Macroscopic Floquet topological crystalline steel and superconductor pump

Abstract

The transport of a steel sphere on top of two dimensional periodic magnetic patterns is studied experimentally. Transport of the sphere is achieved by moving an external permanent magnet on a closed loop around the two dimensional crystal. The transport is topological i.e. the steel sphere is transported by a primitive unit vector of the lattice when the external magnet loop winds around specific directions. We experimentally determine the set of directions the loops must enclose for nontrivial transport of the steel sphere into various directions.

Hard topological versus soft geometrical magnetic particle transport

“…Here, we show experimentally and with computer simulations that a macroscopic topological magnetic particle pump [21], that transports paramagnetic or soft magnetic particles across a magnetic lattice, is topological when transporting a small number of particles per unit cell. The transport is robust for those modulation loops of a driving homogeneous external field that share the same topological invariant.…”

“…Our two dimensional magnetic hexagonal lattice is built from an arrangement of NbB-magnets [21]. The lattice ( Fig.…”

“…There are topologically nontrivial trajectories, where the steel sphere ends at a position differing from the initial position by one unit vector of the magnetic lattice. Nontrivial closed reorientation loops in control space are those loops that have loop segments in both, the excess region and the region of the unique minimum [17,21]. Here, the reorientation loop enters the excess region with a longitude φ entry between the Q 2 and the −a 2 directions and exits the excess region between the Q 2 and the a 3 longitudes at φ exit = 4.4π/6.…”

“…We have reported in Refs. [17,21,22] how the transport of a single paramagnetic particle changes as we move the entry longitude 4.4π/6 < φ entry < 8.5π/6 of the reorientation closed loop. Here we briefly repeat the findings which are important for this work.…”

The geometric phase and the dry friction of sleeping tops on inclined planes

“…The geometric phase also named Berry-phase in quantum sytems and Hannay-angle in classical systems is invariant under rescaling of the time schedule with which one passes the path in parameter space. It also carries along a gauge freedom of choice of reference points and the concept has been used in high energy particle physics [4], in solid state physics of topological materials [5][6][7], in the explanation of the rotation of the Foucaultpendulum [8], in the explanation of the propulsion of active swimmers in low Reynolds number fluids [9,10], the propulsion of light in twisted fibers [11,12], the propulsion of acoustic [13] or stochastic [14] waves, the motion of edge waves in coupled gyroscope lattices [15], the rolling of nucleons [16] and in the control of the transport of macroscopic [17] and colloidal [18][19][20][21] particles above magnetic lattices. The independence of the geometric phase of the speed, makes the Foucault pendulum rotation independent of the length of the pendulum as well as independent of the value of the gravitational acceleration, similarly the propulsion of an active shape changing swimmer is independent of the viscosity of the embedding fluid.…”