Kondo insulators are a particularly simple type of heavy electron material, where a filled band of heavy quasiparticles gives rise to a narrow band insulator. Starting with the Anderson lattice Hamiltonian, we develop a topological classification of emergent band structures for Kondo insulators and show that these materials may host three-dimensional topological insulating phases. We propose a general and practical prescription of calculating the Z(2) topological indices for various lattice structures. Experimental implications of the topological Kondo insulating behavior are discussed.

We discuss non-Fermi liquid and quantum critical behavior in heavy fermion materials, focussing on the mechanism by which the electron mass appears to diverge at the quantum critical point. We ask whether the basic mechanism for the transformation involves electron diffraction off a quantum critical spin density wave, or whether a break-down in the composite nature of the heavy electron takes place at the quantum critical point. We show that the Hall constant changes continously in the first scenario, but may "jump" discontinuously at a quantum critical point where the composite character of the electron quasiparticles changes.

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 1-5 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 6 on theheavy-electron material Y bRh 2 Si 2 found that near a field-induced quantum critical point 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 cross-section. These studies could not shed light on whether these properties were an artifact of the applied field 7,8 , or a more general feature of field-free QCPs. Here we report that when Germanium-doped Y bRh 2 Si 2 is tuned away from a chemically induced quantum critical point by magnetic fields there is a universal behavior 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 1 electrons decay into collective current carrying motions of the electron fluid.Recent work 6 on the heavy electron material YbRh 2 Si 2 9 has demonstrated that a magnetic field can be used to probe the heavy electron quantum critical point. This material exhibits a small antiferromagnetic (AFM) ordering temperature T N = 70 mK (Fig. 1a) that is driven to zero by a critical magnetic field B c = 0.66 T (if the field is applied parallel to the crystallographic c-axis, perpendicular to the easy magnetic plane) 6 . For 2 Past experience 7,8 suggested that a finite field quantum critical point has properties which are qualitatively different to a zero field transition, shedding doubt on the reliability of these measurements as an indicator of the physics of a quantum phase transition at zero field. However, the zero-field properties of YbRh 2 (Si 1−x Ge x ) 2 above T ≈ 70 mK for the undoped (x = 0) and doped (x = 0.05) crystals are essentially identical (Fig. 2a), suggesting that by suppressing the critical field we are still probing the same quantum critical point.In both compounds, the ac-susceptibility follows a temperature dependence χ −1 ∝ T α from 0.3 K to ≤ T ≤ 1.5 K, with α = 0.75 14 , and the coefficient of the electronic specific heat, C el (T )/T , exhibits 9 a logarithmic divergence between 0.3 K and 10 K. However, in the low-T paramagnetic regime, i. e. , T N < T < ∼ 0.3 K, the ac-susceptibility follows a CurieWeiss law (inset of Fig. 2a) with a Weiss temperature Θ W ≈ 0.3 K, and a surprisingly large effective moment µ eff ≈ 1.4µ B /Yb 3+ , indicating the emergence of coupled, unquenched spins at the quantum critical point. The electronic specific heat coefficient, C e...

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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 CeCu(6-x)Au(x), 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 (x(c) = 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.

A modern, graduate-level introduction to many-body physics in condensed matter, this textbook explains the tools and concepts needed for a research-level understanding of the correlated behavior of quantum fluids. Starting with an operator-based introduction to the quantum field theory of many-body physics, this textbook presents the Feynman diagram approach, Green's functions and finite-temperature many-body physics before developing the path integral approach to interacting systems. Special chapters are devoted to the concepts of Fermi liquid theory, broken symmetry, conduction in disordered systems, superconductivity and the physics of local-moment metals. A strong emphasis on concepts and numerous exercises make this an invaluable course book for graduate students in condensed matter physics. It will also interest students in nuclear, atomic and particle physics.

A quantum critical point (QCP) develops in a material at absolute zero when a new form of order smoothly emerges in its ground state. QCPs are of great current interest because of their singular ability to influence the finite temperature properties of materials. Recently, heavy-fermion metals have played a key role in the study of antiferromagnetic QCPs. To accommodate the heavy electrons, the Fermi surface of the heavy-fermion paramagnet is larger than that of an antiferromagnet. An important unsolved question is whether the Fermi surface transformation at the QCP develops gradually, as expected if the magnetism is of spin-density-wave (SDW) type, or suddenly, as expected if the heavy electrons are abruptly localized by magnetism. Here we report measurements of the low-temperature Hall coefficient (R(H))--a measure of the Fermi surface volume--in the heavy-fermion metal YbRh2Si2 upon field-tuning it from an antiferromagnetic to a paramagnetic state. R(H) undergoes an increasingly rapid change near the QCP as the temperature is lowered, extrapolating to a sudden jump in the zero temperature limit. We interpret these results in terms of a collapse of the large Fermi surface and of the heavy-fermion state itself precisely at the QCP.

As we mark the centenary of Albert Einstein's seminal contribution to both quantum mechanics and special relativity, we approach another anniversary--that of Einstein's foundation of the quantum theory of solids. But 100 years on, the same experimental measurement that puzzled Einstein and his contemporaries is forcing us to question our understanding of how quantum matter transforms at ultra-low temperatures.