Transition from insulating to metallic phase induced by in-plane magnetic field in HgTe quantum wells

We report transport measurements in HgTe-based quantum wells with well width of 8 nm, corresponding to the quantum spin Hall state, subject to in-plane magnetic field. In the absence of the magnetic field the local and nonlocal resistances behave very similarly, which confirms the edge state transport in our system. In the magnetic field, we observe a monotonic decrease of the resistance with saturation of local resistance, while nonlocal resistance disappears completely, independent of the gate voltage. We believe that this evidence of metallic behavior indicates a transition to a gapless two-dimensional phase, according to theoretical predictions. The influence of disorder on resistivity properties of HgTe quantum wells under in-plane magnetic field is discussed.

Figure 1

Four-terminal local $R_{I=1,4;V=2,3}$ (black) and nonlocal $R_{I=6,2;V=5,3}$ (red dashes) resistances as a function of the gate voltage at $T=4.2$ K and $B=0$ for the Hall bar devices A (a), B (b), and C (c) with dimensions of the gate (length and width) indicated. The numbers indicate the coding of the leads.

Figure 2

Nonlocal resistance as a function of the gate voltage for the Hall bar device B and different nonlocal configurations (from top to bottom): $R_{I=6,2;V=3,5}$, $R_{I=1,2;V=3,5}$, and $R_{I=1,6;V=3,5}$, at $T=4.2$ K and $B=0$.

Figure 3

Four-terminal local $R_{I=1,4;V=2,3}$ resistance as a function of the gate voltage for the Hall bar devices and for different parallel magnetic fields, $T=4.2$ K.

Figure 4

(a) The local $R_{xx}=R_{I=1,4;V=6,5}$ and nonlocal $R_{I=2,6;V=5,3}$ resistances as a function of in-plane magnetic field for device A at $V_g=-3.63$ V, T $=$ 1.5 K. The gate voltage corresponds to the resistance peak. The nonlocal resistance disappears at $B>10$ T.

Figure 5

(a) The local resistance $R_{I=1,2;V=3,5}$ as a function of in-plane magnetic field for different temperatures $T$ (K): 1.5, 2.5, 3.5, 4.2 at $V_g=-2.43$ V. (b) The nonlocal resistance $R_{I=2,6;V=5,3}$ as a function of in-plane magnetic field for different temperatures $T$ (K): 1.5, 3, 3.6, 4.2 at $V_g=-2.4$ V. The gate voltage corresponds to the resistance peak. The nonlocal resistance disappears at $B=12$ T.

Figure 6

The nonlocal $R_{I=1,2;V=3,5}$ resistance as a function of gate voltage for different magnetic fields, $T=4.2$ K.

Figure 7

Dependence of electron energy on 2D wave number $k$ calculated for [001]-grown 8-nm-wide symmetric quantum wells Cd${}_{0.65}$Hg${}_{0.35}$Te/HgTe/Cd${}_{0.65}$Hg${}_{0.35}$Te at zero magnetic field and under in-plane magnetic field $B=10$ T directed along [100]. Dashed lines schematically show edge state spectrum.

Figure 8

Dependence of electron energy on 2D wave number $k$ calculated for [001]-grown 8-nm-wide symmetric quantum wells Cd${}_{0.65}$Hg${}_{0.35}$Te/HgTe/Cd${}_{0.65}$Hg${}_{0.35}$Te at the transition field $B=13.75$ T and at $B=18$ T. Both $\mathbf{B}$ and $\mathbf{k}$ are directed along [100]. Above the transition field the spectrum is gapless.

Figure 9

Magnetic-field dependence of the fraction of 2D plane covered by insulator for spatially inhomogeneous 8-nm-wide symmetric quantum wells Cd${}_{0.65}$Hg${}_{0.35}$Te/HgTe/Cd${}_{0.65}$Hg${}_{0.35}$Te (see text for details). The dashed line shows the result where only well width variations are taken into account.

Figure 10

Fraction of 2D plane covered by insulator as function of electron density for spatially inhomogeneous 8-nm-wide symmetric quantum wells Cd${}_{0.65}$Hg${}_{0.35}$Te/HgTe/Cd${}_{0.65}$Hg${}_{0.35}$Te. The plots are taken for in-plane magnetic fields $B=0$, 5, 10, 12, and 14 T (from top to bottom). The inset shows the dependence of electron density on Fermi energy for the given set of magnetic fields.