Piers Coleman

The break-up of heavy electrons at a quantum critical point

The point at absolute zero where matter becomes unstable to new forms of order is called a quantum critical point (QCP). The quantum fluctuations between order and disorder that develop at this point induce profound transformations in the finite temperature electronic properties of the material. Magnetic fields are ideal for tuning a material as close as possible to a QCP, where the most intense effects of criticality can be studied. A previous study on the heavy-electron material YbRh2Si2 found that near a field-induced QCP electrons move ever more slowly and scatter off one another with ever increasing probability, as indicated by a divergence to infinity of the electron effective mass and scattering cross-section. But these studies could not shed light on whether these properties were an artefact of the applied field, or a more general feature of field-free QCPs. Here we report that, when germanium-doped YbRh2Si2 is tuned away from a chemically induced QCP by magnetic fields, there is a universal behaviour in the temperature dependence of the specific heat and resistivity: the characteristic kinetic energy of electrons is directly proportional to the strength of the applied field. We infer that all ballistic motion of electrons vanishes at a QCP, forming a new class of conductor in which individual electrons decay into collective current-carrying motions of the electron fluid.

Onset of antiferromagnetism in heavy-fermion metals

There are two main theoretical descriptions of antiferromagnets. The first arises from atomic physics, which predicts that atoms with unpaired electrons develop magnetic moments. In a solid, the coupling between moments on nearby ions then yields antiferromagnetic order at low temperatures. The second description, based on the physics of electron fluids or ‘Fermi liquids’, states that Coulomb interactions can drive the fluid to adopt a more stable configuration by developing a spin density wave. It is at present unknown which view is appropriate at a ‘quantum critical point’, where the antiferromagnetic transition temperature vanishes. Here we report neutron scattering and bulk magnetometry measurements of the metal CeCu6-xAux, which allow us to discriminate between the two models. We find evidence for an atomically local contribution to the magnetic correlations which develops at the critical gold concentration (xc = 0.1 ), corresponding to a magnetic ordering temperature of zero. This contribution implies that a Fermi-liquid-destroying spin-localizing transition, unanticipated from the spin density wave description, coincides with the antiferromagnetic quantum critical point.

Quantum Criticality Without Tuning in the Mixed Valence Compound β-YbAlB4

A quantum phase transition is observed in a stoichiometric compound at ambient pressure and in zero magnetic field. Fermi liquid theory, the standard theory of metals, has been challenged by a number of observations of anomalous metallic behavior found in the vicinity of a quantum phase transition. The breakdown of the Fermi liquid is accomplished by fine-tuning the material to a quantum critical point by using a control parameter such as the magnetic field, pressure, or chemical composition. Our high-precision magnetization measurements of the ultrapure f-electron–based superconductor β-YbAlB4 demonstrate a scaling of its free energy that is indicative of zero-field quantum criticality without tuning in a metal. The breakdown of Fermi liquid behavior takes place in a mixed-valence state, which is in sharp contrast with other known examples of quantum critical f-electron systems that are magnetic Kondo lattice systems with integral valence.

Scaling of magnetic fluctuations near a quantum phase transition

We use inelastic neutron scattering to measure the magnetic fluctuations in a single crystal of the heavy fermion alloy CeCu_5.9Au_0.1 close to the antiferromagnetic quantum critical point. The energy and temperature-dependent spectra obey (E/T) scaling at Q near (1,0,0). The neutron data and earlier bulk susceptibility are consistent with the form 1/X ~ f(Q)+(-iE+bT)^a, with an anomalous exponent a=0.8. We confirm the earlier observation of quasi-low dimensionality and show how both the magnetic fluctuations and the thermodynamics can be understood in terms of a quantum Lifshitz point.

Theory of topological Kondo insulators

We examine how the properties of the Kondo insulators change when the symmetry of the underlying crystal field multiplets is taken into account. We employ the Anderson lattice model and consider its low-energy physics. We show that in a large class of crystal field configurations, Kondo insulators can develop a topological nontrivial ground state. Such topological Kondo insulators are adiabatically connected to noninteracting insulators with unphysically large spin-orbit coupling, and as such may be regarded as interaction-driven topological insulators. We analyze the entanglement entropy of the Anderson lattice model of Kondo insulators by evaluating its entanglement spectrum. Our results for the entanglement spectrum are consistent with the surface state calculations. Last, we discuss the construction of the maximally localized Wannier wave functions for generic Kondo insulators.

Kondo-stabilised spin liquids and heavy fermion superconductivity

The authors consider an SU(2) path integral formulation of a Kondo lattice model for heavy fermions that treats the RKKY interaction explicitly. At low temperatures they find the heavy Fermi liquid becomes unstable to the formation of a spin liquid amongst the f spins. Kondo coupling to the spin liquid stabilises it against antiferromagnetism, causing the resonating valence bonds of the spin liquid to occasionally escape into the conduction sea. This process induces off-diagonal resonant scattering in the conduction sea, thereby generating anisotropic superconductivity in the heavy fermion system.

Coherence Factors in a High-Tc Cuprate Probed by Quasi-Particle Scattering Off Vortices

When electrons pair in a superconductor, quasi-particles develop an acute sensitivity to different types of scattering potential that is described by the appearance of coherence factors in the scattering amplitudes. Although the effects of coherence factors are well established in isotropic superconductors, they are much harder to detect in their anisotropic counterparts, such as high-superconducting-transition-temperature cuprates. We demonstrate an approach that highlights the momentum-dependent coherence factors in Ca2–xNaxCuO2Cl2. We used Fourier-transform scanning tunneling spectroscopy to reveal a magnetic-field dependence in quasi-particle scattering interference patterns that is sensitive to the sign of the anisotropic gap. This result is associated with the d-wave coherence factors and quasi-particle scattering off vortices. Our technique thus provides insights into the nature of electron pairing as well as quasi-particle scattering processes in unconventional superconductors.

Hidden order in URu 2 Si 2

We review current attempts to characterize the underlying nature of the hidden order in

Frustration and the Kondo Effect in Heavy Fermion Materials

URu_2Si_2

Hastatic order in the heavy-fermion compound URu2Si2.

. A wide variety of experiments point to the existence of two order parameters: a large primary order parameter of unknown character which co-exists with secondary antiferromagnetic order. Current theories can be divided into two groups determined by whether or not the primary order parameter breaks time-reversal symmetry. We propose a series of experiments designed to test the time-reversal nature of the underlying primary order in