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The progressing miniaturization of electronic circuits raises the question what controls the transport when a contact is shrunk to its minimal possible size, a single atom. Electrical single-atom contacts have recently been fabricated using the break junction technique [1]. By analyzing the subgap structure of superconducting contacts it was demonstrated that the valence orbitals of the junction atom act as the transmission channels for the electronic current and that the transmissions T m of the individual orbitals m=1,…, N add up to the total transmission of the contact, which was measured independently [1]. Naturally, the transmissions T m can take any value 0 ≤ T m ≤ 1, since they depend on the microscopic details like the coupling matrix elements of the atomic orbitals to the leads. Therefore, it came as a surprise that in Al junctions the total conductance remained nearly constant with a value close to the conductance quantum 2e2/h, when the contact was mechanically stretched, although at the same time the individual channel transmissions T m varied over a wide range [2]. As a consequence, certain conductance values are preferred in Al contacts as shown in Fig. 1. In the present work we prove a sum rule for the total conductance in atomic junctions where the Coulomb repulsion between electrons in the valence orbitals of the junction atom is large. We propose that this correlation effect is the microscopic origin of the observed approximate conductance quantization.

Generalized Conductance Sum Rule in Atomic Break Junctions