Two-dimensional topological insulator edge state backscattering by dephasing

To understand the seemingly absent temperature dependence in the conductance of two-dimensional topological insulator edge states, we perform a numerical study which identifies the quantitative influence of the combined effect of dephasing and elastic scattering in charge puddles close to the edges. We show that this mechanism may be responsible for the experimental signatures in HgTe/CdTe quantum wells if the puddles in the samples are large and weakly coupled to the sample edges. We propose experiments on artificial puddles which allow one to verify this hypothesis and to extract the real dephasing time scale using our predictions. In addition, we present a method to include the effect of dephasing in wave-packet-time-evolution algorithms.

Figure 1

Snapshots of the calculated wave function (the color encodes the spin) in the device geometry. A wave packet is approaching a puddle (top panel) in which it is fully spin-mixed by spin-orbit scattering (bottom). A video of the dynamics including dephasing is available in the Supplemental Material [24].

Figure 2

Time-dependent probability density in a puddle of length $L$ close to the edge which is traversed by a wave packet starting on the edge close to the puddle at $t=0\mathrm{ps}$; see Fig. 1. (a) Behavior for short times showing the steep rise in density from the wave packet entering the puddle and a small fraction which is leaving the puddle after traversing it ballistically. Most of the density decays linearly (black dashed fit lines), for longer times shown in (b). The inset shows the extracted linear decay coefficients ${\tau }_{\mathrm{lin}}$ (see main text) from the fit as a function of $L$ together with a power-law fit. (c) Log-log plot of the derivative of the density (the current) demonstrating also the power-law decay of the density for long times.

Figure 3

Average transmission of a single quantum dot at the edge as a function of the dephasing time for different dot sizes. The full lines are evaluated from the full time-dependent density, using Eq. (1), while the dotted lines show the result from Eq. (2), assuming a linear decay.

Figure 4

(a)–(c) Time-dependent density in the puddle obtained including different effective dephasing times in the time evolution. The colors correspond to different puddle geometries and couplings as shown in the inset in (d). (d) Averaged transmission through the puddle as a function of the chosen dephasing time for the different puddle geometries. The dashed lines are fits to the numerical data (symbols) using Eq. (2).

Figure 5

The figure illustrates the workings of the dephasing algorithm. At a dephasing event, the current wave function—here showing a wave packet spread in an electrostatic puddle (the color encodes the spin)—is spectrally decomposed in a set of pseudo-eigenstates and recomposed with random phases, leading to a new dephased wave function. A video using this type of dephasing is available in the Supplemental Material [24].