Tunnel view of how electrons play

Scanning tunnelling microscopes provide insights into mysterious electronic effects in some metals

Electrons behave like football teams: the match becomes interesting when the teamwork is as good as that conjured up by the players of FC Barcelona. Electrons which interact strongly with each other give rise to superconductivity, the lossless transport of current, for example. A team headed by researchers at the Max Planck Institute for Chemical Physics of Solids in Dresden is now taking a completely new look at the teamwork between electrons. They have used a scanning tunnelling microscope to investigate the Kondo effect in the metal ytterbium rhodium silicide YbRh₂Si₂, which contains unpaired electrons and thus magnetic moments. At low temperatures, the strong interactions between the electrons completely shield the magnetic moments from each other. The Dresden-based physicists have now observed how this shielding is created. Their work also shows how well electronic processes in solids can be investigated with scanning tunnelling microscopes.

At low temperatures, quasi-particles are formed

“We can unequivocally assign the three peaks which occur at distinct energies,” says Steffen Wirth. Thus at – 17, – 27 and – 43 millivolts relatively large numbers of electrons tunnel from the sample to the microscope tip. These voltages correspond to energies where the electrons collect more or less in bands. The bands are caused by the crystal field splitting: if the 4f electrons of the ytterbium choose to occupy those orbital groups of the four possible ones where they avoid neighbouring atoms in the crystal as much as possible, they save energy. The corresponding band is therefore at lower energies than one where the electrons may meet their neighbours in the crystal. The effect itself has been known for quite a while. “We are the first to observe the crystal field splitting in the scanning tunnelling microscope,” says Steffen Wirth.  From these bands with the different energies the electrons then tunnel into the microscope tip.

The fact that the crystal field splitting becomes visible in the tunnelling microscope also shows the researchers that they are measuring not only surface properties, but mostly properties of the interior of their samples. “This was not clear before the investigation,” says Steffen Wirth. Scanning tunnelling microscopes are particularly sensitive to the characteristics of the surface and everything which lies or happens on it. It could also have been the case that the physicists saw only special effects of the surface. “We can now exclude this,” says Wirth.

This is also one of the reasons why the physicists in Dresden are quite confident in their explanation as to why the tunnelling current collapses when the voltage decreases to zero. At low temperatures, hardly any current continues to flow between the sample and the tip of the tunnelling microscope. The researchers put this decrease down to the Kondo effect on individual ytterbium atoms – the very phenomenon which the experiments were actually designed to investigate.

The 4f electrons, which are localized at the ytterbium atoms, rotate about their own axis and thus create the usual magnetic moments of the ytterbium atoms – physicists call this rotation spin. The Kondo effect causes the conduction electrons, which transport the current, to form quasi-particles with these magnetic moments at around minus 170 degrees Celsius. These quasi-particles can possibly be visualized as a cloud of the local magnetic moments and the conduction electrons surrounding them. The spins of the conduction electrons here are oriented in precisely the opposite direction to the spins of the local 4f electrons and thus shield the magnetic moments of the 4f electrons. Since the quasi-particles are relatively heavy compared to an individual electron, the heavy fermion metals have been named after them.

“We assume that fewer and fewer conduction electrons contribute to the tunnelling conductivity at temperatures below minus 170 degrees Celsius, because they are increasingly bound in quasi-particles,” says Steffen Wirth. “We therefore take the decrease of the tunnelling current to be strong evidence for the Kondo effect.”

Wirth and his colleagues can interpret the final conspicuous detail of the tunnelling current curve with less clarity: a hump at - 6 millivolts, which only occurs below minus 245 degrees Celsius, but markedly dents the current-voltage curve at minus 268 degrees Celsius. “We interpret this as an indication of a Kondo lattice,” says Steffen Wirth. Quasi-particles formed by the Kondo effect join together to form a Kondo lattice. The quasi-particles then cease to lead an isolated existence in the material, but interact with each other. This process also leads them to form an energy band, in which the mixture of 4f and conduction electrons likes to be – this is the assumption.

“Whether a Kondo lattice exists and when it forms is a very controversial issue,” says Steffen Wirth. Some physicists assume that the lattice forms before the quasi-particles. “I cannot imagine that physically,” says Steffen Wirth: “And we actually observe the decrease of the tunnelling current at higher temperatures than the signal which we assume to be caused by the Kondo lattice,” explains Wirth. If the interpretation of the signal at – 6 millivolts is correct, the quasi-particles would only form a lattice after they have been produced, as corresponds to the natural sequence of cause and effect.