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Register a new userStatistical measures and the Klein tunneling in single-layer graphene
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Statistical complexity and Fisher-Shannon information are calculated in a problem of quantum scattering, namely the Klein tunneling across a potential barrier in graphene. The treatment of electron wave functions as masless Dirac fermions allows us to compute these statistical measures. The comparison of these magnitudes with the transmission coefficient through the barrier is performed. We show that these statistical measures take their minimum values in the situations of total transparency through the barrier, a phenomenon highly anisotropic for the Klein tunneling in graphene.
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The problem of the Klein tunneling across a potential barrier in bi-layer graphene is addressed. The electron wave functions are treated as massive chiral particles. This treatment allows us to compute the statistical complexity and Fisher-Shannon information for each angle of incidence. The comparison of these magnitudes with the transmission coefficient through the barrier is performed. The role played by the evanescent waves on these magnitudes is disclosed. Due to the influence of these waves, it is found that the statistical measures take their minimum values not only in the situations of total transparency through the barrier, a phenomenon highly anisotropic for the Klein tunneling in bi-layer graphene.
We show that in gapped bilayer graphene, quasiparticle tunneling and the corresponding Berry phase can be controlled such that it exhibits features of single layer graphene such as Klein tunneling. The Berry phase is detected by a high-quality Fabry-P{e}rot interferometer based on bilayer graphene. By raising the Fermi energy of the charge carriers, we find that the Berry phase can be continuously tuned from $2pi$ down to $0.68pi$ in gapped bilayer graphene, in contrast to the constant Berry phase of $2pi$ in pristine bilayer graphene. Particularly, we observe a Berry phase of $pi$, the standard value for single layer graphene. As the Berry phase decreases, the corresponding transmission probability of charge carriers at normal incidence clearly demonstrates a transition from anti-Klein tunneling to nearly perfect Klein tunneling.
Graphene electrons feature a pair of massless Dirac cones of opposite pseudospin chirality at two valleys. Klein tunneling refers to the intriguing capability of these chiral electrons to penetrate through high and wide potential barrier. The two valleys have been treated independently in the literature, where time reversal symmetry dictates that neither the normal incidence transmission nor the angle-averaged one can have any valley polarization. Here we show that, when intervalley scattering by barrier is accounted, graphene electrons normally incident at a superlattice barrier can experience a fully valley-selective Klein tunneling, i.e. perfect transmission in one valley, and perfect reflection in the other. Intervalley backscattering creates staggered pseudospin gaps in the superlattice barrier, which, combined with the valley contrast in pseudospin chirality, determines the valley polarity of Klein tunneling. The angle averaged transmission can have a net valley polarization of 20% for a 5-period barrier, and exceed 75% for a 20-period barrier. Our finding points to an unexpected opportunity to realize valley functionalities in graphene electronics.
We use the Wick-rotated time-dependent supersymmetry to construct models of two-dimensional Dirac fermions in presence of an electrostatic grating. We show that there appears omnidirectional perfect transmission through the grating at specific energy. Additionally to being transparent for incoming fermions, the grating hosts strongly localized states.
The inherent asymmetry of the electric transport in graphene is attributed to Klein tunneling across barriers defined by $textit{pn}$-interfaces between positively and negatively charged regions. By combining conductance and shot noise experiments we determine the main characteristics of the tunneling barrier (height and slope) in a high-quality suspended sample with Au/Cr/Au contacts. We observe an asymmetric resistance $R_{textrm{odd}}=100-70$ $Omega$ across the Dirac point of the suspended graphene at carrier density $|n_{rm G}|=0.3-4 cdot 10^{11}$ cm$^{-2}$, while the Fano factor displays a non-monotonic asymmetry in the range $F_{textrm{odd}} sim 0.03 - 0.1$. Our findings agree with analytical calculations based on the Dirac equation with a trapezoidal barrier. Comparison between the model and the data yields the barrier height for tunneling, an estimate of the thickness of the $textit{pn}$-interface $d < 20$ nm, and the contact region doping corresponding to a Fermi level offset of $sim - 18$ meV. The strength of pinning of the Fermi level under the metallic contact is characterized in terms of the contact capacitance $C_c=19 times 10^{-6}$ F/cm$^2$. Additionally, we show that the gate voltage corresponding to the Dirac point is given by the work function difference between the backgate material and graphene.
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