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The present study develops a general framework for weak antilocalization (WAL) in a three-dimensional (3D) system, which can be applied for a consistent description of longitudinal resistivity    $$\rho_{xx} \left( B \right)$$  ρ xx B and Hall resistivity    $$\rho_{xy} \left( B \right)$$  ρ xy B over a wide temperature ( T ) range. Compared to the previous approach Vu et al. (Phys Rev B 100:125162, 2019), which assumes infinite phase coherence length ( l   ϕ  ) and a zero spin–orbit scattering length ( l  SO ), the present framework is more general, covering high  T  and the intermediate spin–orbit coupling strength. Based on the new approach, the    $$\rho_{xx} \left( B \right)$$  ρ xx B and    $$\rho_{xy} \left( B \right)$$  ρ xy B of the Dirac semimetal Bi 0.97 Sb 0.03  was analyzed over a wide  T  range from 1.7 to 300 K. The present framework not only explains the main features of the experimental data but also enables one to estimate  l   ϕ   and  l  SO  at different temperatures. The  l   ϕ   has a power-law  T  dependence at high  T  and saturates at low  T . In contrast, the  l  SO  shows negligible  T  dependence. Because of the different  T  dependence, a crossover occurs from the  l  SO -dominant low- T  to the  l   ϕ  -dominant high- T  regions. Accordingly, the hallmark features of weak antilocalization (WAL) in    $$\rho_{xx} \left( B \right)$$  ρ xx B and    $$\rho_{xy} \left( B \right)$$  ρ xy B are gradually suppressed across the crossover with increasing  T . The present theory describes both low- T  and high- T  regions successfully, which is impossible in the previous approximate approach. This work offers insights for understanding quantum electrical transport phenomena and their underlying physics, particularly when multiple WAL length scales are competing.

Weak antilocalization, spin–orbit interaction, and phase coherence length of a Dirac semimetal Bi0.97Sb0.03