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We report a high-field magnetotransport study on selected low-carriercrystals of the topological insulator Bi$_{2-x}$Sb${_x}$Te$_{3-y}$Se$_{y}$.Monochromatic Shubnikov - de Haas (SdH) oscillations are observed at 4.2~K andtheir two-dimensional nature is confirmed by tilting the magnetic field withrespect to the sample surface. With help of Lifshitz-Kosevich theory, importanttransport parameters of the surface states are obtained, including the carrierdensity, cyclotron mass and mobility. For $(x,y)=(0.50,1.3)$ the Landau levelplot is analyzed in terms of a model based on a topological surface state inthe presence of a non-ideal linear dispersion relation and a Zeeman term with$g_s = 70$ or $-54$. Input parameters were taken from the electronic dispersionrelation measured directly by angle resolved photoemission spectroscopy oncrystals from the same batch. The Hall resistivity of the same crystal(thickness of 40~$\mu$m) is analyzed in a two-band model, from which weconclude that the ratio of the surface conductance to the total conductanceamounts to 32~\%.

Quantum oscillations of the topological surface states in low carrier concentration crystals of Bi$_{2-x}$Sb$_{x}$Te$_{3-y}$Se$_{y}$