Persistence of a Two-Dimensional Topological Insulator State in Wide HgTe Quantum Wells

Our experimental studies of electron transport in wide (14 nm) HgTe quantum wells confirm the persistence of a two-dimensional topological insulator state reported previously for narrower wells, where it was justified theoretically. Comparison of local and nonlocal resistance measurements indicate edge state transport in the samples of about 1 mm size at temperatures below 1 K. Temperature dependence of the resistances suggests an insulating gap of the order of a few meV. In samples with sizes smaller than $10\mu \mathrm{m}$ a quasiballistic transport via the edge states is observed.

Figure 1

(a) Cross section of a 3D TI sample (schematic) with surface state channels shown in red. As the thickness of the sample decreases, a transition to 2D TI takes place. (b) Energy spectrum of size-quantized subbands in a symmetric 14 nm wide ${\mathrm{Cd}}_{0.65}{\mathrm{Hg}}_{0.35}\mathrm{Te}/\mathrm{HgTe}/{\mathrm{Cd}}_{0.65}{\mathrm{Hg}}_{0.35}\mathrm{Te}$ QW, calculated numerically by using Kane Hamiltonian (the Kane model parameters are presented in the Supplemental Material [10]). Dashed (blue) lines show the spectrum of interface states at a single $\mathrm{HgTe}/{\mathrm{Cd}}_{0.65}{\mathrm{Hg}}_{0.35}\mathrm{Te}$ boundary under approximation that mixing of these states with hh states is neglected. (c) A magnified picture of two upper hh subbands and the expected edge state spectrum, thin (red) lines, in the gap between them.

Figure 2

Local (a) and nonlocal (b) resistance at different temperatures, sample I, $B=0$ (the inset shows a schematic view of the sample). (c) Temperature dependence of local and nonlocal resistance when the Fermi energy is situated in the center of the insulating bulk gap (the inset shows calculations).

Figure 3

$R(V_g)$ dependences for local (red curves) and nonlocal (green curves or a lighter shade of grey) resistance measurement configurations obtained in two different types of microscopic samples. The samples layouts are shown schematically in the insets. All curves were obtained at 0.2 K except the black curves measured at temperatures 4.2 and 4.6 K. Opposite to each curve the corresponding measurement configuration is shown schematically. The dashed horizontal lines mark the resistance values expected for these configurations in the case of a purely ballistic transport via edge current states.