Tunneling in partial coherence through a series of barriers: an explicit result from a pure dephasing model

Within the Büttiker dephasing model, the backscattering in the dephasing process is eliminated by setting a proper boundary condition. Explicit expression is carried out for the effective total tunneling probability in the presence of multiple pure dephasing scatterers with partial coherence. The derived formula is illustrated analytically by various limiting cases, and numerically for its application in tunneling through multi-barrier systems. PACS numbers:73.23.-b,73.40.-c Typeset using REVTEX 1 To simulate the phase-breaking effect in partially coherent transport through a mesoscopic system, Büttiker proposed a conceptually simple model by coupling electronic reservoirs to the conductor. The dephasing reservoir can be thought of as either a fictitious or a real branch voltage probe. Although this approach appears to be purely phenomenological, it however can be justified from a microscopic theory with proper approximations,3–5 by viewing that both the electron-phonon interactions and the dephasing reservoir can be described by a self-energy function. Owing to the simplicity, the Büttiker dephasing model has received noticeable attention, and been applied to transport through various mesoscopic systems.9–19 Noticeably, in the original work of Büttiker and the later applications mentioned above, in addition to randomizing the electronic phase, the phase-breaking scatterer would also randomize the electronicmomentum. Randomization of momentum means backscattering in the dephasing process, thus introduces an additional resistance. This undesired feature has been noticed and analyzed by a few authors,20–23 commonly following the idea by coupling two voltage probes to model a single pure dephasing scatterer. In this paper, based on the original work of Büttiker (i.e. using a single reservoir to model a single dephasing scatterer), an explicit expression will be derived for the effective total tunneling probability through a multi-barrier mesoscopic system in the presence of multiple pure dephasing scatterers with arbitrary dephasing strength. The underlying physics and practical application will be illustrated clearly. In general, consider the tunneling through a series of barriers shown in Fig. 1, where the squares stand for tunnel barriers, and the triangles for dephasing scatterers. They can be described in terms of scattering matrices as follows. For the individual (symmetric) barrier (e.g. the jth one), the tunneling property is characterized by S j = 