Topological phase transitions as function of Sb content and temperature of Bi_1-xSb_x topological insulators

Given the isoelectronic nature of Bi and Sb, small variances in stoichiometric ratios have minimal effect on carry concentrations allowing for Bi_1-xSb_x alloys to be ideal topological insulators (TI). First discovered in 2008, ARPES measurements showed clear surface states due to the inversion of the L bands allowing for a TI phase between 9% < x < 15%. ¹ The decrease in lattice constant through the increase in Sb content enhances spin-orbit interactions, so much so that the bands at L-points invert resulting in a transition from trivial semimetal to TI.^2,3 Furthermore, this inversion drives the energy of the rival band at the T-point below the valence band creating a TI for 9% < x < 15%. This produces three distinct regimes for Bi_1-xSb_x alloys (x < 20%), trivial semimetal, topological insulators, and indirect-gap semiconductors. As thermal expansion increases the lattice constant, the impact of increasing Sb concentration is countermanded by the effect of increasing T. As a result, for, e.g. Bi₉₁Sb₉, the material goes through reverse phase transitions with increasing T, going from a TI phase when T < 120 K, to indirect-gap semiconductor phase when 120 K < T < 200 K, to a trivial semimetal phase when T > 200 K. Here we present a series of temperature dependent measurements of resistivity, thermal conductivity, and Seebeck coefficients of Bi_1-xSb_x single-crystal alloys at various Sb concentrations (x < 14%) with a much narrower temperature step than previous measurements preformed, allowing for a more coherent understanding of these phase transitions. The measurements are carried out along both the trigonal and bisectrix directions. Discontinuities of these transport properties correlating to the phase transitions will be presented as the temperature dependence of Sb concentration phase diagram of Bi_1-xSb_x alloys.