▎ 摘　　要

The behavior of a monolayer undoped graphene sheet in presence of a weak gravitational wave is discussed. In the low-energy limit, the linear dispersion of the energy levels near the Dirac points can be ascribed to massless excitations obeying a Dirac equation in a 2+1D spacetime. Starting from a 2+1 dimensional (2+1D) Lagrangian, the equations of motion for the electron (hole) wavefunction in the graphene sheet are deduced and solved. The Bogolubov coefficients are then obtained and the gravitationally induced amplitude of the electron-hole pair excitations is evaluated. The typical quadrupolar distribution of the pair creation probability appears rotated by a pi/4 angle in the plane of the graphene sheet, when compared to the case of a confined 2+1D massless scalar field in the same gravitational background. Such behavior can be understood taking into account the role of helicity in graphene during the interaction with the gravitational wave. Although very small, the effect offers an interesting example of interaction at nanoscale between a non-trivial quantum system and a time-dependent gravitational background. The strong analogy between the quantum theoretical description of the graphene physics and the standard quantum field theory can also suggest a similar analysis in different physical contexts.