In situ Magnetotransport Measurements in Ultrathin Bi Films: Evidence for Surface-Bulk Coherent Transport

We performed in situ magnetotransport measurements on ultrathin Bi(111) films [4–30 bilayers (BLs), 16–120 Å thick] to elucidate the role of bulk or surface states in the transport phenomena. We found that the temperature dependence of the film conductivity shows no thickness dependence for the 6–16 BL films and is affected by the electron-electron scattering, suggesting surface-state dominant contribution. In contrast, the weak antilocalization effect observed by applying a magnetic field shows clear thickness dependence, indicating bulk transport. This apparent inconsistency is explained by a coherent bulk-surface coupling that produces a single channel transport. For the films thicker than 20 BLs, the behavior changes drastically which can likely be interpreted as a bulk dominant conduction.

Figure 1

Normalized magnetoresistance $\{\rho (B)-\rho (0)\}/\rho (0)$ at 0.8 K as a function of the magnetic field for ultrathin Bi(111) films with various thicknesses. The inset shows the magnification for small magnetic field. (b) WAL analyses (conductivity change as a function of the magnetic field) from the raw data of (a). The solid lines show the fitted curves to Eq. (1). (c), (d) Thickness dependence of $\alpha$ (c) and $l_{\varphi }$ (d) in Eq. (1), respectively. The dashed line in (c) shows the expected value for the single channel WAL and the solid line in (d) shows the fitted curve to a linear function.

Figure 2

(a), (b) The temperature dependence of WAL for the 6 (a), and 20 BL (b) Bi(111) film, respectively. The solid lines show the fitted curves to Eq. (1). (c), (d) Temperature dependence of $\alpha$ (c) and $l_{\varphi }$ (d) for the 6 and 20 BL films. The dashed line in (c) shows the expected value for the single channel WAL and the solid line in (d) shows the fitted curve to $l_{\varphi }\propto T^{-P/2}$.

Figure 3

Temperature dependence of the change in sheet conductivity with respect to the value at 2.5 K for Bi(111) films with various thicknesses. No magnetic field is applied. The inset shows the raw data of the resistivity as a function of the temperature. (b) Temperature dependence of the sheet conductivity for the 16 BL film when applying a magnetic field. The solid lines show the fitted curves to $\mathrm{\Delta }\sigma \propto -\kappa \ln T$ for the data below 2 K. (c) Thickness dependence of $\kappa$ from the data of (a). The dashed line shows the value expected (0.5) from the combination of electron-electron interaction (EEI) and WAL. (d) The magnetic field dependence of $\kappa$ from the data of (b). The two dashed lines show the values expected from EEI and WAL ($\kappa =0.5$) and EEI only ($\kappa =1.0$).