Revealing the band structure of InSb nanowires by high-field magnetotransport in the quasiballistic regime

The charge transport properties of individual InSb nanowires based transistors are studied at 4.2 K in the quasiballistic regime. The energy level separations at zero magnetic field are extracted from a bias voltage spectroscopy. The magnetoconductance under a magnetic field applied perpendicularly to the nanowire axis is investigated up to 50 T. Owing to the magnetic reduction of the backscattering, the electronic states of the quasi-one-dimensional electron gas are revealed by Landauer-Büttiker conductance quantization. The results are compared to theoretical predictions revealing the spin and orbital degeneracy lifting. At sufficiently high magnetic field the measurements show the evolution to the quantum Hall effect regime with the formation of Landau orbits and conducting edge states.

Figure 1

Computed band structure of an InSb NW device. (a)–(c) Band structure for a magnetic field (a) $B=0$ T, (b) $B=2$ T, and (c) $B=6$ T for, respectively, the top left, middle left, and bottom left graphs. $a$ stands for the lattice parameter. (d) Bottom edge of the eight first subbands ($E_{1–8}$) as a function of the magnetic field. The two colors represent spin up and spin down.

Figure 2

(a) Comparison between the non-self-consistent (NSC) and self-consistent (SC) band structures at $B=0$ T and carrier density $n=2.37\times {10}^6$ ${\mathrm{cm}}^{-1}$ ($V_g-V_{\text{th}}\approx 2.9$ V). The zero of energy is the chemical potential $\mu$. (b) Comparison between the number of occupied bands calculated at $B=0$ T from the NSC, and from the SC band structures. The gate voltage is measured with respect to the threshold voltage $V_{\text{th}}$.

Figure 3

Bias voltage spectroscopy performed on device A at 4.2 K. (a) Conductance vs bias voltage for a set of gate voltages from 8 to 18 V in steps of 0.2 V. (b) Transfer characteristic (blue) at low bias interpolated from the data of (a) superimposed with conductance simulation (red). The low bias conductance of each curve in (a) is represented by black points. (c) Color plot of the transconductance $\partial G/\partial V_g$ derived from data in (a). Black lines are guides for the eyes to follow the evolution of the transconductance maxima in yellow.

Figure 4

Transport measurement of device B. (a) Temperature dependence of the transfer characteristic at zero magnetic field. An offset on $V_g$ is added for clarity. (b) Conductance vs magnetic field for a few gate voltages corresponding to the colored points in (a) at 4.2 K. (c) Evolution of the transfer characteristic with magnetic field from 0 to 26 T at 4.2 K interpolated from $G\left(B\right)$ measurements. The color points are the experimental values. An offset on $V_g$ is added for clarity.

Figure 5

Color plot of the transconductance $\partial G/\partial V_g$ vs gate voltage and magnetic field calculated (NSC) for a ballistic conductor (top) and obtained from the experimental results (bottom) of device A. The maxima of transconductance appear in yellow. The coordinates where the simulated Fermi energy crosses the bottom of each subband is calculated and plotted in black and gray curves according to the spin state considering a gate coupling of 13 pF/m. The subbands are indexed $E_{1–4}\uparrow \downarrow$ according to the subband number in Fig. 4 and the spin state.

Figure 6

Conductance and filling factor vs $1/B$ measured from 0 to 50 T at 4.2 K for a gate voltage of $V_g=8$ V. The conductance increase between two plateaus reveals the occupation of one additional subband. The number of occupied subbands is given in the open squares. In order to take the contact transmission into account, a reflexion coefficient of 0.35 was removed.