Magneto-transport and Berry phase in magnetically doped Bi${}_{0.97-x}$Sb${}_{0.03}$ single crystals

Abstract

We report large magnetoresistance (MR) and Shubnikov-de Haas (SdH) oscillations in single crystals of magnetically (M= Ni and Fe) doped M${}_x$Bi${}_{0.97-x}$Sb${}_{0.03}$ ($x=$ 0, 0.02) topological insulators. The R$\bar{3}$m symmetry and phase have been confirmed by the Rietveld refinement of x-ray diffraction data. Interestingly, a magnetic field induced phase transition from semi-metallic to semi-conducting type is found with the energy gap around 80 meV at 15 Tesla in the $x=$ 0 sample. Moreover, we observe linear behavior of MR up to 15 Tesla in transverse mode and SdH oscillations in longitudinal mode where the field direction is with respect to the current and crystal plane. For the parent sample, we found the coherence length L${}_{\varphi }=$ 12.7 nm through the fitting of MR data in transverse mode with modified H-L-N equation. The extracted frequencies of SdH oscillations using the fast Fourier transform method and Landau level (LL) fan diagram are found to be consistent for the parent and Ni doped samples. The determined Fermi surface area is found to be slightly larger in Ni doped as compared to the parent sample possibly due to change in the Fermi energy. The Kohler's plot indicates a single scattering mechanism below 100 K. More importantly, the analysis with the help of LL fan diagram reveals the non-zero Berry phase ${\varphi }_{\mathrm{B}}=-$(1$\pm$0.1)$\pi$, which demonstrates the non-trivial topological states near the Dirac point in the parent and Ni doped samples.

submitted, added fig2c, corrected fig4

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