![]() Below 10 K, it is accompanied by Shubnikov-de Haas oscillations. The linear magnetoresistance is observed up to room temperature. Above about 1.5 T, the magnetoresistance becomes linear and does not saturate in fields up to 9 T. The magnetoresistance is huge and clearly shows a weak antilocalization effect in small magnetic fields. Temperature dependence of the electrical resistivity suggests existence of two parallel conduction channels: metallic and semiconducting, with the latter making negligible contribution at low temperatures. ![]() Although superconducting state is clearly reflected in the electrical resistivity and magnetic susceptibility data, no corresponding anomaly can be seen in the specific heat. The compound exhibits superconductivity below a critical temperature T c = 1.8 K, with a zero-temperature upper critical field B c2 ≈ 2.3 T. ISSN 0031-9007.We present electronic transport and magnetic properties of single crystals of semimetallic half-Heusler phase LuPdBi, having theoretically predicted band inversion requisite for nontrivial topological properties. "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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