Abstract
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) and Hall resistivity rho_{xy} left( B right) 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 (lϕ) and a zero spin–orbit scattering length (lSO), 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) and rho_{xy} left( B right) of the Dirac semimetal Bi0.97Sb0.03 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 lϕ and lSO at different temperatures. The lϕ has a power-law T dependence at high T and saturates at low T. In contrast, the lSO shows negligible T dependence. Because of the different T dependence, a crossover occurs from the lSO-dominant low-T to the lϕ-dominant high-T regions. Accordingly, the hallmark features of weak antilocalization (WAL) in rho_{xx} left( B right) and rho_{xy} left( B right) 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.
Highlights
The quantum interference effects of electron waves in a system with linear dispersion have been of great interest in modern condensed matter physics
Four fundamental length scales which determine the B dependence of σ exist; the mean free path l, which measures the average distance that an electron travels before its momentum is changed by elastic scattering, the phase coherence length lφ, which denotes the average distance over which an electron can maintain its phase coherence, the magnetic length lB, and the spin–orbit scattering length lSO, which represent the strength of the magnetic field and spin–orbit coupling, respectively
At low T, MR does not show conventional B-quadratic behavior, but a sharp dip appears at low B in this system, whose origin is ascribed to weak antilocalization
Summary
We grew B i1−xSbx single crystals at x ~ 3–4% using a Bridgeman method, as previously r eported[22]. Energy dispersive X-ray analysis was used to measure the concentrations of antimony. The temperature dependences of resistivity ρ(T) for the B i0.97Sb0.03 single crystals were measured from 1.7 to 300 K using a six-probe method. The ρxx(B) and ρxy(B) measurements were carried out using a cryogen-free magnet system (Cryogenic Inc.) under a magnetic field B ranging from − 9 to 9 T. The B was applied along the trigonal axis with the current perpendicular to B [binary direction (B ⊥ I)]
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