A calculation of dynamical conductivity is performed for low-dimensional systems, by taking into account the screening of field. Our calculation is valid for all value of wave vector and frequency. The Drude conductivity of three, two and one-dimensional free electron gas, layered electron gas and quantum wire system can be deduced from our calculation. However, our calculation suggests that the use of Drude formulae of conductivity to explain experimental result on microwave and infra-red conductivity, in long wave length limit, can be highly erroneous in case of low-dimensional system that offer larger value of relaxation time. It is found that; (i) screening of a dynamical field becomes less significant on reduction in dimensionality and (ii) unlike the case of three dimensional electron gas, transverse electric field cannot excite collective excitation modes (penetration depth cannot be defined) in a two-dimensional electron gas and quantum wire system. In comparison with prior reported calculation ours is more rigorous calculation as it includes the possibility of propagation of collective excitation modes in all direction. The plasmons in a low-dimensional system cannot be excited for negligibly small value of momentum transfer.
Quasi-Low-Dimensional Electron Gas with One Populated Band as a Testing Ground for Time-Dependent Density-Functional Theory of Mesoscopic Systems
