Multiple crossings of Landau levels of two-dimensional fermions in double HgTe quantum wells

The double quantum well systems consisting of two HgTe layers separated by a tunnel-transparent barrier are expected to manifest a variety of phase states including two-dimensional gapless semimetal and two-dimensional topological insulator. The presence of several subbands in such systems leads to a rich filling factor diagram in the quantum Hall regime. We have performed magnetotransport measurements of the HgTe-based double quantum wells in both a gapless and gapped state and observed numerous crossings between the Landau levels belonging to different subbands. We analyze the Landau level crossing patterns and compare them to the results of theoretical calculations.

Figure 1

(a) Band profile of the symmetric [013]-grown HgTe DQW with $d=6.5$ nm, $t=3$ nm, and Cd content $x_{\text{Cd}}=0.65$. (b) Energy dispersion of 2D subbands along two directions of the wave vector $\mathbf{k}$ in the growth plane $xy, k_y=0$ ([10]), and $k_y=k_x$ ([11]).

Figure 2

Zero-field resistance (blue), longitudinal (red) and Hall (black) resistances at $B=4$ T and $T=4.2$ K as functions of the gate bias for the gapless ($d=6.5$ nm, $x_{\text{Cd}}=0.65$) double quantum well. The top panel shows the device layout and numbering of the probes.

Figure 3

The conductivities ${\sigma }_{xx}$ (a) and ${\sigma }_{xy}$ (b) as functions of the gate voltage and magnetic field for a single quantum well with Dirac cone energy spectrum, and traces of ${\sigma }_{xx}$ and ${\sigma }_{xy}$ at $B=3$ T (c).

Figure 4

The conductivities ${\sigma }_{xx}$ (a) and ${\sigma }_{xy}$ (b) as functions of the gate voltage and magnetic field for the gapless double quantum well, and traces of ${\sigma }_{xx}$ and ${\sigma }_{xy}$ at $B=4$ T (c).

Figure 5

(a) Calculated energy spectrum in the symmetric double quantum well with $d=6.5$ nm, $t=3$ nm, and $x_{\text{Cd}}=0.65$. The color map of $dR(N_s,B)/d{N}_s$ versus $N_s$ and $B$ at $T=4.2$ K is given for low (b) and high (c) filling factors. Circles indicate LL crossing points, the empty circle stands for the anticrossing point. The numbers at the right margin and inside the map represent the filling factors $\nu$.

Figure 6

(a) Calculated energy spectrum (conduction band only) in the biased (gapped) double quantum well with $d=6$ nm, $t=3$ nm, and $x_{\text{Cd}}=0.37$. (b) The color map of $dR(N_s,B)/d{N}_s$ versus $N_s$ and $B$ at $T=4.2$ K. Circles indicate LL crossing points, the empty circle stands for the anticrossing point. The numbers at the right margin and inside the map represent the filling factors $\nu$.