Integer quantum Hall effect and enhanced $g$ factor in quantum-confined ${\mathrm{Cd}}_3{\mathrm{As}}_2$ films

We investigate the integer quantum Hall effect in ${\mathrm{Cd}}_3{\mathrm{As}}_2$ thin films under conditions of strong to moderate quantum confinement (thicknesses of 10, 12, and 15 nm). In all the films, we observe the integer quantum Hall effect in the spin-polarized lowest Landau level (filling factor $\nu =1$) and at spin-degenerate higher index Landau levels with even filling factors ($\nu =2,4,6$). With increasing quantum confinement, we also observe a lifting of the Landau-level spin degeneracy at $\nu =3$, manifest as the emergence of an anomaly in the longitudinal and Hall resistivities. Tight-binding calculations show that the enhanced $g$ factor likely arises from a combination of quantum confinement and corrections from nearby subbands.

Figure 1

IQHE in a moderately quantum confined 15-nm-thick ${\mathrm{Cd}}_3{\mathrm{As}}_2$ film at $T=50$ mK. (a) Gate-voltage dependence of ${\rho }_{xx}$ at zero magnetic field. The inset shows a schematic of the Van der Pauw geometry. (b) Gate voltage dependence of ${\rho }_{xx}$ (red, left axis) and ${\rho }_{yx}$ (blue, right axis) at $B=9$ T, showing quantized Hall plateaus at filling factor $\nu =1,2,4,6$ accompanied by deep minima in ${\rho }_{xx}$. The finite minimum at $\nu =1$ (${\rho }_{xx} \sim 200\mathrm{\Omega }$) is attributed to the incomplete development of the first LL at $B=9$ T. (c) Gate voltage dependence of ${\sigma }_{xx}$ (red, left axis) and ${\sigma }_{xx}$ (blue, right axis) at $B=9$ T. These values are obtained from the data in (b). (d) Variation of $R_{14,23}$ with $B$ and $V_{\mathrm{g}}$, where $R_{14,23}=V_{23}/I_{14}$. The plot is generated by sweeping $V_{\mathrm{g}}$ at fixed values of $B$. The magnetic field is incremented in steps of 0.2 T for $B\ge 4$ T and in steps of 1 T for $B<4$ T. The data are then smoothly interpolated. A raw plot is provided in the Supplemental Material [34].

Figure 2

IQHE in a strongly quantum confined 10-nm-thick ${\mathrm{Cd}}_3{\mathrm{As}}_2$ thin film at $T=50$ mK. (a) Variation of ${\sigma }_{xx}$ with $V_{\mathrm{g}}$ at $B=0$. When the chemical potential is close to the CNP, we cannot reliably measure ${\sigma }_{xx}$ using lock-in techniques (represented by the dashed line). (b) $V_{\mathrm{g}}$ dependence of ${\sigma }_{xx}$ (red, left axis) and ${\sigma }_{xy}$(blue, right axis) at $B=9$ T. For the $\nu =1,2,4$ quantum Hall plateaus, ${\rho }_{xx}$ has values of 4.8, 0.98, 5.9 $\mathrm{\Omega }$, whereas ${\rho }_{yx}$ has values of 0.9937, 0.4973, and $0.2483\mathrm{h}/e^2$, respectively. (c) $V_{\mathrm{g}}$ dependence of ${\sigma }_{xx}$ (red, left axis) and ${\sigma }_{xy}$ (blue, right axis) at $B=9$ T. These values are obtained from the data in (b). (d) The first derivative plot of the data in (b), showing the quantum Hall states with filling factor $\nu =1–4$.

Figure 3

(a)–(c) Experimentally measured evolution of the $\nu =3$ feature in ${\mathrm{Cd}}_3{\mathrm{As}}_2$ films with different thickness: (a) 15, (b) 12, and (c) 10 nm. Each panel shows the $V_{\mathrm{g}}$ dependence of ${\sigma }_{xx}$ (red, left axis) and ${\sigma }_{xy}$ (blue, right axis) at $B=9$ T. (d) and (e) Band structure in the surface Brillouin zone of [112]-oriented films, based on a tight-binding model of two different thicknesses: (d) 280 nm (e) 13 nm. The vertical dashed line indicates the projection of the bulk Dirac point ${\mathbf{k}}_D^{+}$ in the SBZ at $(0.3\pi ,0)$. Blue and red indicate bulk and surface states, respectively, in panel (d). The calculation shows a quantum confinement induced band gap of 2.3 meV in the thinner case. (f) Calculated $g$ factors as a function of ${\mathrm{Cd}}_3{\mathrm{As}}_2$ film thickness.