![]() ![]() The phase coherence length l ϕ shows a power law dependence with temperature, l ϕ∼ T -1/2, revealing an electron-electron interaction-dominated dephasing mechanism. The WAL magnitudes in magnetoconductance can be perfectly fitted by the 2D Hikami-Larkin-Nagaoka (HLN) equation in the presence of strong SOC, by which the spin-orbit scattering length l SO and phase coherence length l ϕ have been extracted. Here, we report on the observation of quasi-2D transport and WAL effect in sublimed-salt-assisted low-temperature chemical vapor deposition (CVD) grown few-layered high-quality VSe 2 nanosheets. The observation of WAL effect in VSe 2 is challenging due to the relative weak SOC and three-dimensional (3D) transport nature in thick VSe 2. ISSN 0031-9007.With strong spin-orbit coupling (SOC), ultrathin two-dimensional (2D) transitional metal chalcogenides (TMDs) are predicted to exhibit weak antilocalization (WAL) effect at low temperatures. "Influence of Spin-Orbit Coupling on Weak Localization". Journal of Physics C: Solid State Physics. "Spin-orbit coupling and weak localisation in the 2D inversion layer of indium phosphide". "Spin–Orbit Interaction and Magnetoresistance in the Two-Dimensional Random System". Electronic Transport in Mesoscopic Systems. "Magnetoresistance and Hall effect in a disordered two-dimensional electron gas". The strength of either weak localization or weak anti-localization falls off quickly in the presence of a magnetic field, which causes carriers to acquire an additional phase as they move around paths. In this equation α \alpha is -1 for weak antilocalization and +1/2 for weak localization. In two dimensions the change in conductivity from applying a magnetic field, due to either weak localization or weak anti-localization can be described by the Hikami-Larkin-Nagaoka equation: σ ( B ) − σ ( 0 ) = − e 2 2 π 2 ℏ Because of this, the two paths along any loop interfere destructively which leads to a lower net resistivity. The spin of the carrier rotates as it goes around a self-intersecting path, and the direction of this rotation is opposite for the two directions about the loop. In a system with spin–orbit coupling, the spin of a carrier is coupled to its momentum. ![]() Since it is much more likely to find a self-crossing trajectory in low dimensions, the weak localization effect manifests itself much more strongly in low-dimensional systems (films and wires). Due to the identical length of the two paths along a loop, the quantum phases cancel each other exactly and these (otherwise random in sign) quantum interference terms survive disorder averaging. The weak localization correction can be shown to come mostly from quantum interference between self-crossing paths in which an electron can propagate in the clock-wise and counter-clockwise direction around a loop. The usual formula for the conductivity of a metal (the so-called Drude formula) corresponds to the former classical terms, while the weak localization correction corresponds to the latter quantum interference terms averaged over disorder realizations. These interference terms effectively make it more likely that a carrier will "wander around in a circle" than it would otherwise, which leads to an increase in the net resistivity. Therefore, the correct (quantum-mechanical) formula for the probability for an electron to move from a point A to a point B includes the classical part (individual probabilities of diffusive paths) and a number of interference terms (products of the amplitudes corresponding to different paths). However quantum mechanics tells us that to find the total probability we have to sum up the quantum-mechanical amplitudes of the paths rather than the probabilities themselves. Classical physics assumes that the total probability is just the sum of the probabilities of the paths connecting the two points. The resistivity of the system is related to the probability of an electron to propagate between two given points in space. That is, an electron does not move along a straight line, but experiences a series of random scatterings off impurities which results in a random walk. The effect is quantum-mechanical in nature and has the following origin: In a disordered electronic system, the electron motion is diffusive rather than ballistic. The name emphasizes the fact that weak localization is a precursor of Anderson localization, which occurs at strong disorder. The effect manifests itself as a positive correction to the resistivity of a metal or semiconductor. Weak localization is a physical effect which occurs in disordered electronic systems at very low temperatures. There are many possible scattering paths in a disordered system Weak localization is due primarily to self-intersecting scattering paths ![]()
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