Magnetotransport and high-resolution angle-resolved photoelectron spectroscopy studies of palladium-doped ${\mathrm{Bi}}_2{\mathrm{Te}}_3$

We have performed magnetotransport and high-resolution angle-resolved photoelectron spectroscopy (ARPES) measurements on topological insulator ${\mathrm{Pd}}_x{\mathrm{Bi}}_2{\mathrm{Te}}_3(0\le x\le 0.20)$ single crystals. We have observed unusually high values of magnetoresistance ($\sim 1500\%$) and mobility $(\sim 93000\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{–1}{\mathrm{s}}^{–1})$ at low temperatures for pristine ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ that decrease upon Pd doping. Shubnikov–de Haas (SdH) oscillations were detected for $x=0.05$, 0.10, confirming the presence of two-dimensional topological surface states (TSSs) for these samples. Hall measurement shows the crossover from $n$-type charge carriers in pristine ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ to $p$-type charge carriers upon Pd doping. The ARPES measurements show that the conduction band crosses the Fermi level for pristine ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, and the Dirac point of the TSSs and bulk-derived valence bands indicated a shift to lower binding energy upon Pd doping in a rigid-band-like way up to $x\sim 0.10$. Based on the comparison of the parameters obtained from the SdH and ARPES measurements, the reduction in the $k_{\mathrm{F}}$ value in the magnetotransport measurements is likely due to the band bending induced by the Schottky barrier.

Figure 1

(a) Temperature dependence of zero-field longitudinal resistivity (${\rho }_{xx}$) for ${\mathrm{Pd}}_x{\mathrm{Bi}}_2{\mathrm{Te}}_3$ ($x=0$, 0.05, 0.10, 0.15, 0.20) of crystals, and (b) and (c) show the variation of carrier density ($n$) and mobility (μ) with temperature, respectively, calculated from Hall resistivity data.

Figure 2

Magnetic field dependence of magnetoresistance (MR) at $T=1.8\mathrm{K}$ (a), and temperature dependence of MR at 8 T (b) for ${\mathrm{Pd}}_x{\mathrm{Bi}}_2{\mathrm{Te}}_3 (x=0–0.20)$.

Figure 3

Weak antilocalization (WAL) effect in ${\mathrm{Pd}}_{0.05}{\mathrm{Bi}}_2{\mathrm{Te}}_3$: the change in magnetoconductance ($\mathrm{\Delta }{G}_{xx}$) at low temperatures and HLN fit (black line) in the field range ±1 T.

Figure 4

(a),(c) Resistivity as a function of $1/H$, after subtracting the background contribution; the inset shows the (left) LK formula fit and (right) Dingle plot; (b),(d) the fast Fourier transform analysis for $x=0.05$ and 0.10 with fundamental frequency at 2.75 and 4 T, respectively. The inset [(b),(d)] shows the Landau level fan diagram. The zeroth Landau level $n_0$ is 0.33 and 0.35 for $x=0.05$ and 0.10, respectively.

Figure 5

(a) Surface Brillouin zone (SBZ) with three high-symmetry points, $\overline{\mathrm{\Gamma }}$ (black), $\overline{M}$ (red), and $\overline{K}$ (blue). The ARPES spectra were measured along the green line, i.e., along the $\overline{\mathrm{\Gamma }}-\overline{M}$ high-symmetry line in the SBZ. (b)–(f) The ARPES image plots of ${\mathrm{Pd}}_x{\mathrm{Bi}}_2{\mathrm{Te}}_3$ showing the rigid-band-like shift on Pd doping. (g)–(k) Energy distribution curves (EDCs) at the $\overline{\mathrm{\Gamma }}$-point ($k_x=0$). The EDC peak at the Dirac point can be fitted with a single Lorentzian suggesting no energy gap.

Figure 6

A set of constant energy contours at different energies (a) ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, (b) ${\mathrm{Pd}}_{0.05}{\mathrm{Bi}}_2{\mathrm{Te}}_3$, and (c) ${\mathrm{Pd}}_{0.10}{\mathrm{Bi}}_2{\mathrm{Te}}_3$, respectively. The arrow indicates the position of the Dirac point. (d) The electron charge carrier density at the surface as a function of Pd doping concentration.