Magnetotransport and Berry phase tuning in Gd-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ topological insulator single crystals

The Berry phase is an important concept in solids, correlated to the band topology, axion electrodynamics, and potential applications of topological materials. Here, we investigate the magnetotransport and Berry phase of rare earth element Gd-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ $(\mathrm{Gd}:{\mathrm{Bi}}_2{\mathrm{Se}}_3)$ topological insulators (TIs) at low temperatures and high magnetic fields. $\mathrm{Gd}:{\mathrm{Bi}}_2{\mathrm{Se}}_3$ single crystals show Shubnikov–de Haas (SdH) oscillations with nontrivial Berry phase, while ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ single crystals show zero Berry phase in SdH oscillations. A fitting of the temperature-dependent magnetization curves using the Curie-Weiss law reveals that the Gd dopants in the crystals show paramagnetism in the 3–300 K region, indicating that the origin of the Berry phase is not long-range magnetic ordering. Moreover, Gd doping has limited influence on the quantum oscillation parameters (e.g., frequency of oscillation, area of Fermi surface, effective electron mass, and Fermi wave vectors) but has a significant impact on the Hall mobility, carrier density, and band topology. Our results demonstrate that Gd doping can tune the Berry phase of TIs effectively, which may pave the way for the future realization of many predicted exotic transport phenomena of topological origin.

Figure 1

Scanning electron microscopy (SEM) and EDS characterization of a freshly cleaved $\mathrm{Gd}:{\mathrm{Bi}}_2{\mathrm{Se}}_3$ single-crystal surface. (a) The secondary electron image and elemental mapping image are plotted in superposition to illustrate the uniform distribution of all elements. The element mapping of Bi, Se, and Gd in the same area are shown separately on the right side. (b) The EDS of the area scan, in which the peaks are indexed with elements.

Figure 2

A glimpse of the magnetotransport properties of a pure ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ single crystal. (a) and (b) Temperature and angle $\left(T=3\mathrm{K}\right)$ dependence of the magnetoresistance (MR) vs $B$ curves. (c) Temperature- and angle-dependent oscillation patterns whose amplitude decreases with heating (plotted in superposition of all temperatures, as pointed by the blue arrow) and increasing rotating angle. (d) The Lifshitz-Kosevich (LK) formula fitting of oscillation patterns at $T=3\mathrm{K}$ and $\theta =0^{\circ }$. (e) The Landau fan diagram of the oscillation patterns at 0°. (f) and (g) Fast Fourier transform (FFT) amplitude plot during rotating and heating.

Figure 3

A glimpse of the magnetotransport and magnetic properties of a $\mathrm{Gd}:{\mathrm{Bi}}_2{\mathrm{Se}}_3$ single crystal. (a) Magnetoresistance (MR) vs $B$ curves at fixed temperatures ranging from 3 to 300 K. (b) The oscillatory patterns of the MR vs 1/$B$ curves. Inset: A fitting of the 3-K oscillatory pattern using the Lifshitz-Kosevich (LK) formula. (c) The Landau fan diagram is plotted to illustrate the Berry phase, in which the dot lines guide between the oscillation peaks and dips. (d) Temperature dependence of the zero-field-cooled (ZFC) and field-cooled (FC) magnetic susceptibility. Inset: A fitting of the magnetic data using the Curie-Weiss law. (e) The fast Fourier transform (FFT) spectra of oscillatory patterns. (f) Magnetic hysteresis loops at $T=3$, 30, and 300 K.

Figure 4

The carrier's properties of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and $\mathrm{Gd}:{\mathrm{Bi}}_2{\mathrm{Se}}_3$ single crystals. (a) The Lifshitz-Kosevich (LK) formula fitting to obtain the effective mass of electrons. (b) The Dingle plots. Temperature dependence of the (c) carrier density and (d) mobility obtained from Hall measurements.

Figure 5

Angular-dependent Shubnikov–de Haas (SdH) oscillations of $\mathrm{Gd}:{\mathrm{Bi}}_2{\mathrm{Se}}_3$ single crystals. (a) The SdH oscillation patterns obtained from the angular dependent magnetoresistance (MR) curves from which smooth backgrounds have been subtracted. (b) Fast Fourier transform (FFT) spectra of the oscillation patterns in (a). (c) The SdH oscillation frequencies and Berry phase are plotted as a function of the rotation angle. Note that the blue line is the cosine fitting of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ SdH oscillation frequency, which indicates the frequency change of an ideal two-dimensional (2D) Fermi surface.