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PERSPECTIVES

zon synchronized in- 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 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). -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 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 , probe 10.1126/science.1172427

PHYSICS

The Thermodynamics of Thermodynamic signatures have been obtained for phase transitions that occur Critical Points as approach . on February 5, 2016 Zachary Fisk

thermodynamic state, such as a The study of new phase behavior at tem- thermodynamic superconducting state arose; or , 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 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 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 can also 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 can affect the proper- their treatment of the quantum mechan- ties of a material well above absolute zero, the ics of free- 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 ∆C, across a gas-to-liquid phase 3 2 7 2 ( 2). These results show that the transition as temperature T changes is called a 50 nematic state, an analog of the molecular fi rst-order . Rost et al. examined electron-spin transitions of Sr3Ru2O7 in the limit of

ordering that occurs in nematic liquid crystals, K (mJ/mol 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 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 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 , 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 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 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 , 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. Geiger, K. Scheel, Eds., Handbuch der Physik Sr Ru O , whose presence was inferred on the Sr Ru O , observing this new phase requires (Springer, Berlin, 1933), vol. 24, part 2, pp. 233–622. 3 2 7 3 2 7 6. S. Sachdev, Quantum Phase Transitions (Cambridge Univ. basis of large, anisotropic magnetoresistance increasing the distance an electron traveled in Press, Cambridge, UK, 1999). 7. G. R. Stewart, Rev. Mod. Phys. 73, 797 (2001). effects. The layers within Sr3Ru2O7 support a the before scattering from 300 to 3000 quasi–two-dimensional electron gas whose Å. The exotic superconductivity found in the 8. Y. Maeno et al., 372, 532 (1994). 9. Supported by the National Science Foundation under spins have a net magnetization. This magne- closely related material Sr2RuO4 was also grant NSF-DMR-0854781. tization is characterized by a spin texture— observed only when high-quality single crys- the ordering of the orientation of the electron tals were grown ( 8). 10.1126/science.1179046 spins that are still freely moving as a fl uid— and resembles the ordering of molecules in nematic liquid crystals. NEUROSCIENCE Experiments have revealed that metals in the vicinity of a quantum critical point have temperature dependences in their physical Low-Cost Travel in Neurons properties unlike those normally exhibited by metals as they approach absolute zero (7 ). For Pierre J. Magistretti example, the electrical resistivity of a metal More precise measurements are now available for energy budgets in the brain. at low temperatures should be the sum of a T 2 electron scattering term plus a T 5 lattice bout 20% of the energy consumed Information processing consumes much vibration scattering term. In the cuprates, an by the body sustains brain function of the energy used by the brain. The neu- anomalous linear temperature dependence is A( 1), yet the brain represents only ronal signaling involved is based on the seen near the quantum critical point, as well 2% of human body mass. This consump- rapid fl ow of electrical charges—carried by as the divergence of various properties. tion, reflected by the use of glucose and such as sodium (Na+), potassium (K+), In looking at changes in thermodynamic delivered by blood fl ow, provides and calcium (Ca2+)—across neuronal mem- properties such as entropy around a quan- signals that can be detected in real time branes. This is not expected to consume tum critical point, it is useful to see if they with imaging techniques such as positron much energy because the fl ow of ions fol- are fi rst order (the property itself diverges) or emission tomography and functional mag- lows favorable electrochemical gradients. second order (the property does not diverge netic resonance imaging ( 2). On page 1405 However, reestablishing these gradients but one of its derivatives does). Rost et al. of this issue, Alle et al. ( 3) weigh in on the through ionic pumps, such as the Na+/K+- found that the change in entropy divided by ongoing debate about how energy utiliza- ATPase (adenosine triphosphatase), does temperature (∆S/T) of the almost defect-free tion by brain neurons contributes to the sig- indeed cost energy ( 4).

Sr3Ru2O7 sample diverges on approaching the nals detected by these techniques. Two processes mediate signaling between fi rst-order phase boundaries from both the neurons: action potentials that carry electri- low– and high–magnetic fi eld sides at fi xed Brain Mind Institute, Ecole Polytechnique Fédérale de Lau- cal signals along the axon (and dendrites), sanne (EPFL) and Center for Psychiatric Neuroscience, UNIL/ temperature (see the fi gure). These fi rst-order CHUV Lausanne, Switzerland. E-mail: pierre.magistretti@ and postsynaptic potentials, which are gen- phase boundaries are connected by an upper e p fl . c h erated by neurotransmitters that are released

www.sciencemag.org SCIENCE VOL 325 11 SEPTEMBER 2009 1349 Published by AAAS The Thermodynamics of Quantum Critical Points Zachary Fisk Science 325, 1348 (2009); DOI: 10.1126/science.1179046

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