Strongly correlated electrons

Landau theory takes a pounding

The destruction of particles is normally associated with high-energy physics and particle detectors. But in solid-state physics the destruction of particles, or rather quasiparticles, is taking place routinely in standard laboratories.

Lev Landau. His Fermi-liquid theory works well for most metals, but the list of exceptions is growing. Credit: AIP EMILIO SEGRÈ VISUAL ARCHIVES

The concept of quasiparticles was introduced by Lev Landau in his seminal Fermi-liquid theory to explain heuristically the physical properties of 3He. This theory has since been applied universally to common metals. Landau's quasiparticles are essentially electrons whose properties have been modified, typically through interactions with the atomic lattice and/or other electrons, leading to (amongst other things) larger effective masses. His theory has stood as the Standard Model for understanding metal physics for almost 50 years. Indeed, it seemed for a long while that it was sufficient simply to ascribe a one-to-one correspondence between the low-energy excitations of a free Fermi gas and those of an interacting Fermi liquid, through a renormalization process, to account for almost all the many-body interactions that exist inside a metallic system.

In a certain class of materials, known collectively as strongly correlated electron systems, metallicity is weakened or even lost altogether and the limits of applicability of the Fermi-liquid model are now being exposed. In addition, a bewildering range of novel states is beginning to be realized, in which magnetic, orbital, structural and electronic order all compete for the ground state at zero temperature. In these systems, small changes in a sample's environment (for example, through changes in its temperature, dimensionality or doping level) can dramatically alter the spectrum of quasiparticle excitations and lead to fundamentally new physics, and in some circumstances, to the breakdown of the quasiparticle itself. The International Conference on Strongly Correlated Electron Systems, held in Houston 14–18 May, was dedicated to this class of rebellious solids, which are not only interesting from a fundamental perspective; some of them may even form the basis of the next generation of electronic and magnetic devices.

The conference was dominated by three broad areas: frustrated magnetism, quantum criticality and unconventional superconductivity. In the former, the key question was “Can quantum spin liquids (the absence of magnetic order in a system with strong magnetic exchange interactions) exist in dimensions greater than one?” In such systems, exotic excitations, possibly involving quasiparticles with fractional quantum numbers and unusual statistics, are predicted to appear1. An isolated triangle with a single, localized, half-integer spin on each vertex is the ideal geometrical configuration for total magnetic frustration, and two promising candidates for a genuine spin-liquid state, both involving two-dimensional triangular networks of half-integer spins, were reported by Young Lee2 (in ZnCu2(OH)6Cl2) and by Kazushi Kanoda3 (in the organic salt κ-(ET)2Cu2(CN)3). Perhaps more surprisingly, evidence for spin-liquid physics in the three-dimensional hyper-kagome lattice Na4Ir3O8 was also reported at the conference (unpublished work by Y. Okamoto et al.). The challenge now is to find evidence of these exotic, possibly fractional, excitations, and low-temperature thermal transport seems as good a place as any to start.

In keeping with tradition, heavy-fermion compounds, often containing cerium or uranium, featured largely in the programme, particularly in the sessions devoted to quantum criticality. A quantum critical point is a locus in phase space in the limit of absolute zero, which separates a magnetically ordered phase from one that either shows a different type of order or has no order whatsoever (as for a paramagnetic phase). Quantum fluctuations — caused by quantum tunnelling between these two competing ordered states — are believed to cause intense scattering of the quasiparticles, leading to novel power-law dependencies in the transport properties and, ultimately, to the destruction of the quasiparticles themselves. Each phase has associated with it a particular energy scale that should collapse to zero in the vicinity of the quantum critical point. One surprising development in this area was the announcement by Philipp Gegenwart of a second higher-energy scale on the metallic side of the temperature–magnetic field phase diagram of YbRh2Si2 (ref. 4), which manifests itself in a series of transport and thermodynamic kinks. The physics associated with this new energy scale is a conundrum; it violates not only Landau's theory, but also the conventional view of quantum criticality and the standard theory of phase transitions. Identification of this unexpected visitor is now of paramount importance for both experimentalists and theorists alike.

The existence of a secondary, elevated energy scale is reminiscent of the pseudogap energy scale seen in low-carrier-density, high-temperature superconductors. When the carrier density is high, the Fermi surface — the locus in momentum space (k-space) defining the most energetic electronic states — is large, continuous and robust to changes in temperature5. At lower carrier concentrations, however, the Fermi surface is seen to be carved up into segments or disconnected 'Fermi arcs' centred along the Brillouin zone diagonals as the temperature is reduced6. This reduction in the volume of occupied states violates a fundamental sum rule, and as such is regarded as a further indication of violation of Fermi-liquid theory. The observation by Louis Taillefer and co-workers, reported for the first time at this conference, of quantum oscillations in a high-purity, low-carrier-density copper oxide superconductor7 therefore came as a big surprise to the community. Quantum oscillations are a manifestation of quantized orbits of quasiparticles at or near the Fermi surface induced by a strong magnetic field. Although the paradigm of quantum oscillations as proof of the existence of fermionic quasiparticles was challenged later in the conference, their observation in a low-doped high-temperature superconductor seemed to signal the end of a twenty-year quest and the beginning of a new chapter in the field. It has also brought the two sides (underdoped and overdoped) of the phase diagram together, almost for the first time, and demonstrated that some vestige of quasiparticle physics survives deep into the underdoped region of the phase diagram. The key question now of course is how these small Fermi pockets evolve with carrier number into the large Fermi surface seen on the opposite side.

Coupled with the continuing, fruitful search for non-Fermi-liquid physics in quasi-one-dimensional conductors (which also featured at the conference), these are exciting times for the correlated-electron community. As fate would have it, there was a jewellery shop in the foyer of the conference hotel called 'Landau'. The jewels could have been Landau's metaphorical quasiparticles. Rather appropriately, the shop was advertising most of its stock at half price, as though the spirit of Lev Landau was on the verge of moving out, just as strongly correlated electrons were moving in. Despite the sense of foreboding, there were certain exclusions to the sale. Perhaps these were the faint rays of optimism emanating from the auditorium, most notably in that most notorious of non-Fermi-liquids, the high-temperature superconductors. Don't pack up just yet, Landau. All is not lost.

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Hussey, N. Landau theory takes a pounding. Nature Phys 3, 445–446 (2007). https://doi.org/10.1038/nphys666

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