While the influence of quantum interference effects on ρ xx B is well investigated and understood, that on ρ xy B is rarely studied 9. Even though there are several tools to investigate the influence of quantum interference, magnetotransport measurement has become a very effective method to experimentally study this phenomenon. This is the weak antilocalization (WAL) effect, readily observable when l SO ≪ l ϕ.Īn external magnetic field destroys interference conditions, resulting in a magnetoresistance carrying quantitative information about phase coherence length and spin scattering length 4. Here, the interference of time-reversed paths reduces the backscattering probability below its classical value at zero magnetic field. The stronger the SOI is, the smaller the l SO 4, 5, 8. As the spin experiences a sequence of scattering events along its path, the spin orientation is randomized on a characteristic length scale of spin–orbit scattering length l SO. At the same time, the spin dynamics of the carriers, which in systems with strong spin–orbit interaction (SOI) is coupled to their orbital motion, introduce interference of time-reversed paths with consequences beyond the WL effect. This interference effect is relevant for diffusive orbits up to the length scale of the phase-coherence length l ϕ. This leads to an enhanced probability of carrier backscattering, enhancing resistivity 4– 7. In disordered materials, weak localization (WL) arises from constructive interference between time-reversed partial waves of the charge carriers. The traditionally, well-known technique for detecting this effect has been the measurement of the spin coherence and phase coherence length of the electron wave function. Recently, several device applications have been proposed that rely on the interference effect in 3D systems 1– 3. The quantum interference effects of electron waves in a system with linear dispersion have been of great interest in modern condensed matter physics. This work offers insights for understanding quantum electrical transport phenomena and their underlying physics, particularly when multiple WAL length scales are competing. The present theory describes both low- T and high- T regions successfully, which is impossible in the previous approximate approach. Accordingly, the hallmark features of weak antilocalization (WAL) in ρ xx B and ρ xy B are gradually suppressed across the crossover with increasing T. Because of the different T dependence, a crossover occurs from the l SO-dominant low- T to the l ϕ-dominant high- T regions. In contrast, the l SO shows negligible T dependence. The l ϕ has a power-law T dependence at high T and saturates at low T. 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. Based on the new approach, the ρ xx B and ρ xy B of the Dirac semimetal Bi 0.97Sb 0.03 was analyzed over a wide T range from 1.7 to 300 K. (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. Compared to the previous approach Vu et al. 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 ρ xx B and Hall resistivity ρ xy B over a wide temperature ( T) range.
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