junction -- a resonance peak

$$H = \sum_{\langle i j \rangle \ne 0 } t c_i^+ c_j + f c_0^+ c_0 + ( s c_1^+ c_0 + s c_{-1}^+ c_0 + {\rm h.c.} )$$ (260)

Only site0 is in the central region. Because and $s$ enters only through $H_{CR}$ and $H_{RC}$,

$$\Sigma_R(\omega ) = (s/t)^2 \Sigma_{R0}(\omega )$$ (261)

where $\Sigma_{R0}$ is the value of $\Sigma_R$ when $s=t$. Then

$$G = \left( \omega - (s/t)^2\omega _0 - i(s/t)^2\Gamma _0 -f \right)^{-1}$$ (262)

$$T = \frac{(s/t)^4\Gamma _0^2}{ ( \omega -(s/t)^2\omega _0-f)^2 + (s/t)^4\Gamma _0^2 }$$ (263)

$$= \frac{ \frac{(s/t)^4\Gamma _0^2}{\left(1-(s/t)^2\right)^2} } { \l... ...{f}{1-(s/t)^2}\right)^2 + \frac{(s/t)^4\Gamma _0^2}{\left(1-(s/t)^2\right)^2} }$$ (264)

$T=1$ at the center of the peak, , and the half-width of the maximum is . Smaller $s$, and smaller $\Gamma _0$, which means smaller $t$ or the energy is near the edge of the band, give a shaper resonance peak on the conductance.

$T$ takes some value, for $s=t$. ($\Gamma _0$ is a function of $\omega$.) The broad peak locates not at $\omega =f$, but at $\omega =0$, which is the center of the band.