Mesoscopic Charge Density Wave in a Magnetic Flux
Abstract
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. It 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 coherence length
ξ
, 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 also calculated. We derive the harmonics expansion of the persistent current in a presence of a finite gap.