Low-frequency plasma mode and its effect on the tunneling density of states in thin superconducting wires

The plasma mode in thin superconducting wires is studied within the random- phase approximation in the dirty limit at zero temperature. The plasma freq uency w(p) is calculated as a function of the wave number. In the limit of w(p) much less than Delta/h the result is in agreement with a nearly linear dispersion relation obtained by the phenomenological theory [Mooij and Sch on: Phys. Rev. Lett. 55 (1985) 114.]. It is found that, except in the low-f requency limit, the phenomenological theory leads to an overestimation of w (p). The finite length of the sample limits the number of allowed modes in actual situations, and the corresponding plasma frequencies are quantized a s w(pn) (n = 1,2,). Due to this quantization and a divergent state density at the gap edge, a sharp structure is shown to arise in the tunneling densi ty of states at epsilon = w(pn) + Delta due to the plasmon exchange process .