  We propose to measure band topology via quantized drift of Bloch oscillations
in a two-dimensional Harper-Hofstadter lattice subjected to tilted fields in
both directions. When the difference between the two tilted fields is large,
Bloch oscillations uniformly sample all momenta, and hence the displacement in
each direction tends to be quantized at multiples of the overall period,
regardless of any momentum of initial state. The quantized displacement is
related to a reduced Chern number defined as a line integral of Berry curvature
in each direction, providing an almost perfect measurement of Chern number. Our
scheme can apply to detect Chern number and topological phase transitions not
only for the energy-separable band, but also for energy-inseparable bands which
cannot be achieved by conventional Thouless pumping or integer quantum Hall
effect.
