About diffusive systems, please open the book by Akkermans and Montambaux, Mesoscopic Physics of Electrons and Photons, Cambridge University Press (translated from the french original edition). In such systems, an important effect if the universal conductance flutuations. Nevertheless, phase coherence plays important role in diffusive systems, both electronic or photonic ones. One may at first think that the electron phase coherence is easier to maintain in ballistic structures, when the electrons mean-free-path (basically, the distance between two scattering events of an electron between two impurities) is larger than the size of the device. The reason why is now understood as the effects of temperature and size of the device: taking a reservoir of Landauer resistors finally restaures the Ohm's law. This clearly disagrees with the Ohm's law of classical resistors. When the phase coherence length becomes smaller than the size of the electronic device, the quantum effects wash out and only classical effect survive.Īn important example of phase coherence of electron is the Landauer quantisation formula of the conductance: when one sees an electron as a pure wave, the conductance of a resistive element should follow the concept of tunneling in quantum structures. As a result, a decrease in the probability of electron backscattering occurs, resulting in an overall decrease of electrical resistance. For instance, the phase coherence length associated to the electrons becomes smaller at high temperature, since the phonon bath allows more incoherent scatterings between electrons, finally changing the phase of the electrons wave-function by a significant amount, say $2\pi$. decoherence, though this word is sometimes use in the more restrictive meaning of destructing the entanglement). This is also the topic where one studies the effects destroying quantum phenomena (i.e. The branch of physics studying the interference effects of electrons in metallic, superconducting and semi-conducting structures is called the mesoscopic physics. The interference effects are one of the many signatures of the quantum regime, hence the importance of the concept of phase coherence. Among those effects, interference effects are certainly the immediate ones we can think of. Signatures of weak anti-localization are observed near the superconducting. A remnant, saturating resistance persists below the transition temperature as superconducting puddles fail to reach phase coherence. Figure 2 (a) shows the differential magneto-conductance of the sample as a function of magnetic field for different applied back-gate bias at a temperature of 400 mK. The notion of phase coherence is important for modern electronics of small size devices (especially at low temperatures), since it means that for devices smaller than the phase coherence length, quantum effects associated to the phase of the wave functions are no more negligible. We report on the observation of two-dimensional superconductivity and weak anti-localization at the TiO x /KTaO 3 (111) interfaces. We have characterized weak localization in few-layer MoS 2, allowing us to probe the phase coherence, spin coherence, and intervalley scattering in this material. The length associated to the phase coherence is the length after which the phase has changed significantly, say by $2\pi$ to quantify the concept. So, what is a phase coherence length? To each electron, one associates a wave-function $\Psi=\Psi_$. This definition is the one adopted in mesoscopic physics. National Research Council of Canada.Strictly speaking, a phase coherent electron device is an electronic device whose dimensions is smaller than the phase coherence length of the electrons.Weak antilocalization effect in high-mobility two-dimensional electron gas in an inversion layer on p-type HgCdTe DOI
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