Punctuated equilibrium, the notion that evolution in nature is stepwise rather than continuous, sometimes applies to evolution in science as well. It happens that the seed of a scientific breakthrough slumbers for a decade or even longer, without generating much interest. The seed can be a theoretical concept without clear predictions to test experimentally, or an intriguing but confusing experiment without a lucid interpretation. When the seed finally germinates, an entire field of science can reach maturity in a few years.In hindsight, this is what happened ten years ago, when the authors (newly hired PhD's at Philips Research in Eindhoven) ventured into the field of quantum ballistic transport. Together with Bart van Wees, then a graduate student at Delft University of Technology, we were confronted with some pretty vague challenges. On the experimental side, there was the search for a quantum-size effect on the conductance, which would reveal in a clear-cut way the one-dimensional density of states of electrons confined to a narrow wire. Experiments on narrow silicon transistors (at Yale University and AT&T Bell Labs., Holmdel) had come close, but suffered from irregularities due to disorder. (These irregularities would become known as "universal conductance fluctuations", see PHYSICS TODAY, December 1988, page 36.) We anticipated that the electron motion should be ballistic, i.e. without scattering by impurities. Moty Heiblum (IBM, Yorktown Heights) had demonstrated ballistic transport of hot electrons, high above the Fermi level. For a quantum-size effect one needs ballistic motion at the Fermi energy. Our colleague Thomas Foxon from Philips Research in Redhill (UK) could provide us with heterojunctions of GaAs and AlGaAs, containing at the interface a thin layer of highly mobile electrons. Such a "two-dimensional electron gas" seemed an ideal system for ballistic transport.
On the theoretical side, there was the debate whether a wire without impurities could have any resistance at all [1]. Ultimately, the question was: "What is measured when you measure a resistance?" The conventional point of view (held in the classical Drude-Sommerfeld or the quantum mechanical Kubo theories) is that conduction is the flow of current in response to an electric field. An alternative point of view was put forward in 1957 by Rolf Landauer (IBM, Yorktown Heights), who proposed that "conduction is transmission" [2]. Landauer's formula, a relationship between conductance and transmission probability, had evolved into two versions. One gave infinite conductance (= zero resistance) in the absence of impurity scattering, while the other gave a finite answer. Although the origin of the difference between the two versions was understood by at least one of the theorists involved in the debate [3], the experimental implications remained unclear.
Looking back ten years later, we find that the seed planted by Landauer in the fifties has developed into a sophisticated theory, at the basis of the entire field of quantum ballistic transport. The breakthrough can be traced back to experiments on an elementary conductor: a point contact. In this article we present a brief account of these developments. For a more comprehensive and detailed discussion, we direct the reader to the reviews in the bibliography.