We compute the absolute Poisson's ratio ν and the bending rigidity exponent η of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality d = 2+d c , d c 1. We demonstrate that, in the regime of anomalous Hooke's law, the absolute Poisson's ratio approaches material independent value determined solely by the spatial dimensionality d c :where a ≈ 1.76 ± 0.02. Also, we find the following expression for the exponent of the bending rigidity: η = 2/d c + (73 − 68ζ(3))/(27d 2 c ) + . . . . These results cannot be captured by self-consistent screening approximation.
We study Landau levels (LLs) of Weyl semimetal (WSM) with two adjacent Weyl nodes. We consider different orientations η = ∠(B, k0) of magnetic field B with respect to k0, the vector of Weyl nodes splitting. Magnetic field facilitates the tunneling between the nodes giving rise to a gap in the transverse energy of the zeroth LL. We show how the spectrum is rearranged at different η and how this manifests itself in the change of behavior of differential magnetoconductance dG(B)/dB of a ballistic p−n junction. Unlike the single-cone model where Klein tunneling reveals itself in positive dG(B)/dB, in the two-cone case G(B) is non-monotonic with maximum at Bc ∝ Φ0k 2 0 / ln(k0lE) for large k0lE, where lE = v/|e|E with E for built in electric field and Φ0 for magnetic flux quantum.
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