# Sr2RuO4 reveals universal fermi-liquid scaling and quasiparticles beyond Landau theory

# Summary

Interacting many-body systems constitute one of the greatest challenges of physics. Attempts to understand the behavior of interacting fermions (such as electrons in a metal or the atoms of liquid 3He) led Landau to postulate a phenomenological model, which became known as Fermi-liquid theory. However since 60 years, the electrical properties of metals with strong electron correlations are unconventional and still poorly understood theoretically. A recent collaboration of physicist from the MaNEP network successfully shed light this complicated problem by involving both theory, numerical calculations and quantitative experimental data. The behaviour of the low energy excitations confirm in unprecedented detail Landau’s model. The experiments and theoretical modeling demonstrate that excitations at higher energy are surprisingly long-lived.

# Sr2RuO4 reveals universal fermi-liquid scaling and quasiparticles beyond Landau theory

by Damien Stricker and Dirk van der Marel, UNIGE

after an article published in Physical Review Letters

## Fermi liquid

A Fermi liquid, when the temperature approaches the absolute zero, starts to behave like a gas of “quasi-particles” which do not interact with each other. A quasi-particle is similar to an electron, except that its effective inertial mass, m*, is higher than that of a free electron, m_{e}. This mass enhancement, m*/m_{e}, is proportional to the strength of the interactions between the electrons in the metal. Some of the predicted properties still remain to be confirmed by experiments. One of those properties has to do with the life-time of the excited state after which we excite the electrons by absorbing a low energy photon. With our optical experiments we confirmed these predictions in great detail when we cooled down the canonical Fermi liquid material Sr_{2}RuO_{4} . Going in the opposite way by increasing temperature and/or excitation energy, the behavior is non-universal, and for the case of Sr_{2}RuO_{4} both our calculations and optical spectra indicate that quasi-particles in a certain range of (relatively high) excitation energy are also weakly scattered [2].

(Experiment) Once cooled down Sr_{2}RuO_{4} gradually tends to follow the standard Fermi-liquid picture with the expected scaling parameter p=2.

## Solid state analogue of ^{3}He

Sr_{2}RuO_{4} is a transition metal oxide. It is also a metal but not a conventional one: By virtue of the confining potential of the ruthenium transition metal atoms, the interactions between the conduction electrons are much stronger than in ordinary metals such as copper or aluminum. Found to be superconducting at about 1 degree above the absolute zero of temperature [3] experiments indicate that this material is a chiral p-wave superconductor.

The properties both in the normal state and in the superconducting state make that Sr_{2}RuO_{4} is a solid state analogue of the archetypal Fermi-Liquid, liquid ^{3}He. In this respect it is, in fact, quite unique, and there are a number of unique consequences of this state of affairs. Among other things Majorana fermions may occur in the superconducting state, which could be used for quantum computing.

(Numerical calculations) On top of the band structure (dashed lines) Resilient quasiparticles can be seen as large and soft blue waterfall-like structures.

## Resilient quasiparticles

Predicted to fail at high energy and temperature the quasi-particle picture seems to persist well above the temperature and limits predicted by theory. Indeed both experiment and dynamical mean field theory (DMFT) calculations indicate the presence of “resilient” quasi-particles at high energy (typically 0.1 eV) and thanks to the versatility of the latter it is even possible to describe them qualitatively.

## MaNEP collaboration

Theory (black), numerical computation (circles) and experiment (blue) allows to understand and define the limits of the fermi-liquid picture.

This is a collaboration involving scientists of several groups within MaNEP, as well as from Salerno (Vecchione and Fittiapldi) and Ljubliana (Mravlje): Damien Stricker is a PhD student working with Dirk van der Marel on manifestations of strong electron correlations in the properties of materials, using optical spectroscopy as the main experimental tool. Antoine Georges concentrates on the theory of strongly correlated electrons. Christophe Berthod works on analytical tools for theoretical modeling of data.

[1] Phys. Rev. Lett. 113, 087404 – Published 22 August 2014[2] Phys. Rev. Lett. 110, 086401 (2013)

[3] Catherine Kallin Rep. Prog. Phys. 75 042501 (2012)