Low-temperature magnetoresistance hysteresis in Vanadium-doped Bi${}_2$Te${}_{2.4}$Se${}_{0.6}$ bulk topological insulators

Bi${}_2$Te${}_{2.4}$Se${}_{0.6}$ single crystals show gapless topological surface states and doping ($x$) with Vanadium allows to shift the chemical potential in the bulk band gap. Accordingly, the resistivity, carrier density, and mobility are constant below 10 K and the magnetoresistance shows weak antilocalization as expected for low-temperature transport properties dominated by gapless surface states of so-called three-dimensional topological “insulators”. However, the magnetoresistance also shows a hysteresis depending on the sweep rate and the magnetic field direction. Here, we provide evidence that such magnetoresistance hysteresis is enhanced if both three-dimensional bulk states and quasi-two-dimensional topological states contribute to the transport ($x$ = 0 and 0.03), and it is mostly suppressed if the topological states govern transport ($x$ = 0.015). The results are discussed in terms of spin-dependent scattering between the different available states