Band structure and Klein paradox for a pn junction in ABCA-tetralayer graphene. (arXiv:1903.05676v1 [cond-mat.mes-hall])

We investigate the band structure of ABCA-tetralayer graphene (ABCA-TTLG)
subjected to an external potential $V$ applied between top and bottom layers.
Using the tight-binding model, including the nearest $t$ and
next-nearest-neighbor $t'$ hopping, low-energy model and two-band approximation
model we study the band structure variation along the lines $\Gamma-M-K-\Gamma$
in the first Brillouin zone, electronic band gap near Dirac point $K$ and
transmission properties, respectively. Our results reveal that ABCA-TTLG
exhibits markedly different properties as functions of $t'$ and $V$. We show
that the hopping parameter $t'$ changes the energy dispersion, the position of
$K$ and breaks sublattice symmetries. A sizable band gap is created at $K$,
which could be opened and controlled by the applied potential $V$. This gives
rise to 1D-like van Hove singularities (VHS) in the density of states (DOS). We
study the relevance of the skew hopping parameters $\gamma_3$ and $\gamma_4$ to
these properties and show that for energies $E\gtrsim6$meV their effects are
negligible. Our results are numerically discussed and compared with the

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