Chemical-Potential-Dependent Gap Opening at the Dirac Surface States of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ Induced by Aggregated Substitutional Cr Atoms

With angle-resolved photoemission spectroscopy, gap opening is resolved at up to room temperature in the Dirac surface states of molecular beam epitaxy grown Cr-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ topological insulator films, which, however, show no long-range ferromagnetic order down to 1.5 K. The gap size is found decreasing with increasing electron-doping level. Scanning tunneling microscopy and first-principles calculations demonstrate that substitutional Cr atoms aggregate into superparamagnetic multimers in the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ matrix, which contribute to the observed chemical-potential-dependent gap opening in the Dirac surface states without long-range ferromagnetic order.

Figure 1

ARPES gray-scale band maps (along the $\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ direction) (a),(b) and the corresponding EDCs (c),(d) of an 8 QL ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ film (a),(c) and an 8 QL ${\mathrm{Bi}}_{1.96}{\mathrm{Cr}}_{0.04}{\mathrm{Se}}_3$film (b),(d) taken at RT.

Figure 2

Hall traces (a) and magnetoconductivity (b) of a 8 QL ${\mathrm{Bi}}_{1.96}{\mathrm{Cr}}_{0.04}{\mathrm{Se}}_3$ film measured at varied temperatures.

Figure 3

(a)–(c) The ARPES EDCs of 8 QL ${\mathrm{Bi}}_{1.96}{\mathrm{Mg}}_y{\mathrm{Cr}}_{0.04}{\mathrm{Se}}_3$ films taken at $\sim 150\mathrm{K}$ with $y=0$ (a), $y=0.0015$ (b), and $y=0.003$ (c). (d)–(f) The ARPES EDCs of an 8 QL ${\mathrm{Bi}}_{1.96}{\mathrm{Cr}}_{0.04}{\mathrm{Se}}_3$ film taken at $\sim 80\mathrm{K}$ (d), $\sim 150\mathrm{K}$ (e), and $\sim 300\mathrm{K}$ (f). (g) The relation between $\mathrm{\Delta }$ and $\left|E_0\right|$ obtained from different ARPES measurements. The inset shows the fitting result of the $\overline{\mathrm{\Gamma }}$ point spectrum of an 8 QL ${\mathrm{Bi}}_{1.96}{\mathrm{Cr}}_{0.04}{\mathrm{Se}}_3$ film with double Lorentzian function.

Figure 4

(a)–(c) STM images of $(50\times 50)\mathrm{nm}$ (a), $(3.8\times 3.8)\mathrm{nm}$ (b), and $(4\times 4)\mathrm{nm}$ (c) taken from an 8 QL ${\mathrm{Bi}}_{1.96}{\mathrm{Cr}}_{0.04}{\mathrm{Se}}_3$ film. (d),(e),(h),(i) Top (d),(h) and side (e),(i) views of the geometrical structures of $C_1$ (d),(e) and $C_2$ (h),(i) in a ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ QL, respectively. (f),(g),(j),(k) Simulated (f),(j) and measured (g),(k) STM images of $C_1$ (f),(g) and $C_2$ (j),(k), respectively. (l)–(n) PDOS of ${\mathrm{Se}}^{\mathrm{I}}$, ${\mathrm{Se}}^{\mathrm{II}}$, and Cr atoms in $C_1$.