loop measurement of ref. 31 highlighted a fundamental relation between two intriguing properties of multi-band systems: the quantization of Wilson loops, a topological property related to the Wilczek-Zee connection[32], and the existence of “multiple Bloch oscillations”, which are characterized by a multiplied Bloch period[31,33,34,35,36,37,38,39]
We identify a distinct topological effect that manifests in the BOs of higher-order topological insulators (HOTIs)
Summary
On the C path, the Berry curvature has only off-diagonal components and the Hall dynamics is determined by the relative phase φ, whereas θ is a constant of motion In this case, the populations of the two bands do not exchange over time but the relative phase does by an angle π. The projected Hamiltonian reveals how the external force induces a quantum dynamics between the eigenstates of non-commuting position operators, in the form of a Rabi oscillation This result is in sharp contrast with the classical point-charge picture introduced in ref. A force oriented along the diagonal axes allows to synchronize the Wannier centers dynamics with the BOs, whereas the other directions yield out-of-sync oscillations that does not bring the wavepacket back to its initial position at integer multiples of the fundamental Bloch period.
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