Transport through single-channel atomic wires: Effects of connected sites on scattering phase and odd-even parity oscillations

Abstract

Theoretical studies of scattering phase and odd-even parity oscillations of the conductance are presented for a finite atomic wire system, which is either connected with two single-channel leads or side-coupled to a single-channel perfect wire. The effects of connected sites on the scattering properties are examined. For a uniform atomic wire connected with two single-channel leads, it is found that when the number of atoms in the wire, $n$, and the two sequence numbers of the connected atomic sites, ${n}_{1}$ and ${n}_{2}$ $(1\ensuremath{\leqslant}{n}_{1}\ensuremath{\leqslant}{n}_{2}\ensuremath{\leqslant}n)$, satisfy the condition that $(n+1)∕\mathrm{gcd}({n}_{1},n+1\ensuremath{-}{n}_{2})$ is not an integer, the transmission coefficient, as a function of the incident electron energy, has zeros of second order. At these zeros the transmission phase is continuous. The zeros of the reflection coefficient, however, are always of first order, and the reflection phase has a lapse precisely by $\ensuremath{\pi}$ at each of these zeros. For an atomic wire system side coupled to a perfect lead, the conclusions are reversed: the transmission zeros are always of first order, while the reflection zeros can be of high order. It is also shown that in this side-coupled configuration, both the transmission zeros and the reflection zeros are related to the generic properties of the isolated atomic wire system. The odd-even oscillations of the conductance have also been investigated for finite atomic wire systems in both configurations. It is found that the transmission of a finite atomic wire system depends not only on the parity of the number of atomic sites in the system, but also on the parity of the sequence numbers of the atomic sites through which the atomic wire system is connected with the leads. Finally, by taking a simple one-dimensional quantum wire system with several attached side branches as an example, we show that the transmission zeros of higher order can be found in a quantum system built from one-dimensional wires.