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The relationship between the universal conductance fluctuation and the weak localization effect in monolayer graphene is investigated. By comparing experimental results with the predictions of the weak localization theory for graphene, we find that the ratio of the elastic intervalley scattering time to the inelastic dephasing time varies in accordance with the conductance fluctuation; this is a clear evidence connecting the universal conductance fluctuation with the weak localization effect. We also find a series of scattering lengths that are related to the phase shifts caused by magnetic flux by Fourier analysis.
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The temperature effect of quantum interference on resistivity is examined in monolayer graphene, with experimental results showing that the amplitude of the conductance fluctuation increases as temperature decreases. We find that this behavior can be attributed to the decrease in the inelastic scattering (dephasing) rate, which enhances the weak localization (WL) correction to resistivity. Following a previous report that explained the relationship between the universal conductance fluctuation (UCF) and WL regarding the gate voltage dependence (D. Terasawa, et al., Phys. Rev. B 95 125427 (2017)), we propose that the temperature dependence of the UCF in monolayer graphene can be interpreted by the WL theory.
We describe the weak localization correction to conductivity in ultra-thin graphene films, taking into account disorder scattering and the influence of trigonal warping of the Fermi surface. A possible manifestation of the chiral nature of electrons in the localization properties is hampered by trigonal warping, resulting in a suppression of the weak anti-localization effect in monolayer graphene and of weak localization in bilayer graphene. Intervalley scattering due to atomically sharp scatterers in a realistic graphene sheet or by edges in a narrow wire tends to restore weak localization resulting in negative magnetoresistance in both materials.
The contact conductance between graphene and two quantum wires which serve as the leads to connect graphene and electron reservoirs is theoretically studied. Our investigation indicates that the contact conductance depends sensitively on the graphene-lead coupling configuration. When each quantum wire couples solely to one carbon atom, the contact conductance vanishes at the Dirac point if the two carbon atoms coupling to the two leads belong to the same sublattice of graphene. We find that such a feature arises from the chirality of the Dirac electron in graphene. Such a chirality associated with conductance zero disappears when a quantum wire couples to multiple carbon atoms. The general result irrelevant to the coupling configuration is that the contact conductance decays rapidly with the increase of the distance between the two leads. In addition, in the weak graphene-lead coupling limit, when the distance between the two leads is much larger than the size of the graphene-lead contact areas and the incident electron energy is close to the Dirac point, the contact conductance is proportional to the square of the product of the two graphene-lead contact areas, and inversely proportional to the square of the distance between the two leads.
Weak localization in graphene is studied as a function of carrier density in the range from 1 x $10^{11}$,cm$^{-2}$ to 1.43 x $10^{13}$,cm$^{-2}$ using devices produced by epitaxial growth onto SiC and CVD growth on thin metal film. The magnetic field dependent weak localization is found to be well fitted by theory, which is then used to analyse the dependence of the scattering lengths L$_varphi$, L$_i$, and L$_*$ on carrier density. We find no significant carrier dependence for L$_varphi$, a weak decrease for L$_i$ with increasing carrier density just beyond a large standard error, and a n$^{-frac{1}{4}}$ dependence for L$_*$. We demonstrate that currents as low as 0.01,nA are required in smaller devices to avoid hot-electron artefacts in measurements of the quantum corrections to conductivity.
In this study, we address the phase coherent transport in a sub-micrometer-sized Hall bar made of epitaxial Bi2Se3 thin film by probing the weak antilocalization (WAL) and the magnetoresistance fluctuation below 22 K. The WAL effect is well described by the Hikami-Larkin-Nagaoka model, where the temperature dependence of the coherence length indicates that electron conduction occurs quasi-one-dimensionally in the narrow Hall bar. The temperature-dependent magnetoresistance fluctuation is analyzed in terms of the universal conductance fluctuation, which gives a coherence length consistent with that derived from the WAL effect.
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