Indicators of wavefunction (de)localisation for avoided crossing in a quadrupole quantum billiard

The relationship between wavefunction (de)localisation and avoided crossing in a quadrupole billiard is analysed. The following three-types of measures are employed for wavefunction (de)localisation: inverse participation ratio, inverse of Rényi entropy, and root-mean-square (RMS) image contrast. All these measures exhibit minimal values at the centre of the avoided crossing, where the wavefunction is maximally delocalised. Our results indicate that these quantities can be sufficient for the indication of wavefunction (de)localisation.

Investigation of quantum transport and local density of states in a graphene strip connected to a square lattice

We theoretically express quantum transport at Dirac points via graphene quantum billiard as a non-magnetic material to connect metallic leads. Our results indicate that the quantum billiard of graphene is similar to a resonant tunnelling device. The centerpiece size and the Fermi energy of the graphene quantum billiard play an important role in the resonant tunnelling. In graphene, change of carrier density can affect plasmon polaritons. At the Dirac point, the conductivity of graphene depends on the geometry, so that the conduction of the evanescent modes is close to the theoretical value of 4e2/πh (where Planck's constant and the electron charge are denoted by h and e, respectively.). This transport property can be used to justify chaotic quantum systems and ballistic transistors. Our theoretical results demonstrate that the local density of state of the graphene sheet for EL = ER = 0 is larger than EL = ER = t (where EL (ER) is onsite energy of the left (right) metallic lead) unlike the current obtained from the calculations.