Square-gradient mechanism of surface scattering in quasi-one-dimensional rough waveguides

Abstract

We develop a perturbative approach that allows one to study surface scattering in quasi-one-dimensional waveguides with rough boundaries. Our approach is based on the construction of an effective "bulk" potential of a very complicated structure. A detailed analysis of this potential reveals that apart from well-known terms considered in previous studies, one should keep specific terms that depend on the square of the derivative of the boundaries. As was found, in spite of an apparent smallness of these square-gradient scattering ͑SGS͒ terms, there is a physically important region of parameters in which they cannot be neglected. Our approach also demonstrates that the contribution of the SGS mechanism of scattering strongly depends on the type of rough boundaries ͑uncorrelated, symmetric, or antisymmetric͒.

Ballistic, diffusive, and localized transport in surface-disordered systems: Two-mode waveguide

“…In accordance with Ref. 20, both backward and forward scattering lengths consist of two fundamentally different partial lengths. One of these partial lengths is related to the amplitude and gradient mechanisms of surface scattering, whereas the other partial length is associated with the square-gradient mechanism (the connection between these partial lengths and the scattering potentialÛ (x, z) is discussed below).…”

“…Eqs. (3.8) and (3.9) can be directly found from the general expression (2.3) with the use of well developed methods, such as, e.g., the perturbative diagrammatic technique of Berezinski [2,31], the invariant imbedding method [32,33] or the two-scale approach [30,34,35].…”

“…The transport of quantum quasi-particles through thin metal films and semiconductor nano-structures, such as nanowires and strips, supperlattices and quantumwell systems, has been a hot topic since more than four decades [1][2][3][4][5][6]. Nowadays, it is known that transport properties of conductors with extremely small cross sections, are substantially controlled by the scattering of electrons at random inhomogeneities of the conductor boundaries [7][8][9][10][11].…”

Discrimination between two mechanisms of surface scattering in a single-mode waveguide

“…As was predicted in Refs. [13][14][15][16], the weak surface scattering in single-mode waveguides is determined by two different mechanisms: amplitude (A) and square-gradient (SG) surface scattering. Correspondingly, the transport is specified by two power spectra.…”

“…Thus, one can discriminate one of them through the selection of the wave number k x . In the other situation, with Gaussian correlations [13][14][15][16][17], when both terms 1/L (A) loc and 1/L (SG) loc are nonzero, one has to compare which mechanism prevails.…”