Tunneling effect in gapped graphene disk in magnetic flux and electrostatic potential

We investigate the tunneling effect of a Corbino disk in graphene in the presence of a variable magnetic flux Φi created by a solenoid piercing the inner disk under the effect of a finite mass term in the disk region (R1 < r < R2) and an electrostatic potential. Considering different regions, we explicitly determine the associated eigenspinors in terms of Hankel functions. The use of matching conditions and asymptotic behavior of Hankel functions for large arguments, enables us to calculate transmission and other transport quantities. Our results show that the energy gap suppresses the tunneling effect by creating singularity points of zero transmission corresponding to the maximum shot noise peaks quantified by the Fano factor F . The transmission as a function of the radii ratio R2/R1 becomes oscillatory with a decrease in periods and amplitudes. It can even reach one (Klein tunneling) for large values of the energy gap. The appearance of the minimal conductance at the points kF R1 = R1δ is observed. Finally we find that the electrostatic potential can control the effect of the band gap.

The Nernst effect in Corbino geometry

We study the manifestation of the Nernst effect in the Corbino disk subjected to the normal external magnetic field and to the radial temperature gradient. The Corbino geometry offers a precious opportunity for the direct measurement of the magnetization currents that are masked by kinetic contributions to the Nernst current in the conventional geometry. The magnetization currents, also referred to as the edge currents, are independent on the conductivity of the sample which is why they can be conveniently described within the thermodynamic approach. They can be related to the Landau thermodynamic potential for an infinite system. We demonstrate that the observable manifestation of this, purely thermodynamic, Nernst effect consists in the strong oscillations of the magnetic field measured in the center of the disk as a function of the external field. The oscillations depend on the temperature difference at the edges of the disk. Dirac fermions and 2D electrons with a parabolic spectrum are characterized by oscillations of different phase and frequency. We predict qualitatively different power dependencies of the magnitude of the Nernst signal on the chemical potential for normal and Dirac carriers.

Transport properties of fermions with moat spectra

We present here polarization operator of non-relativistic fermions with spin-orbit (SO) Rashba interaction. The spectrum of this fermions is moat type having minimum on a circle. Contrary to Dirac or non-relativistic fermions, Fermi sea here has a geometry of Corbino disk which reflects in a transport properties of excitation’s.