Unconventional transport properties in systems with triply degenerate quadratic band crossings

TL;DR

This paper investigates triply degenerate quadratic band crossings (TQBCs), revealing unique quantum Hall effects and tunneling behaviors, expanding understanding of multi-band crossing phenomena in condensed matter systems.

Contribution

It introduces and analyzes two types of TQBCs, demonstrating their distinct electronic properties and responses to magnetic fields and potential barriers, which are novel extensions of quadratic band crossing concepts.

Findings

TQBCs exhibit an anomalous Landau level structure.

Distinct quantum Hall effect with infinite Hall plateaus near zero chemical potential.

Different tunneling behaviors for the two TQBC types, including exponential decay and perfect reflection.

Abstract

A quadratic band crossing (QBC) is a crossing of two bands with quadratic dispersion, which has been intensively investigated due to its appearance in Bernal-stacked bilayer graphene. Here, we study an extension of QBCs, the triply degenerate quadratic band crossing (TQBC), which is a three-band crossing node containing two quadratic dispersing bands and a flat band. We focus on two types of TQBCs. The first type contains a symmetry-protected QBC and a free-electron band, the prototype of which is the AA-stacked bilayer squareoctagon lattice. In a magnetic field, such a TQBC exhibits an anomalous Landau level structure, leading to a distinctive quantum Hall effect which displays an infinite ladder of Hall plateaus when the chemical potential approaches zero. The other type of TQBC can be viewed as a pseudospin-1 extension of the bilayer-graphene QBC. Under perturbations, this type of TQBCs may split into linear pseudospin-1 Dirac-Weyl fermions. When tunneling through a potential barrier, the transmission probability of the first type decays exponentially with the barrier width for any incident angle, similar to the free-electron case, while the second type hosts an all-angle perfect reflection when the energy of the incident particles is equal to half the barrier height.