Quantum oscillations in iron-doped single crystals of the topological insulator $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$

We investigated the magnetotransport properties of Fe-doped topological insulator $\mathrm{S}{\mathrm{b}}_{1.96}\mathrm{F}{\mathrm{e}}_{0.04}\mathrm{T}{\mathrm{e}}_3$ single crystals. With doping, the band structure changes significantly and multiple Fermi pockets become evident in the Shubnikov–de Haas oscillations, in contrast to the single frequency detected for pure $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$. Using complementary density functional theory calculations, we identify an additional bulk hole pocket introduced at the Γ point which originates from the chemical distortion associated with the Fe dopant. Experimentally, both doped and undoped samples are hole-carrier dominated; however, Fe doping also reduces the carrier density and mobility. The angle dependent quantum oscillations of $\mathrm{S}{\mathrm{b}}_{1.96}\mathrm{F}{\mathrm{e}}_{0.04}\mathrm{T}{\mathrm{e}}_3$ were analyzed to characterize the complex Fermi surface and isolate the dimensionality of each SdH feature. Among those components, we found two oscillations frequencies, which related to two Fermi pockets are highly angle dependent. Moreover, the fermiology changes via Fe doping and may also provide a different Berry phase, as demonstrated by the Landau fan diagram, thus indicating a rich complexity in the underlying electronic structure.

Figure 1

(a) Resistivity of $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ and $\mathrm{F}{\mathrm{e}}_{0.04}\mathrm{S}{\mathrm{b}}_{1.96}\mathrm{T}{\mathrm{e}}_3$ as a function of temperature from 3 to 300 K. The inset shows the MR at 3 K up to 14 T. (b, c) The x-ray-diffraction patterns of $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ and FST single crystals along the $c$ direction. The inset photos are crystal pieces cleaved from the ingot. (d) Sketches of the band structure and Fermi surface of $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ and FST.

Figure 2

SdH oscillations of both $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ and FST single crystals. (a, b) MR curves of $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ and FST single crystals measured at different temperatures. (c, d) Oscillation patterns obtained by subtracting the smooth backgrounds at various temperatures, plotted as a function of 1/H. (e, f) Amplitudes of the fast Fourier transform from the oscillations.

Figure 3

Angular dependence of the SdH oscillations of the FST single crystal. (a) FST single crystal's MR curves measured at different angles at 3 K. (b) Oscillation patterns obtained by subtracting the smooth backgrounds at various angles, plotted as a function of B. (c) Amplitude plots of fast Fourier transform from the oscillations. (d) Two selected frequencies evolve with rotation, in which the star symbols are experimental data, while curves are fitted with $F\left(\theta \right)=F\left(0\right)/\cos \left(\theta \text{–}45\right)$.

Figure 4

Hall effect of $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ and FST single crystals. (a) and (b) ${\rho }_{xy}$ plots of $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ and FST single crystals at various temperatures. (c) The Hall coefficient and the carrier density calculated from the relative Hall curves are plotted as functions of temperature.

Figure 5

DFT calculations for $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ and $\mathrm{S}{\mathrm{b}}_{2-x}\mathrm{F}{\mathrm{e}}_x\mathrm{T}{\mathrm{e}}_3$. (a) The undoped $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ cell is characterized by a large Sb-Te bond distance $d=3.18\AA$. The shaded area indicates the valence electron density. (b) The Fermi surface calculated for $p$-type $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ viewed along the (001) projection includes six major ellipsoids from the hole bands. For comparison, the red ellipsoid depicts an area of $0.405\mathrm{n}{\mathrm{m}}^{\text{–}2}$. (c) The Fe dopant (black) causes a crystallographic distortion in the $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ supercell and yields a reduced cation-anion distance $d=2.84\AA$ with an enhanced electron density near the Fe. (d) The inner Fermi surface for the $\mathrm{S}{\mathrm{b}}_{2-x}\mathrm{F}{\mathrm{e}}_x\mathrm{T}{\mathrm{e}}_3$ includes an additional pocket at the Γ point. The cross-sectional areas of the two highlighted features are 0.72 and $1.98\mathrm{n}{\mathrm{m}}^{\text{–}2}$, respectively. (e) The exchange splitting forms a second Fermi surface (right) that wraps the inner $\mathrm{S}{\mathrm{b}}_{2-x}\mathrm{F}{\mathrm{e}}_x\mathrm{T}{\mathrm{e}}_3$ surface. (f) The band structure of pure $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ indicates a predominant s-p character and shows the light and heavy hole bands at the Fermi surface. The green line is the energy used to draw the Fermi surface. The dashed lines correspond to the band structure of the experimental structure parameters, and the solid lines correspond to the DFT (PBE) structure after ionic relaxation. (g) The band structure of the $\mathrm{S}{\mathrm{b}}_{2-x}\mathrm{F}{\mathrm{e}}_x\mathrm{T}{\mathrm{e}}_3$ shows an additional hole band at Γ at the valence band.