Fractional quantization of the topological charge pumping in a one-dimensional superlattice

Abstract

A one-dimensional quantum charge pump transfers a quantized charge in each pumping cycle. This quantization is topologically robust being analogous to the quantum Hall effect. The charge transferred in a fraction of the pumping period is instead generally unquantized. We show, however, that with specific symmetries in parameter space the charge transferred at well-defined fractions of the pumping period is quantized as integer fractions of the Chern number. We illustrate this in a one-dimensional Harper-Hofstadter model and show that the fractional quantization of the topological charge pumping is independent of the specific boundary conditions taken into account. We further discuss the relevance of this phenomenon for cold atomic gases in optical superlattices.

Simulation and measurement of the fractional particle number in one-dimensional optical lattices

“…In addition, the finite temperature effects do not interfere with the particle transport progression for temperatures smaller than the energy gap [33]. This requires the temperature of the order of 0.08E R /k B ∼ 20 nk (k B is the Boltzmann constant), which has been achieved in current experiments with, e.g., 40 K atoms. So we can conclude that the required Hamiltonian with tunable parameters and the adiabatic condition are able to be realized under realistic circumstances.…”

“…The shift of the Wannier center encodes the adiabatic particle transport (the variation of polarization) as [33,39,40]…”

“…This is an analog of the adiabatic charge pumping proposed by Thouless [32]; however, the parametric driving in our case does not form a closed cycle but only a half one. The topological pumping in cold atom systems and photonic quasi-crystals has been discussed in the contexts of SSH model [33][34][35] and 1D quasi-periodic Harper model [36][37][38][39][40], where the pumping particle is shown to be quantized one over one period and can be fractional over a fraction of one period [40].…”

Electronic interference transport and its electron–phonon interaction in the Sb-doped Bi2Se3nanoplates synthesized by a solvothermal method

“…The same topological invariant was also used to classify the integer quantum Hall effect [3]. There have been continuous interest in the topological charge pumping [4,5,6,7,8,9,10].…”

Effects of dephasing on quantum adiabatic pumping with nonequilibrium initial states

“…In particular, the sum of the Chern numbers of all the filled bands below the Fermi surface determines the number of pumped charges over one adiabatic cycle in a one-dimensional (1D) periodic lattice. To date various quantum pumps have been proposed to study topological phases and topological phase transitions [3][4][5][6][7][8][9][10][11][12]. Thouless's concept, which can be deemed as a dynamical version of the integer quantum Hall effect, is directly simulated this year in two cold-atom experiments [13,14].…”