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Register a new userOn the effect of weak disorder on the density of states in graphene
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The effect of weak potential and bond disorder on the density of states of graphene is studied. By comparing the self-consistent non-crossing approximation on the honeycomb lattice with perturbation theory on the Dirac fermions, we conclude, that the linear density of states of pure graphene changes to a non-universal power-law, whose exponent depends on the strength of disorder like 1-4g/sqrt{3}t^2pi, with g the variance of the Gaussian disorder, t the hopping integral. This can result in a significant suppression of the exponent of the density of states in the weak-disorder limit. We argue, that even a non-linear density of states can result in a conductivity being proportional to the number of charge carriers, in accordance with experimental findings.
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The effect of Coulomb scattering on graphene conductivity in field effect transistor structures is discussed. Inter-particle scattering (electron-electron, hole-hole, and electron-hole) and scattering on charged defects are taken into account in a wide range of gate voltages. It is shown that an intrinsic conductivity of graphene (purely ambipolar system where both electron and hole densities exactly coincide) is defined by strong electron-hole scattering. It has a universal value independent of temperature. We give an explicit derivation based on scaling theory. When there is even a small discrepancy in electron and hole densities caused by applied gate voltage the conductivity is determined by both strong electron-hole scattering and weak external scattering: on defects or phonons. We suggest that a density of charged defects (occupancy of defects) depends on Fermi energy to explain a sub-linear dependence of conductivity on a fairly high gate voltage observed in experiments. We also eliminate contradictions between experimental data obtained in deposited and suspended graphene structures regarding graphene conductivity.
We study the disorder effect of resonant spin Hall effect in a two-dimension electron system with Rashba coupling in the presence of a tilted magnetic field. The competition between the Rashba coupling and the Zeeman coupling leads to the energy crossing of the Landau levels, which gives rise to the resonant spin Hall effect. Utilizing the Stredas formula within the self-consistent Born approximation, we find that the impurity scattering broadens the energy levels, and the resonant spin Hall conductance exhibits a double peak around the resonant point, which is recovered in an applied titled magnetic field.
We report the observation of the quantized Hall effect in suspended graphene probed with a two-terminal lead geometry. The failure of earlier Hall-bar measurements is discussed and attributed to the placement of voltage probes in mesoscopic samples. New quantized states are found at integer Landau level fillings outside the sequence 2,6,10.., as well as at a fractional filling u=1/3. Their presence is revealed by plateaus in the two-terminal conductance which appear in magnetic fields as low as 2 Tesla at low temperatures and persist up to 20 Kelvin in 12 Tesla. The excitation gaps, extracted from the data with the help of a theoretical model, are found to be significantly larger than in GaAs based electron systems.
We study two lattice models, the honeycomb lattice (HCL) and a special square lattice (SQL), both reducing to the Dirac equation in the continuum limit. In the presence of disorder (gaussian potential disorder and random vector potential), we investigate the behaviour of the density of states (DOS) numerically and analytically. While an upper bound can be derived for the DOS on the SQL at the Dirac point, which is also confirmed by numerical calculations, no such upper limit exists for the HCL in the presence of random vector potential. A careful investigation of the lowest eigenvalues indeed indicate, that the DOS can possibly be divergent at the Dirac point on the HCL. In spite of sharing a common continuum limit, these lattice models exhibit different behaviour.
We consider the theory of Kondo effect and Fano factor energy dependence for magnetic impurity (Co) on graphene. We have performed a first principles calculation and find that the two dimensional $E_1$ representation made of $d_{xz},d_{yz}$ orbitals is likely to be responsible for the hybridization and ultimately Kondo screening for cobalt on graphene. There are few high symmetry sites where magnetic impurity atom can be adsorbed. For the case of Co atom in the middle of hexagon of carbon lattice we find anomalously large Fano $q$-factor, $qapprox 80$ and strongly suppressed coupling to conduction band. This anomaly is a striking example of quantum mechanical interference related to the Berry phase inherent to graphene band structure.
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