When Landau and Lifshitz meet

Transcription

1 Yukawa International Seminar 2007 "Interaction and Nanostructural Effects in Low-Dimensional Systems" November 5-30, 2007, Kyoto When Landau and Lifshitz meet Unconventional Quantum Criticalities November 21, 2007 Kyoto M. Imada Univ. Tokyo Collaboration with T. Misawa, Y. Yamaji, Y.Z. Zhang

2 Conventional picture of QCP ; Landau s lineage transverse Ising H = J S S h S Γ S z z z x i j i i i, j i i QCP: same concept with classical symmetry breaking but in d + z dim. Elliott itinerant electrons magnetism Moriya,Hertz,Millis low-energy excitation: bosonic fluctuations symmetry breaking non-fermi liquid

3 Standard non-fermi liquid around QCP ~ T 2 Ferm liquid ~ T 3/2 3D AF ~T 5/3 F ~ T 2D AF ~ T 4/3 F Ueda, Moriya Quantum criticality expected only around QCP V shape structure Custers, Steglich et al. (2003) All arisie from symmetry breaking QCP

4 Quantum Critical Phenomena beyond Standard Picture 4f, 5f YbRh 2 Si 2, CeRu 2 Ge 2, UGe 2, URu 2 Si 2, CeIn 3, CeIn 3, Ce(Cu,Au) 6,. 3d,4d ZrZn 2, MnSi, NiS 2, Sr 3 Ru 2 O 7, YCo5,.

5 YbRh 2 Si 2 ; weak antiferromagnet Heavy fermion compound ~2JK 2 /mole ~ T -0.6 QCP by magnetic field or pressure Ferromagnetic fluctuation around QCP M~B 1/2 Gegenwart et al. PRL(2005) Tokiwa et al. PRL (2005)

6 Puzzling exponents C/T 0 Q Fermi liquid T 2 constant 3D AF T 3/2 c-t 1/2 c T -3/2 C.W. F T 5/3 -lnt T -4/3 C.W. 2D AF T Moriya, Ueda RG study; Hertz, Millis -lnt c T/ ln T C.W. F T 4/3 T -1/3 -T ln T C.W. YbRh 2 Si 2 T -lnt ~T -0.6

7 ZrZn 2 weak F continuous F transition at ambient P cubic Laves; Zr 4d Yelland et al. T 5/3 in ordered region T 3/2 in paramagnetic region too wide region violation of standard QCP picture Takashima, Takagi et al. (2007)

8 Hint: Near First-Order Transition YbRh 2 Si 2 ZrZn 2 first order above 1.65GPa first order transition under pressure at H 0 Knebel, Flouquet et al. JPSJ 75 (2006) Uhlarz, Pfleiderer, Hayden (2004)

9 Unconventional QCP found in various compounds proximity of 1st order magnetic transition 4f,5f YbRh 2 Si 2, CeRu 2 Ge 2,Fontes et al, UGe 2 Huxley et al. URu 2 Si 2, CeIn 3, Co(S,Se) 2,YCo 5, CeIn 3 3d,4d ZrZn 2, MnSi, NiS 2, Sr 3 Ru 2 O 7.

10 common tendency 1st order MI transitions cuprates Kohsaka et al. Hanaguri et al. T V 2 O 3 Limelette et al. (2003) sensitive impurity effect 1st order SC Kanoda group κ-(et) 2 Cu[N(CN) 2 ]Cl P Diverging charge fluctuations at T c

11 Tricriticality does not solve puzzle tricriticality? Yamaji Metamagnetic transition in ZrZn 2 continuous 1st order Yamaji, Misawa, MI JPSJ 76 (2007) (2006) Uhlarz et al. m-m* (B-B*) 1/ ~ 3/2 3 for any GLW symmetry-breaking transition

12 MI transition of κ-(et) 2 Cu[N(CN) 2 ]Cl T c ~ 40K P (P - P c ) -1/ d /dp ~ (T - T c ) - T T c - β 1, δ 2, γ 1 Kagawa, Miyagawa, Kanoda Nature, 2005 < 1/2 > 3 for symmetry breaking transitions

13 Issue Origin of deviation from standard QCP Key: Proximity of first-order transition Novel concept beyond conventional GLW framework of QCP

14 Two categories of quantum phase transitions Two major sources of our interest in condensed matter Interaction Quantum mechanics Interaction effect symmetry-breaking transition Landau Quantum effect topological transition ex. Lifshitz tr. in momentum space Lifshitz

15 Lineage of Lifshitz: topological transition topology change of Fermi surface; Lifshitz transition, MI transition k y k x gapless phase quantum order : Wen topological transition gapful phase topological order Quantum Hall state QSH Noninteracting No change in symmetry continuous transition at T = 0

16 Link between Landau type and Lifshitz type PRB 72 (2005) ; 74 (2007) GLW scheme symmetry breaking JPSJ 73 (2004) 1851; 74 (2005) 859, 75 (2006) Z 2 critical line; GLW symmetry breaking marginal QCP T = 0 topological transition

17 proximity of first-order transition Physics of Marginal Quantum Critical Phenomena

18 Metal-Insulator Transitions

19 Hartree-Fock Phase Diagram Metal-Insulator Transition for 2D Hubbard Model classical Ising symmetry breaking g MQMCP T=0 T = 0 quantum critical line Charge order insulator topological Para metal First-order charge order transition (PM COI) Continuous charge order transition (PM COM) First-order metal-insulator transition Continuous metal-insulator transition t marginal quantum critical point (MQCP) cf. Ising universality at T 0; DMFT, Kotliar (2000, 2002) Misawa,Yamaji, Imada JPSJ 75 (2006) Misawa, Imada PRB 75 (2007) cf. Hirsch Hofstetter- Vollhardt Kondo-Moriya..

20 non-ginzburg-landau-wilson scheme Y: order parameter measured from MI transition Y > 0; insulator, Y < 0; metal unique expansiotn, but B, C : jump at Y=0 because of jump of DOS at E F non-ginzburg-landau-wilson topological nature B m > 0 ; continuous ; A > 0 metal, A < 0 insulator B m < 0 ; first order A = B m = 0; MQCP β δ γ = 1, = 2, = 1 new universality class experimental confirmation: κ-(et) 2 Cu[N(CN) 2 ]Cl

21 scaling laws at MQCP in 2D density /S ~ z unusual universality with large z cf.symm. breaking 1/2, 3 (Widom) (Rushbrooke) (Fisher) Ginzburg criterion d + z (2 β + γ)/ ν = d + 4 : hyperscaling relation d = 2; upper critical dim. hyperscaling and mean field compatible

22 Does MQCP really exist beyond Hartree Fock? Exact approach beyond mean-field PIRG & QMC numerical results 1st order continuous MQCP unconventional universality X -1, D r X 2, z = 4, =2 compressibility (Furukawa, 1992, Kohno 1997) Drude weight D r (Tsunetsugu, 1998, Nakano, 2006) MI JPSJ 64 (1995) (1994) 4294 Divergence of uniform fluctuations at MQCP Kashima, Imada (2001)

23 Electron differentiation in momentum space topological character of transition Extension of DMFT differentiation in momentum space Y. Z. Zhang & Imada Phys.Rev.B (2007) A(k, ) ARPES data for cuprates Yoshida et al. Arc structure t-t Hubbard with t /t=-0.2 Hanasaki & Imada (2006) see also Civelli.Kotliar et al. PRL 95 (2005) Macridin, Jarrell et al. PRL 97 (2006) Far from picture of local criticality

24 Coherent peak? Georges et al. cellular DMFT pseudogap absence of coherent peak Y. Z. Zhang & Imada Phys.Rev.B (2007) Shin s group SrVO 3 single-site DMFT quasiparticle weight Z 0 Dramatically different from single-site DMFT

25 Unconventional Lifshitz transition in ZrZn 2 Another proximity of first-order transition Yamaji: Poster PS28

26 Lifshitz transition of ZrZn 2 Singh (2002) Harima Harima (2007) Freeman (1988) de Haas Yates et al. (2003) neck-collapsing Lifshitz transition MQCP Density of states from LDA = 0 + 1/2 ( - L ) 1/2 + Y magnetization beyond Wohlfarth-Rhodes-Shimizu 6 description

27 Comparison with experiment a 0, b 0; Marginal Quantum Critical Point df/dy=0 Y B-B* 2/3 m-m* B-B* 1/ Y B 2/3 =3/2 Exp. Theory experiments: at 3K

28 Quantum Tricritical Phenomena Proximity of 1st order transition within GLW scheme Case of YbRh 2 Si 2 Misawa: poster PS27

29 Physics of tricritical point classical tricritical point: r = 0, u = 0 concomitant divergence of S(Q) at ordering wavenumber Q (AF) and S(q=0) at uniform mode q=0 (F)

30 Spin Fluctuation Theory of Quantum Tricriticality Misawa arxiv: poster PS27 SCR theory with mode coupling of spin fluctuations Coexistence of ferromagnetic fluctuations with AF Stronger non Fermi liquid

31 Quantum tricriticality vs. experiments YbRh 2 Si 2 0 ~ T M ~ H 1/2 -lnt ~T -0.6 at T > 0.5K quantum tricriticality with new universality class: agreement with YbRh 2 Si 2 proximity of 1st order transition

32 Summary Unconventional quantum critical phenomena arising from proximity of 1st order transitions Interaction drives topological transition to 1st order & symmetry breaking Internal structure of MIT: QCL, MQCP, Z 2 line MQCP new universality class : diverging k = 0 mode electron differentiation Mott transitions -ET, V 2 O 3, Lifshitz transitions ZrZn 2 Quantum tricriticality unconventional non-fermi liquid Diverging fluctuations at k = 0 YbRh 2 Si 2

33 Outlook Low-energy excitation around MQCP Quasiparticle survives or fractionalization? Detailed structure of electron differentiation MQCP structure for nontrivial topological order QH QSH Effects of MQCP on superconductivity