Session D1: New Developments in Quantum Criticality

Quantum critical points and novel phases in heavy fermion metals

Quantum criticality arises from competing interactions of correlated systems that favor rivaling ground states. It not only influences physical properties over a wide temperature and parameter ranges, but also gives rise to a plethora of new quantum phases. Magnetic heavy fermion metals represent a prototype system in this context, and have in particular provided the setting to study local quantum criticality that involves not only order-parameter fluctuations but also a Kondo breakdown [1]. Surprisingly, recent theoretical and experimental developments have revealed some unusual phases proximate to the heavy-fermion quantum critical points, thereby opening up an entirely new frontier on the relationship between quantum criticality and novel phases [1]. I will summarize the relevant recent experiments [2] and discuss them within the framework of a global phase diagram that was put forward several years ago [3] and has recently been discussed more extensively [4,5]. Our theoretical studies emphasize the interplay between two effects. One is the Kondo screening and its breakdown, and the other is the fluctuations in the quantum magnetism of local moments alone. The insights gained from these studies of the well-defined quantum criticality in heavy fermions may have broader relevance. Such implications will be discussed, in particular on the interplay between metallic antiferromagnetism, electronic localization and unconventional superconductivity. \\[4pt] [1] Q. Si and F. Steglich, Science 329, 1161 (2010).\\[0pt] [2] S. Friedemann et al., Nature Phys. 5, 465 (2009);[0pt] J. Custers et al., PRL 104, 186402 (2010).\\[0pt] [3] Q. Si, Physica B 378, 23 (2006); S. J. Yamamoto and Q. Si, PRL 99, 016401 (2007).\\[0pt] [4] Q. Si, Phys. Status Solidi B247, 631 (2010); S. J. Yamamoto and Q. Si, J. Low Temp. Phys. 161, 233 (2010).\\[0pt] [5] P. Coleman and A. H. Nevidomskyy, J. Low Temp. Phys. 161, 182 (2010).   

Two-dimensional Confinement of Heavy Fermions in Artificial Superlattices

Low dimensionality and strong electron-electron Coulomb interactions are both key parameters for novel quantum states of condensed matter. A metallic system with the strongest electron correlations is reported in rare-earth and actinide compounds with $f$ electrons, known as heavy-fermion compounds, where the effective mass of the conduction electrons are strikingly enhanced by the electron correlations up to some hundreds times the free electron mass. To date the electronic structure of all heavy-fermion compounds is essentially three-dimensional. We realized experimentally a two-dimensional heavy fermion system, adjusting the dimensionality in a controllable fashion. We grew artificial superlattices of CeIn$_3$($m$)/LaIn$_3 $($n$), in which $m$-layers of heavy-fermion antiferromagnet CeIn$_3$ and $n$-layers of a non-magnetic isostructual compound LaIn$_3$ are stacked alternately, by a molecular beam epitaxy [1]. By reducing the thickness of the CeIn$_3$ layers, the magnetic order was suppressed and the effective electron mass was further enhanced. The N\'eel temperature becomes zero at around $m$ = 2, concomitant with striking deviations from the standard Fermi liquid low-temperature electronic properties. Standard Fermi liquid behaviors are, however, recovered under high magnetic field. These behaviors imply new ``dimensional tuning'' towards a quantum critical point. We also succeeded to fabricate artificial superlattices of a heavy fermion superconductor CeCoIn$_5$ and non-magnetic divalent Yb-compound YbCoIn$_5$. Superconductivity survives even in CeCoIn$_5$(3)/YbCoIn$_5$(5) films, while the thickness of CeCoIn$_5$ layer, 2.3\,nm, is comparable to the $c$-axis coherence length $\xi_{\rm c}$ $\sim$2\,nm. This work has been done in collaboration with Y. Mizukami, S. Yasumoto, M. Shimozawa, H. Kontani, T. Shibauchi, T. Terashima and Y. Matsuda.superconductivity is realized in the artificial superlattices. \\[4pt] [1] H.Shishido $et$ $al$., Science {\bf 327} 980 (2010).   

Universal Signatures of Metamagnetic Quantum Criticality

The continuous quest for quantum critical materials is inspired by the exotic phases and unusual phenomena that can be observed close to a zero-temperature instability. An appealing realization of such a critical point is found in metamagnetic materials where the magnetization shows a finite step at a certain magnetic field that becomes more pronounced at low temperatures. The most striking advantages of this kind of quantum criticality are that the critical point is i) symmetric in the associated thermodynamic phase diagram and not accompanied by a symmetry-breaking ordered phase and ii) the tuning parameter magnetic field $H$ can be adjusted continuously and makes a very detailed and comprehensive study of this so called quantum critical end-point (QCEP) possible. In the presented talk the qualitative features of a field-driven QCEP are discussed, which result from very basic thermodynamic relations and the two general assumptions that i) the differential magnetic susceptibility diverges at the critical field $H_{c}$ by definition and ii) the QCEP has Ising symmetry. We present real examples of metamagnetic systems, where the characteristics can be found experimentally. Particular emphasis will be placed on the well-known intermetallic material CeRu$_{2}$Si$_{2}$. We argue that a QCEP is approximately realized in this compound and confirm our claims by the combination of new high-resolution thermal expansion, magnetostricion and specific heat results. Very similar behavior was found recently on the prominent material Sr$_{3}$Ru$_{2}$O$_{7}$ whose metamagnetic quantum criticality is masked by the appearance of a phase proposed to be of nematic electronic nature. We believe that our work will facilitate and promote the experimental identification of further metamagnetic systems for quantum criticality in the future. \\[4pt] [1] \textit{Weickert et al}., Phys. Rev. B, \textbf{81}, 134438 (2010).   

Quantum criticality and confinement effects in an Ising chain in transverse field

The Ising chain in transverse field is one of the key paradigms for the theory of continuous zero-temperature quantum phase transitions. We have recently realized this system experimentally by applying strong magnetic fields to the quasi- 1D, low-exchange Ising ferromagnet CoNb2O6 to drive it to its quantum critical point where the spontaneous long-range magnetic order is suppressed by magnetic field [1]. Using high-resolution single-crystal neutron scattering we have probed how the spin dynamics evolves with the applied field and have observed a dramatic change in the character of spin excitations at the quantum critical point, from pairs of domain-wall (kink) quasiparticles in the magnetically-ordered phase, to sharp spin- flip quasiparticles in the paramagnetic phase. The weak, but finite couplings between the chains significantly enrich the physics by stabilizing a complex structure of two-kink bound states due to mean-field confinement effects. In zero field the rich spectrum of bound states can be quantitatitively understood following McCoy and Wu's analytic theory of weak confinement [2]. Just below the critical field the energies of the two lowest bound states approach the ``golden ratio'' as predicted by Zamolodchikov's E8 scaling limit solution of the off-critical Ising model in a weak longitudinal field [3]. \\[4pt] [1] R. Coldea, D.A. Tennant, E.M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, K. Kiefer, Science 327, 177 (2010).\\[0pt] [2] B. M. McCoy and T. T. Wu, Phys. Rev. D 18, 1259 (1978).\\[0pt] [3] A.B. Zamolodchikov, Int. J. Mod. Phys. A4, 4235 (1989).   

Strange metals and quantum phase transitions from gauge/gravity duality

Metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory, so-called non-Fermi liquids, include the strange metal phase of cuprate superconductors, and heavy fermion systems near a quantum phase transition. We use gauge/gravity duality to identify a class of non-Fermi liquids. Their low-energy behavior is governed by a nontrivial infrared fixed point which exhibits non-analytic scaling behavior only in the temporal direction. Some representatives of this class have single-particle spectral functions and transport behavior similar to those of the strange metals, with conductivity inversely proportional to the temperature. Such holographic systems may also exhibit novel ``magnetic instabilities'', where the quantum critical behavior near the transition involves a nontrivial interplay between local and bulk physics, with the local physics again described by a similar infrared fixed point. The resulting quantum phase transitions do not obey the standard Landau-Ginsburg-Wilson paradigm and resemble those of the heavy fermion quantum critical points.