Backscattering of Dirac Fermions in HgTe Quantum Wells with a Finite Gap

The density-dependent mobility of $n$-type HgTe quantum wells with inverted band ordering has been studied both experimentally and theoretically. While semiconductor heterostructures with a parabolic dispersion exhibit an increase in mobility with carrier density, high-quality HgTe quantum wells exhibit a distinct mobility maximum. We show that this mobility anomaly is due to backscattering of Dirac fermions from random fluctuations of the band gap (Dirac mass). Our findings open new avenues for the study of Dirac fermion transport with finite and random mass, which so far has been hard to access.

Figure 1

Hall and magnetoresistance for sample no. 6 at zero gate voltage. The measurement yields an electron mobility of $1.1\times {10}^6{\mathrm{cm}}^{-2}/\mathrm{V}·\mathrm{s}$ and a carrier density of $4.3\times {10}^{11}{\mathrm{cm}}^{-2}$. Inset: Micrograph of the Hall bar structure.

Figure 2

Mobility $\mu$ versus carrier density $n$ for six HgTe QWs (1–6). The experimental $\mu (n)$ dependence (thick lines), including the appearance of the maximum, agrees well with our model [thin gray (red) lines] that takes into account the competition of charged-impurity disorder and QW thickness fluctuations. Inset: Band gap $M$ versus QW thickness $d$ [sample 1 has a positive band gap, sample 2 has approximately zero-gap, while the rest 3–6 are in the inverted regime]. The pronounced maximum is observed in high-quality inverted samples 3, 4, and 6 where the impurity concentration is sufficiently low (see also Table ).

Figure 3

(a) Polar plot of the angular dependence of the normalized scattering rate $w(\theta )$ for massless and massive ($M=-15\mathrm{meV}$ and ${\zeta }^M=1.5\times {10}^{-3}$) Dirac fermions [see Eqs. (5, 6)]. Massive carriers show strong backscattering at angles $\pi /2<\theta <3\pi /2$. (b) Polar plot of the normalized function $w(\theta )$ for different carrier densities $n$ in the inverted regime ($M=-15\mathrm{meV}$ and ${\zeta }^M=1.5\times {10}^{-3}$). The large-angle scattering is enhanced with increasing $n$, which accounts for the nonmonotonic mobility $\mu (n)$ in Fig. 2.