Photon-Inhibited Topological Transport in Quantum Well Heterostructures

Here we provide a picture of transport in quantum well heterostructures with a periodic driving field in terms of a probabilistic occupation of the topologically protected edge states in the system. This is done by generalizing methods from the field of photon-assisted tunneling. We show that the time dependent field dresses the underlying Hamiltonian of the heterostructure and splits the system into sidebands. Each of these sidebands is occupied with a certain probability which depends on the drive frequency and strength. This leads to a reduction in the topological transport signatures of the system because of the probability to absorb or emit a photon. Therefore when the voltage is tuned to the bulk gap the conductance is smaller than the expected $2e^2/h$. We refer to this as photon-inhibited topological transport. Nevertheless, the edge modes reveal their topological origin in the robustness of the edge conductance to disorder and changes in model parameters. In this work the analogy with photon-assisted tunneling allows us to interpret the calculated conductivity and explain the sum rule observed by Kundu and Seradjeh.

Figure 1

The two device geometries considered in this work. Left is a two-terminal device labeled with leads left (“L”), and right (“R”). On the right is a six terminal device labeled with leads 1 through 6. The sites coupled to leads have a solid rectangle around them.

Figure 2

Plots of the differential two-terminal conductivity as a function of $V_{\mathrm{ext}}$. Left: Results for various disorder strengths. Right: Various values of the system size ($L$) and the lead coupling parameter ($\mathrm{\Gamma }$).

Figure 3

Disorder averaged summed conductivity, Eq. (4). The inset shows a zoomed in picture of the first area of conductivity quantization. Note some error bars in the insere too small to see.