Mass acquisition of Dirac fermions in magnetically doped topological insulator $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ films

We report on the mass acquisition of Dirac fermions by doping Cr into the topmost quintuple layer or into the bulk of $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ topological insulator films. By careful investigation of the scanning tunneling microscopy/spectroscopy on the films, we find that the Landau level spectrum keeps a good quality even at a high Cr-doping level, enabling a demonstration of deviation of the zeroth Landau level, induced by the acquisition of a mass term in the surface states in the presence of surface or bulk magnetic doping. The magnitude of the mass term in the surface states increases with increasing Cr-doping level. Our observation suggests Cr-doped $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ is a promising candidate for the realization of the proposed magnetoelectric effects.

Figure 1

(a) Schematic of surface states of a 3D TI and the Landau quantization scheme with and without massive gap neglecting the field induced Zeeman term. The sign of zero-mode deviation depends on the sign of TRS-breaking mass terms of $\mathrm{\Delta }=0,\pm 10$ meV. (b) The STS on an $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ film (sample 2 without Cr doping) at 0 and 7 T. (c) The STS on the $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ film with surface Cr doping of $x=0.18$ (sample 2). The dashed lines indicate Landau levels of $n=-1,0,+1$, while the solid line is the midpoint energy of $n=\pm 1$ Landau levels. Tunneling gap conditions: $V_{\mathrm{bias}}=0.2\mathrm{V},I=200\mathrm{pA}$.

Figure 2

(a) STM image (−1.0 V, 50 pA) of $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ film with surface Cr doping (sample 1, $x=0.006)$. (b) Zoom-in high-resolution image (0.1 V, 40 pA) in (a), showing $\mathrm{C}{\mathrm{r}}_{\mathrm{Sb}1}$ defects after surface Cr doping. (c) High resolution STM image (0.2 V, 400 pA) of $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ film with surface Cr doping (sample 2, $x=0.18)$. (d) STM image (−1.0 V, 200 pA) of $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ film with bulk Cr doping $\left(x=0.03\right)$. The inset in (d) shows the atomic resolution image of dark dots induced by Cr doping. (e) STM image (1.0 V, 50 pA) of $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ film with bulk Cr doping $\left(x=0.08\right)$. (f) Schematic of surface Cr doping and the atomic structure of 1 QL $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$, showing Cr on Sb1 (first Sb layer from the surface).

Figure 3

(a) LL spectra taken at random positions on sample 2 at $x=0.12$, showing the spatial variation of zero-mode deviation (2.4–7.2 meV). The arrows indicate the zeroth LLs coinciding with the dashed lines. The solid line and dashed lines around the zeroth LL indicate the Dirac energy and the range of zero-mode deviations, respectively. We see that the zeroth LL always deviates in the positive directions. (b) STS at 7 T (0.2 V, 200 pA) on sample 2 with increasing Cr doping $x$: 0, 0.03, 0.06, 0.09, 0.12, 0.18, 0.21. The arrows indicate the zeroth LLs. The dashed short lines indicate the ±1 LLs, while the solid short ones indicate the Dirac energies. Spectra of different doping are shifted vertically for clarity. (c) LL energies were plotted against $\mathrm{sgn}\left(n\right)\sqrt{\left|n\right|}$ at various Cr-doping levels in sample 2. The linear fitting to the data except for zeroth LL gives a Fermi velocity of $4.8\times {10}^{-5}\mathrm{m}/\mathrm{s}$ for the Cr-doped case.

Figure 4

(a) Field dependent LL spectra (0.2 V, 200 pA) on sample $3\left(x=0.18\right)$. The solid line indicates the Dirac energy. (b)–(d) LL energies under various magnetic fields plotted versus $\mathrm{sgn}\left(n\right)\sqrt{\left|n\right|B}$ on samples of $x=0.105$ (sample 1), 0.18 (sample 3), 0.21 (sample 2), respectively. The red line in (b) is a linear fitting to the date except the zeroth LL. The dashed curves in (c) and (d) are the fitting according to the quantization condition $E_n=\mathrm{sgn}\left(n\right)\sqrt{2e\hslash {\upsilon }_F^{2}B\left|n\right|+{\mathrm{\Delta }}^2}$ of the gapped surface states.

Figure 5

(a) STM image (derivative) of epitaxial $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ film grown on sample $3\left(x=0.18\right)$. (b) The atomic resolution image of the boundary between doped and undoped region indicated by a dashed rectangle in (a). (c) Schematic of the heterostructure. (d) dI/dV mapping of the squared region in (a) at 135 mV, where the zeroth Landau level appears in the surface state spectra at 7 T. (e) Spectra 1–4 are taken at corresponding positions indicated in (a) and (d) at 7 T. Spectrum 0 is a typical one taken in the squared region at zero magnetic field. The inset shows the dispersion of spectrum 2. The triangle arrow indicates the zeroth LL.

Figure 6

(a) and (b) Spatial averaged zero-field STS and LL spectra [0.2 V, 200 pA for (a); 0.25 V, 200 pA for (b)] taken at random positions on the ${\left(\mathrm{S}{\mathrm{b}}_{1-x}\mathrm{C}{\mathrm{r}}_x\right)}_2\mathrm{T}{\mathrm{e}}_3$ films with bulk Cr doping $(x=0.03$ and 0.08). The LL spectra are shifted vertically for clarity. The insets are the surface state dispersion derived from the LL spectra. The lines are the linear fitting to the Landau levels except the zeroth ones. The +1 LL in (b) is barely resolved because it becomes quite close to the bulklike conduction band edge due to the lifted Dirac energy. (c) and (d) Doping dependence of Dirac energy $E_D$ and the mass term Δ. The inset shows the schematic of the effect of Cr doping on the surface state structure. Here $E_D$ indicates Dirac energy of surface states, which can be obtained from the ±1 LL energies. CBM and VBM indicate the band edge of bulklike conduction band (BCB) and valence band (BVB).