MESOSCOPIC CHARGE-DENSITY-WAVE IN A MAGNETIC-FLUX

The stability of a Charge Density Wave (CDW) in a one-dimensional ring pierced by a Aharonov-Bohm flux is studied in a mean-field picture. I t is found that the stability depends on the parity of the number N of electrons. When the size of the ring becomes as small as the coherenc e length xi, the CDW gap increases for even N and decreases for odd N. Then when N is even, the CDW gap decreases with flux but it increases when N is odd. The variation of the BCS ratio with size and flux is a lso calculated. We derive the harmonics expansion of the persistent cu rrent in a presence of a finite gap.