Quantum-Hall physics and three dimensions.

The discovery of the quantum Hall effect (QHE) in 1980 marked a turning point in condensed matter physics: given appropriate experimental conditions, the Hall conductivityσxyof a two-dimensional electron system is exactly quantized. But what happens to the QHE in three dimensions (3D)? Experiments over the past 40 years showed that some of the remarkable physics of the QHE, in particular plateau-like Hall conductivitiesσxyaccompanied by minima in the longitudinal resistivityρxx, can also be found in 3D materials. However, since typicallyρxxremains finite and a quantitative relation betweenσxyand the conductance quantume2/hcould not be established, the role of quantum Hall physics in 3D remains unsettled.

Field-induced density wave in the heavy-fermion compound CeRhIn₅.

Strong electron correlations lead to a variety of distinct ground states, such as magnetism, charge order or superconductivity. Understanding the competitive or cooperative interplay between neighbouring phases is an outstanding challenge in physics. CeRhIn₅ is a prototypical example of a heavy-fermion superconductor: it orders anti-ferromagnetically below 3.