The response to an electric field (DC and AC) of electronic systems in which the Fermi surface consists of a number of 3D Weyl points (such as some pyrochlore iridates) exhibits a peculiar combination of characteristics usually associated with insula
ting and conducting behaviour. Generically a neutral plasma in clean materials can be described by a tight binding model with a strong spin-orbit interaction. A system of that type has a vanishing DC conductivity; however the current response to the DC field is very slow: the current decays with time in a powerwise manner, different from an insulator. The AC conductivity, in addition to a finite real part which is linear in frequency, exhibits an imaginary part that increases logarithmically as function of the UV cutoff (atomic scale). This leads to substantial dielectric response like a large dielectric constant at low frequencies. This is in contrast to a 2D Weyl semimetal like graphene at neutrality point where the AC conductivity is purely pseudo-dissipative. The Coulomb interaction between electrons is long range and sufficiently strong to make a significant impact on transport. The interaction contribution to the AC conductivity is calculated within the tight binding model.
The long standing controversy concerning the effect of electron - electron interaction on the electrical conductivity of an ideal graphene sheet is settled. Performing the calculation directly in the tight binding approach without the usual prior red
uction to the massless Dirac (Weyl) theory, it is found that, to leading order in the interaction strength alpha =e^2/(hbar*v0), the DC conductivity sigma/sigma0=1+C*alpha is significantly enhanced with respect to the independent-electrons result sigma0, i.e. with the value C = 0.26. The ambiguity characterizing the various existing approaches is nontrivial and related to the chiral anomaly in the system. In order to separate the energy scales in a model with massless fermions, contributions from regions of the Brillouin zone away from the Dirac points have to be accounted for. Experimental consequences of the relatively strong interaction effect are briefly discussed.
The dynamical approach is applied to ballistic transport in mesoscopic graphene samples of length L and contact potential U. At times shorter than both relevant time scales, the flight time and hslash/U, the major effect of the electric field is to c
reate electron - hole pairs, i.e. causing interband transitions. In linear response this leads (for width W>>L) to conductivity pi/2 e^{2}/h. On the other hand, at times lager than the two scales the mechanism and value are different. It is shown that the conductivity approaches its intraband value, equal to the one obtained within the Landauer-Butticker approach resulting from evanescent waves. It is equal to 4/pi e^{2}/h for W>>L. The interband transitions, within linear response, are unimportant in this limit. Between these extremes there is a crossover behaviour dependent on the ratio between the two time scales. At strong electric fields (beyond linear reponse) the interband process dominates. The electron-hole mechanism is universal, namely does not depend on geometry (aspect ratio, topology of boundary conditions, properties of leads), while the evanescent modes mechanism depends on all of them. On basis of the results we determine, that while in absorption measurements and in DC transport in suspended graphene the first conductivity value was measured, the latter one would appear in experiments on small ballistic graphene flakes on substrate.
Electron - hole pairs are copuously created by an applied electric field near the Dirac point in graphene or similar 2D electronic systems. It was shown recently that for sufficiently large electric fields and ballistic times the I-V characteristics
become strongly nonlinear due to Schwingers pair creation. Since there is no energy gap the radiation from the pairs annihilation is enhanced. The spectrum of radiation is calculated. The angular and polarization dependence of the emitted photons with respect to the graphene sheet is quite distinctive. For very large currents the recombination rate becomes so large that it leads to the second Ohmic regime due to radiation friction.
