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The Thermodynamics of Quantum Critical Points Zachary Fisk Science 325, 1348 (2009); DOI: 10.1126/Science.1179046

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The Thermodynamics of Quantum Critical Points Zachary Fisk Science 325, 1348 (2009); DOI: 10.1126/Science.1179046 PERSPECTIVES zon synchronized in-phase across the sky in substantial advances are coming. Much of galaxy evolution, determine the mass of the a series of acoustic oscillations of the tem- what we know today has come from combin- light neutrinos, and test the Gaussianity and perature anisotropy. Clear evidence of this is ing WMAP’s CMB measurements with the power spectrum of infl ation. seen in the peaks and troughs of the tempera- Sloan Digital Sky Survey’s galaxy redshift ture power spectrum and in the superhorizon survey. The recently launched Planck satel- References and Notes 1. E. Hubble, Proc. Natl. Acad. Sci. U.S.A. 15, 168 (1929). temperature-polarization cross-correlation; lite will map the full sky with greater angular 2. F. Zwicky, Helv. Phys. Acta 6, 110 (1933). (v) there should be statistical isotropy with resolution and sensitivity. More than a dozen 3. A. A. Penzias, R. W. Wilson, Astrophys. J. 142, 419 (1965). fl uctuations having Gaussian-distributed ran- ground and balloon-borne measurements are 4. J. C. Mather et al., Astrophys. J. 354, L37 (1990). 5. D. J. Fixsen et al., Astrophys. J. 581, 817 (2002). dom phases. Although some small excep- also in various stages of development and/or 6. A. H. Guth, D. I. Kaiser, Science 307, 884 (2005). tions have been claimed, observations to date observations ( 15). These experiments cover 7. W. Percival et al., Mon. Not. R. Astron. Soc. 381, 1053 match this prediction; and (vi) the generation a wide range of frequencies, vary in angular (2007). 8. W. Freedman et al., Astrophys. J. 553, 47 (2001). of gravitational waves will imprint a polar- resolution and sky coverage, and take diverse 9. A. G. Riess et al., Astrophys. J. 659, 98 (2007). ization pattern on the large and intermediate- approaches to systematic error mitigation. 10. E. Komatsu et al., Astrophys. J. 180 (suppl.), 330 (2009). 11. D. Munshi et al., Phys. Rep. 462, 67 (2008). scale CMB. The amplitude of the curl pattern, New CMB data will improve inflation 12. D. J. Eisenstein, C. L. Bennett, Phys. Today 61, 44 (2008). when detected, will reveal the energy scale at constraints and possibly detect the key gravi- 13. A. D. Miller et al., Astrophys. J. 524, L1 (1999). which infl ation took place. tational wave signature. With new spectro- 14. R. Brandenberger, Phys. Today 61, 44 (2008). 15. Ground CMB experiments include ABS, ACT, BRAIN, The interim report card on inflation is scopic redshift surveys of a quarter of a bil- BICEP2, Keck Array, MBI, Poincare, PolarBeaR, QUIET, excellent, but a specifi c infl ation model is lion galaxies, the new combined data will QUIJOTE, and SPT. Balloon-borne experiments include not yet uniquely preferred and other theo- help elucidate the reason for the accelerated EBEX, SPIDER, and PIPER. ries are not yet ruled out ( 14). Fortunately, expansion, characterize dark matter, probe 10.1126/science.1172427 PHYSICS The Thermodynamics of Quantum Thermodynamic signatures have been obtained for phase transitions that occur Critical Points as temperatures approach absolute zero. on February 5, 2016 Zachary Fisk thermodynamic state, such as a gas The study of new phase behavior at tem- thermodynamic superconducting state arose; or liquid, is usually characterized by peratures near absolute zero began after the the formation of this state in the presence of A well-defi ned properties such as den- successful liquefaction of helium in 1908 and an applied magnetic fi eld seemed to depend sity, but at high temperatures and pressures, a the discovery by Kamerlingh Onnes of super- on whether the fi eld was applied before or critical point can be reached suddenly where conductivity in mercury just above 4 K ( 3). after the material became superconducting. properties such as density fluctuate wildly. An apparent problem in defi ning a unique In 1933, it was discovered that superconduc- Downloaded from Quantum fl uctuations that arise through the tors expelled a magnetic fi eld, which fi xed Heisenberg uncertainty principle can also lead A their thermodynamic state ( 4). to critical behavior but do so in the limit of Accounting for infinite conductivity low temperatures. Quantum critical points are proved more challenging. In the 1930s, often seen as fl uctuations in electronic ordering Sommerfeld and Bethe ( 5) described ordi- driven by an external magnetic fi eld. Because nary electrical conductivity by applying a quantum critical point can affect the proper- their treatment of the quantum mechan- ties of a material well above absolute zero, the ics of free-electron gases to metals, which search for unusual electronic phases of mat- worked surprisingly well despite its sim- ter can be aided by their presence. However, it plicity. However, understanding the origin has proven diffi cult to see the changes in ther- of superconductivity, a macroscopic quan- modynamic properties that must occur near tum phenomenon, did not follow trivially, quantum critical points. On page 1360 of this B issue, Rost et al. ( 1) characterize the entropy ∆C/T A cold critical jump. A jump in the magnitude changes of an unusual electronic phase that 100 ∆S/T of a thermodynamic variable, such as entropy ∆S Fit was observed in highly pure Sr Ru O single ) or specifi c heat ∆C, across a gas-to-liquid phase 3 2 7 2 crystals ( 2). These results show that the spin transition as temperature T changes is called a 50 nematic state, an analog of the molecular fi rst-order phase transition. Rost et al. examined electron-spin transitions of Sr3Ru2O7 in the limit of ordering that occurs in nematic liquid crystals, (mJ/mol K zero temperature using the apparatus shown in (A). is a true thermodynamic phase. 0 They observed jumps in ∆S/T and ∆C/T as the mag- netic fi eld H was varied (B). Both diverge with the functional form (H – H )–1 at a fi xed low tempera- Department of Physics and Astronomy, University of Cali- 4 6 8 10 c fornia, Irvine, Irvine, CA 92697-4575, USA. E-mail: zfi sk@ Field (T) ture; the critical magnetic fi eld Hc is 7.8 T, and the uci.edu red line illustrates this dependence. 1348 11 SEPTEMBER 2009 VOL 325 SCIENCE www.sciencemag.org Published by AAAS PERSPECTIVES and only in recent years has a broader range boundary in temperature, and a second-order Many quantum critical points occur for of possible low-temperature phases of metal- transition is seen when the magnetic fi eld is transition-metal compounds near a mag- lic electrons been discovered ( 6). The quan- fi xed. The unusual new phase can be thought netic/nonmagnetic boundary where elec- tum wave-particle strangeness of matter often of as the material’s solution to the problem of tronic charge and spin degrees of freedom emerges at very low temperatures, where lowering its entropy in accord with the third are strongly coupled and bonding and mag- quantum fl uctuations can dominate thermal law of thermodynamics, which demands that netism interfere. Defects in such materials fl uctuations. For example, the failure of liq- the entropy of a phase at equilibrium goes to stabilize less interesting noncritical behav- uid helium to solidify at atmospheric pressure zero as temperature goes to zero. ior. Defects can also distort the crystal lattice arises from large quantum-mechanical fl uc- What do we learn from these new results? so that it nucleates a stable phase that does tuations in atomic motion, the so-called zero- First, the putative spin nematic state is a true not support the divergences characterizing a point motion. macroscopic phase for Sr3Ru2O7. Such char- quantum critical point, or cause the loss of the Until recently, the experimental search acterization is not yet possible for similar phase coherence needed for collective macro- for new superconductors has been largely phases that occur in two-dimensional electron scopic electronic phases. The interesting and empirical, but a guiding principle that has gases created in atomic-layer heterostruc- unusual physics seen in the study of Rost et emerged in the last decade is that an inter- tures. Second, the symmetric divergence in al. arises because their clean material must esting set of superconductors (including the ∆S/T (also seen in the change in specifi c heat fi nd a way to avoid the quantum critical point cuprate and heavy fermion superconductors) ∆C divided by T) around the critical magnetic and its associated divergences. can reside near a quantum critical point. In field is strong evidence that spin nematic the case of the so-called heavy fermions, fl uc- phase arises from proximity to an underlying References and Notes tuations occur between one state in which the quantum critical point. Third, the magneto- 1. A. W. Rost, R. S. Perry, J.-F. Mercure, A. P. Mackenzie, S. A. Grigera, Science 325, 1360 (2009); published online magnetic moments reside on the atoms and caloric effect used to map out the fi rst-order 6 August 2009 (10.1126/science.1176627). another state in which these moments are boundaries could be applied to other exotic 2. R. A. Borzi et al., Science 315, 214 (2007). screened by itinerant delocalized electrons. phase transitions driven by magnetic fi elds. 3. R. de Bruyn Ouboter, Sci. Am. 276, 98 (1997). 4. W. Meissner, R. Ochsenfeld, Naturwissenshaften 21, 787 Among the unusual electronic phases Finally, these studies reinforce the impor- (1933). driven by quantum fl uctuations near a quan- tance of creating almost defect-free samples 5. A. Sommerfeld, H. Bethe, Elektronentheorie der Metalle, tum critical point is the spin nematic phase in for experimental searches for new phases. In in H.
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