Session Y3: Invited Session: Competing Phases and Quantum Criticality in Strongly Correlated Systems

Correlated Electron State in Ce$_{1-x}$Yb$_{x}$CoIn$_{5}$ Stabilized by Cooperative Valence Fluctuations

Heavy fermion superconductivity has continuously attracted broad scientific attention. One of the important issues in this study is the relationship between quantum criticality, non-Fermi-liquid behavior (NFL), and unconventional superconductivity. It is generally thought that critical fluctuations associated with a magnetic quantum critical point (QCP) can provide a mechanism for NFL behavior and unconventional superconductivity in a narrow dome around the QCP. However, the precise nature of the relationship between these phenomena remains to be understood, particularly since many compounds have been reported where the NFL behavior persists over an extended region of the phase diagram in the absence of any identifiable QCP. Recently, intermediate valence phenomena has been found in the heavy fermion superconductor system Ce$_{1-x}$Yb$_{x}$CoIn$_{5}$. X-ray diffraction, electrical resistivity, magnetic susceptibility, and specific heat measurements reveal that many of the characteristic features of the x = 0 correlated electron state are stable for 0 $\le $ x $\le $ 0.775, and that phase separation occurs for x $>$ 0.775. The stability of the correlated electron state is apparently due to cooperative behavior of the Ce and Yb ions, involving their unstable valences. Low temperature NFL behavior is observed which varies with x, even though there is no readily identifiable quantum critical point. The NFL state is tuned by valence fluctuations. The strongly intermediate-valence state of Yb in Ce$_{1-x}$Yb$_{x}$CoIn$_{5}$ has recently been verified by angle-resolved photoemission spectroscopy, extended x-ray absorption fine structure, and x-ray absorption near-edge structure measurements.   

Tuning Correlations in Low-Dimensional Electron Systems: Fermi liquid versus non-Fermi-liquid behavior in organic conductors

While the electronic properties of cuprates can be modified by electron or hole doping, organic conductors provide the opportunity to tune the strength of electronic correlations more directly. Varying the bandwidth by (physical or chemical) pressure, the $\kappa$-phase BEDT-TTF compounds cross over from a Fermi liquid to a Mott insulator by increasing effective correlations. We systematically investigate the electronic transport properties in organic conductors by dc resistivity and optical measurements in order to extract the temperature and frequency-dependent scattering rate $1/\tau = A(k_BT)^2 + B(\hbar\omega)^2$. We find corresponding temperature and frequency ranges in which the parabolic behaviors are observed. For the first time, we can quantitatively relate the two prefactors ($A/B=56$) and their enhancement as correlations increase upon approaching the Mott transition. Conceptually low-dimensional organic conductors are also good candidates for quantum criticality because often an ordered state is located next to a metallic state when the system is tuned by pressure. Interestingly both are found, order in the spin as well as in the charge sector. Fermi-liquid behavior observed in the metallic state seems to be limited to certain regions of the phase diagram with non-Fermi-liquid properties evolving as the ordered phase is approached. It is not clear whether these deviations from Fermi liquid behavior are actually a signature of quantum criticality.\\[4pt] [1] M. Dressel, {\it Quantum criticality in organic conductors? Fermi-liquid versus non-Fermi-liquid behavior}, J. Phys.: Condens. Matter {\bf 23}, 293201 (2011).\newline [2] S. Yasin, M. Dumm, B. Salameh, P. Batail, C. M{\'e}zi{\'e}re and M. Dressel, {\it Transport studies at the Mott transition of the two-dimensional organic metal} $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br$_x$Cl$_{1-x}$, Eur. Phys. J. B {\bf 79}, 383 (2011).\newline [3] M. Dumm, D. Faltermeier, N. Drichko and M. Dressel, {\it Bandwidth-controlled Mott transition in} $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br$_x$Cl$_{1-x}$: {\it Optical studies of correlated carriers}, Phys. Rev. B {\bf 79}, 195106 (2009)\newpage [4] J. Merino, M. Dumm, N. Drichko, M. Dressel and R. H. McKenzie, {\it Quasiparticles at the verge of localization near the Mott metal-insulator transition in a two-dimensional material}, Phys. Rev. Lett. {\bf 100}, 086404 (2008)   

Superconducting condensation energy of CeCu2Si2 and theoretical implications

Unconventional superconductivity occurs in a broad range of strongly correlated electron systems including the newly discovered iron pnictides and chalcogenides, various intermetallic rare earth metals, the cuprates and the organic superconductors. These systems are not only of varying effective dimensionality but their parent compounds out of which superconductivity emerges ranges from metals to bad metals and Mott insulators. The only unifying characteristic features seems that unconventional superconductivity occurs in close vicinity of zero-temperature instabilities which are most often magnetic in nature. Heavy fermion compounds represent prototype systems to address the interplay between quantum criticality and unconventional superconductivity [1]. In CeCu2Si2, the magnetic quantum phase transition and superconductivity occur at ambient pressure which allows for a detailed study of the energetics across the superconducting transition. Based on an in-depth study of the magnetic excitation spectrum of CeCu2Si2 in the normal and superconducting state we obtain a lower bound for the change in exchange energy [2]. The comparison with the superconducting condensation energy demonstrates that the built-up of magnetic correlations near the quantum critical point does drive superconductivity in CeCu2Si2. In addition, our comparison establishes a huge kinetic energy loss which we relate to the competition of Kondo screening and superconductivity as the opening of the gap weakens the Kondo effect [2,3]. We discuss the relation between kinetic energy loss and the nature of the underlying quantum critical point [1,3]. Our unexpected findings sheds further light on the emerging global phase diagram of heavy fermion compounds [4] and are believed to be relevant to other families of superconductivity which are also located in close proximity to magnetism.\\[4pt] [1] O. Stockert, S. Kirchner, F. Steglich, Q. Si, ``Superconductivity in Ce- and U-based 122 heavy-fermion compounds,'' to be published in JPSJ (invited review paper).\\[0pt] [2] O. Stockert, J. Arndt, E. Faulhaber, C. Geibel, H. S. Jeevan, S. Kirchner, M. Loewenhaupt, K. Schmalzl, W. Schmidt, Q. Si, F. Steglich, ``Magnetically driven superconductivity in CeCu2Si2,'' Nature Physics, 7, 119-124 (2011).\\[0pt] [3] S. Kirchner and Q. Si, to be published.\\[0pt] [4] Q. Si, ``Quantum Criticality and Global Phase Diagram of Magnetic Heavy Fermions,'' Phys. Status Solidi B247, 476 (2010).   

Quantum critical scaling in beta-YbAlB4 and theoretical implications

Emergent phenomena in quantum materials are subject of intense experimental and theoretical research at present. A wonderful example thereof are the sister phases of YbAlB$_4$ - a newly discovered heavy fermion material [1]. While one phase ($\alpha$-YbAlB$_4$) is a heavy Fermi liquid, its sibling $\beta$-YbAlB$_4$ is quantum critical, supporting an unconventional superconductivity with a tiny transition temperature of $\sim80$ mK. Latest experiments [2] uncover the quantum critical $T/B$-scaling in $\beta$-YbAlB$_4$ and prove that superconductivity emerges from a strange metal governed by an extremely fragile quantum criticality, which apparently occurs at zero field, without any external tuning. \newline Here, we will present a theoretical perspective on the quantum critical scaling in $\beta$-YbAlB$_4$ and will show that the critical exponents can be derived from the nodal structure of the hybridization matrix between Yb $f$-band and the conduction electrons. It follows that the free energy at low temperatures can be written in a scaling form $F\propto [(k_B T)^2 + (g\mu_B B)^2]^{3/4}$, which predicts the divergent Sommerfeld coefficient $\gamma$ and quasi-particle effective mass as $B\to 0$: $\gamma\sim m^*/m \propto B^{-1/2}$. This is indeed observed in the experiment [1,2], which places a tiny upper bound on the critical magnetic field $B_c<0.2$~mT. We will discuss theoritical implications of this fragile intrinsic quantum criticality in $\beta$-YbAlB$_4$ and discuss the possibility of a quantum critical phase, rather than a quantum critical point, in this material. \newline \newline [1] S. Nakatsuji \emph{et al.}, Nature Physics {\bf 4}, 603 (2008). \newline [2] Y. Matsumoto, S. Nakatsuji, K. Kuga, Y. Karaki, Y. Shimura, T. Sakakibara, A. H. Nevidomskyy, and P. Coleman, Science {\bf 331}, 316 (2011).   

Chromium at High Pressure

Chromium has long served as the archetype of spin density wave magnetism. Recently, Jaramillo and collaborators have shown that Cr also serves as an archetype of magnetic quantum criticality. Using a combination of x-ray diffraction and electrical transport measurements at high pressures and cryogenic temperatures in a diamond anvil cell, they have demonstrated that the N\'{e}el transition ($T_{N})$ can be continuously suppressed to zero, with no sign of a concurrent structural transition. The order parameter undergoes a broad regime of exponential suppression, consistent with the weak coupling paradigm, before deviating from a BCS-like ground state within a narrow but accessible quantum critical regime. The quantum criticality is characterized by mean field scaling of $T_{N}$ and non mean field scaling of the transport coefficients, which points to a fluctuation-induced reconstruction of the critical Fermi surface. A comparison between pressure and chemical doping as means to suppress $T_{N}$ sheds light on different routes to the quantum critical point and the relevance of Fermi surface nesting and disorder at this quantum phase transition. The work by Jaramillo \textit{et al.} is broadly relevant to the study of magnetic quantum criticality in a physically pure and theoretically tractable system that balances elements of weak and strong coupling. \\[4pt] [1] R. Jaramillo, Y. Feng, J. Wang {\&} T. F. Rosenbaum. Signatures of quantum criticality in pure Cr at high pressure. \textit{Proc. Natl. Acad. Sci. USA} \textbf{107}, 13631 (2010). \\[0pt] [2] R. Jaramillo, Y. Feng, J. C. Lang, Z. Islam, G. Srajer, P. B. Littlewood, D. B. McWhan {\&} T. F. Rosenbaum. Breakdown of the Bardeen-Cooper-Schrieffer ground state at a quantum phase transition. \textit{Nature} \textbf{459}, 405 (2009).