Low-dimensional approach to pair production in an oscillating electric field: Application to bandgap graphene layers

The production of particle-antiparticle pairs from the quantum field theoretic ground state in the presence of an external electric field is studied. Starting with the quantum-kinetic Boltzmann-Vlasov equation in four-dimensional spacetime, we obtain the corresponding equations in lower dimensionalities by way of spatial compactification. Our outcomes in $2+1$ dimensions are applied to bandgap graphene layers, where the charge carriers have the particular property of behaving like light massive Dirac fermions. We calculate the single-particle distribution function for the case of an electric field oscillating in time and show that the creation of particle-hole pairs in this condensed matter system closely resembles electron-positron pair production by the Schwinger effect.

Figure 1

Logarithmic plots of the single-particle distribution functions for models involving massless (upper panel) and massive ($\mathrm{\Delta }ϵ=0.26\mathrm{eV}$, lower panel) charged carriers are displayed. In both cases the external parameters were chosen as follows: $E=6.6\times {10}^4\mathrm{V}/\mathrm{cm}$, $\tau \simeq 41.625\mathrm{ps}$ and $\omega =24.032\mathrm{m}\mathrm{eV}$.

Figure 2

Number of electron-hole pairs produced per ${\mathrm{cm}}^2$ in an OEF. While the result for massless carriers is in green, the outcome for massive charges is shown in red and blue, with the data points connected by straight lines. Also, for comparison, the curves corresponding to the cases driven by a CEF [see Eq. (8)] are displayed in a green dash-dotted line (for massless) and blue dashed line (for massive). Here the vertical grey dashed line indicates the electric field value which was used in Fig. 1. The same benchmark values and notation of Fig. 1 must be understood.