Method of Image and Transmission through Semi-infinite Nanowires

The method of functional integral bosonization is extended to examine the transmission properties of semi-infinite nanowires. In particular, it is shown that edge states will arise at the end point of the dimerized semi-infinite spin-chain and by combining the method of image and the bosonization technique, the system can be properly bosonized. Based on the bosonized action and a renormalization group analysis, it is shown that unlike scattering due to single bulk impurity in the nanowire, the scattering potential remains relevant even for slightly attractive potential due to the interaction between the edge state and its image. When the strength of potential goes beyond a critical strength, the tip of the semi-infinite nanowire may become insulating.