It is well-known that the conductance (G) of a rectangular two-dimensional conductor is directly proportional to its width (W) and inversely proportional to its length (L); that is,

G = σW/L

where the conductivity a is a material property of the sample independent of its dimensions. How small can we make the dimensions (W and/or L) before this ohmic behavior breaks down? This question has intrigued scientists for a long time. During the 1980s it became possible to fabricate small conductors and explore this question experimentally, leading to significant progress in our understanding of the meaning of resistance at the microscopic level. What emerged in the process is a conceptual framework for describing current flow on length scales shorter than a mean free path. We believe that these concepts should be useful to a broad spectrum of scientists and engineers. This book represents an attempt to present these developments in a form accessible to graduate students and to non-specialists.

Small conductors whose dimensions are intermediate between the microscopic and the macroscopic are called mesoscopic. They are much larger than microscopic objects like atoms, but not large enough to be ‘ohmic’. A conductor usually shows ohmic behavior if its dimensions are much larger than each of three characteristic length scales: (1) the de Broglie wavelength, which is related to the kinetic energy of the electrons, (2) the mean free path, which is the distance that an electron travels before its initial momentum is destroyed and (3) the phase-relaxation length, which is the distance that an electron travels before its initial phase is destroyed.