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We experimentally and theoretically study the dynamics of a one-dimensional array of pendula with a mild spatial gradient in their self-frequency and where neighboring pendula are connected with weak and alternating coupling. We map their dynamics to the topological Su-Schrieffer-Heeger (SSH) model of charged quantum particles on a lattice with alternating hopping rates in an external electric field. By directly tracking the dynamics of a wavepacket in the bulk of the lattice, we observe Bloch oscillations, Landau-Zener transitions, and coupling between the isospin (i.e. the inner wave function distribution within the unit cell) and the spatial degrees of freedom (the distribution between unit cells). We then use Bloch oscillations in the bulk to directly measure the non-trivial global topological phase winding and local geometric phase of the band. We measure an overall evolution of 3.1 $\pm$ 0.2 radians for the geometrical phase during the Bloch period, consistent with the expected Zak phase of $\pi$. Our results demonstrate the power of classical analogs of quantum models to directly observe the topological properties of the band structure, and sheds light on the similarities and the differences between quantum and classical topological effects., Comment: 17 pages, 4 figures

In 3+1 dimensional spacetime, two vector gauge anomalies are known: The chiral anomaly and the mixed axial-gravitational anomaly. While the former is well documented and tied to the presence of a magnetic field, the latter instead requires a nonzero spacetime curvature, which has made it rather difficult to study. In this work, we show that a quantum anomaly arises in the second-order electrical response for zero magnetic field, which creates a dc-current that can be either longitudinal or transverse to electric field. Consequently, the continuity equation for the chiral current is not conserved at order $\tau^{-1}$, where $\tau$ is the quasiparticle relaxation time. We can identify the anomaly as a mixed axial-gravitational one, and predict a material in which the anomaly-induced current can be isolated in a purely electrical measurement. Our findings indicate that charge transport generically derives from quasiparticle motion in an emergent curved spacetime, with potentially far-reaching consequences for all types of response functions., Comment: 6+2 pages, 4 figures

Weyl semimetals in a magnetic field give rise to interesting non-local electronic orbits: the ballistic transport through the bulk enabled by the chiral Landau levels is combined with a momentum-space sliding along the surface Fermi-arc driven by the Lorentz force. Bulk chiral Landau levels can also be induced by axial fields whose sign depends on the chirality of the Weyl point. However, the microscopic perturbations that give rise to them can be described in terms of gauge fields only in the low-energy sectors around the Weyl points. In addition, since pseudo-fields are intrinsic, there is no apparent reason for a Lorentz force that causes sliding along the Fermi-arcs. Therefore, the existence of non-local orbits driven exclusively by pseudo-fields is not obvious. Here, we show that for systems with at least four Weyl points in the bulk spectrum, non-local orbits can be induced by axial fields alone. We discuss the underlying mechanisms by a combination of analytical semi-classical theory, the microscopic numerical study of wave-packet dynamics, and a surface Green's function analysis., 12 pages, 5 figures