What is a Pomeranchuk instability? Hiroyuki Yamase National Institute for Materials Science (NIMS), Tsukuba, Japan Ref. PRB 72, 035114 (2005) Tsukuba Tokyo Narita Airport 1 Outline of my talk 1. forward scattering model 2. typical phase diagram 3. analytical understanding 4. universal ratios (c.f. 2∆/kB T = 3.54 in BCS theory) 5. self-masking 6. toward real materials collaboration W. Metzner (MPI-FKF, Germany) P. Jakubczyk (Warsaw University, Poland) R. Zeyher (MPI-FKF, Germany) A. A. Katanin ( Institute of Metal Physics, Russia) V. Oganesyan (Princeton University, USA) Fermi surface: usually same symmetry as the point-group symmetry of the lattice e.g., square lattice 2 What is Pomeranchuk instability? Recently it was found that symmetry of the FS can be broken spontaneously 2D t-J model H.Y. & Kohno, JPSJ 69, 332 (2000) H.Y. & Kohno, JPSJ 69, 2151 (2000) 2D Hubbard model Halboth & Metzenr, PRL 85, 5162 (2000) Valenzuela & Vozmediano, PRB 63, 153103 (2001) ✕ orientational symmetry Pomeranchuk’s stability criterion for isotropic Fermi liquids I. J. Pomeranchuk, JETP 8, 361 (1958) dFSD: also strongly correlated systems dFSD: instability also without breaking his criterion electronic nematic state S.A. Kivelson et al., Nature 393, 550 (1998) dFSD: q=0 instability and no underlying charge stripes 3 f-model H.Y., V. Oganesyan, W. Metzner, PRB 72, 35114 (2005) g>0 : attractive interaction of the dFSD What is Pomeranchuk instability? Recently it was found that symmetry of the FS can be broken spontaneously 2D t-J model H.Y. & Kohno, JPSJ 69, 332 (2000) H.Y. & Kohno, JPSJ 69, 2151 (2000) 2D Hubbard model Halboth & Metzenr, PRL 85, 5162 (2000) Valenzuela & Vozmediano, PRB 63, 153103 (2001) ✕ orientational symmetry 4 f-model H.Y., V. Oganesyan, W. Metzner, PRB 72, 35114 (2005) g>0 : attractive interaction of the dFSD mean-field analysis order parameter of the dFSD self-consistency equation 4 Typical phase diagram t'/t=-1/6, t''/t=0, g/t=1.0 saddle points: (π, 0), (0, π) 0.3 -1 µ/t 1st order at low T 2nd order at high T 0 maximal Tc (µ) near µ= εvH 0.25 ky 1 0 1 -1 -2 -2 -3 -3 -2 -1 0 kx 1 2 3 0.3 0.05 0 0 T c2nd" 0 kx 1 2 3 open Fermi surface in the symmetry broken phase 0.2 0.1 T c2nd Ttri T cPS " -1 µ/t (g) 0.15 0.05 -2 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 0.25 0.1 -3 T=0.01t T=0.15t 0 -1 (e) 0 -1 0.1 t'/t = -1/6 t"/t = 0 0.2 g/t = 1.0 u/t = 0 0.15 (c) T= 0.01t µ/t 0.15 0.05 3 µ= -0.4t 2 T= 0.01t µ= -0.9t -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 0.2 η /t (b) η /t 0.7 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 (f) 0.25 g/t = 1.0 g/t = 0 " -3 N0 (µ) 0.9 0.8 T c2nd" -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 µ/t T/t T/t ky n T c2nd Ttri T c1st 0.05 2 0.4 -1 (d) 1 T=0.01t 0.1 3 0.6 0.5 t'/t = -1/6 t"/t = 0 0.2 g/t = 1.0 u/t = 0 0.15 0 -1 0.7 0 van Hove singularity: εvH =4t' = -2t/3 log-divergence in DOS (a) 0.25 t'/t = -1/6 t"/t = 0 0.8 0 0.7 0.75 0.8 0.85 n 0.9 0.95 µ= - 0.87t µ= - 2t/3 µ= - 0.50t 0.05 0.1 T/t 0.15 0.2 0.25 1 phase separated region 5 Landau expansion ω(η)-ω(0)= 12 a2 η2 + N2 (µ) 2.5 N2 (µ) 1 a η4 4! 4 a2 = g -1 - N2 (µ) a4 = - N'' 4 (µ) T=0 t'/t = -1/6 t"/t = 0 2 + p Np (µ) = - 2 Σ d k f ' (ε0k - µ) L 1.5 a 2 =0, a 4 <0 : necessarily 1st order a 2 =0, a 4 >0 : possible 2nd order 0 0.1 0.2 0 µ−εvH 0.8 0.3 N0 (µ) 20 T=0 t'/t = -1/6 t"/t = 0 0.7 0.6 15 N2' (µ) -0.1 N0 (µ) 10 5 N2' (µ) 2000 T=0 t'/t = -1/6 t"/t = 0 0 T=0 t'/t = -1/6 t"/t = 0 1000 -10 0.5 N"4 (µ) 1500 -5 500 -15 0.8 -0.2 -0.1 0 µ−ε 0 vH 0.1 0.2 0.3 20 T = 0.01t N0 (µ) 15 t'/t = -1/6 t"/t = 0 0.7 -20 -0.3 10 0.6 -0.2 -0.1 0 0.1 0 vH µ−ε N2' (µ) 0.2 2000 T = 0.01t t'/t = -1/6 t"/t = 0 5 -0.1 0 0.1 0 µ−εvH 0.2 0.3 0 0 µ−εvH 0.1 0.2 0.3 N"4 (µ) -4000 -10 -0.2 -0.1 -2000 -20 -0.3 T = 0.01t -6000 -15 0.4 -0.3 0 -0.2 0 -5 0.5 0 -0.3 0.3 N"4 (µ) 0.4 -0.3 N2' (µ) -0.2 N0 (µ) -0.3 N"4 (µ) 1 -0.2 -0.1 0 0.1 0 µ−εvH 0.2 0.3 -8000 -0.3 t'/t = -1/6 t"/t = 0 -0.2 -0.1 0 0.1 0 µ−εvH 0.2 0.3 6 Universal properties 7 Layered systems: interlayer coupling two possible stacking patterns η<0 η<0 η>0 η<0 3 2 η<0 η>0 ferro-type (F) stacking ky 1 0 -1 -2 -3 -3 -2 -1 0 kx 1 2 3 antiferrotype (AF) stacking 3 2 ky Ising symmetry 1 0 -1 -2 -3 -3 -2 -1 0 kx 1 2 3 AF stacking no macroscopic anisotropy! spontaneous symmetry breaking is self-masked!! What is the generic tendency of the dFSD stacking? 8 Self-masking of Pomeranchuk instability H.Y., PRL 102, 116404 (2009) order parameters : AF stacking : F stacking calculate the coupling constant J stacking does not depend on details of interlayer couplings usually AF stacking as long as no macroscopic anisotropy appears !! spontaneous symmetry breaking is self-masked !! 9 Sr3Ru2O7 metamagnetism QCEP? Non-FL 2.0 1.5 Perry et al. PRL 86, 2661 (2001) H-T phase diagram 1.0 Grigera et al. Science 294, 329 (2001) strong anisotropy of ρ, dFSD!? 2nd 2nd dFSD dFSD Grigera et al., Science 306, 1154 (2004) Borzi et al, Science 315, 214 (2007) 10 Everything is OK for Sr3Ru2O7? Pomeranchuk instability around the van Hove singularity Kee & Kim, PRB 71, 184402 (2005) Doh et al., PRL 98, 126407 (2007) HY & Katanin, JPSJ 76, 073706 (2007) HY, PRB 76, 155117 (2007) Ho & Schofield, EPL 84, 127007 (2008) HY, PRB 80, 115102 (2009) Fischer & Sigrist, PRB 81, 064435 (2010) Puetter et al., PRB 81, 081105 (2010) presence of some QCP ? 2nd dFSD van Hove? Raghu et al., PRB 79, 214402 (2009) Lee & Wu, PRB 80, 104438 (2009) more profound story! ? multiple singularity at a continuous phase transition jump of the longitudinal magnetic susceptibility! its divergence in a critical region! non-ordering and ordering susceptibilities YbRh2Si2, CeRu2Si2, β-TbAlB4 HY&Jakubczyk, submitted Misawa & Imada, JPSJ 78, 084707 (2009) analysis of critical fluctuations van Hove singularity: LGW theory is not applicable!! functional RG framework Jakubczyk, Metzner, HY, PRL 103, 220602 (2009) maybe more 11 Relevance to cuprates 1. La-based cuprates with LTT different scenario from stripes 2. Y-based cuprates YBa2Cu3O6.6 YBCO6.85, YBCO6.6 V.Hinkov et al., Nature 430, 650 (2004) V.Hinkov et al., Nat. Phys. 3, 780 (2007) microscopic theory from view of dFSD H.Y. & W. Metzner, PRB 73, 214517 (2006) YBCO6.45 (Tc=35K) V.Hinkov et al., Science 319, 597 (2008) phenomenological theory from view of dFSD H.Y., PRB 79, 052501 (2009) Kim et al., PRB 77, 184514 (2008) Huh et al., PRB 78, 064512 (2008) 12 Other systems N=2 Landau level 2DEG in a magnetic field ( ) Lilly et al, PRL 82, 394 (1999) Du et al, Solid State Comm. 109, 389 (1999) Review: Wexler & Ciftja, Int. J. Mod. Phys. B 20, 747 (2006) 5/3 9/2 11/2 4/3 200 xx higher Landau levels: ν = 9/2, 11/2 T=150mK 300 5/2 100 0 ... 3 0 2 2 the same physics as the dFSD or something different? =2 N=1 4 N=0 6 B (Tesla) 8 10 Lilly et al, (1999) Graphene honeycomb lattice Valenzuela & Vozmediano, New J. Phys. 10, 113009 (2008) ultracold dipolar neutral fermions dipole interaction ≈ Σ<i,j> V ni nj Lin, Zhao, Liu, PRB 81, 045115 (2010) typical materials with high TcvH may have AF stacking spontaneous symmetry breaking is self-masked!! 13 Summary forward scattering model T0 2nd !Λ e−1/2¯g Ttri dFSD (PI) Ising symmetry Ttri /T0 = 0.56 1st µ1 0 two possible stacking patterns η<0 η>0 η<0 3 2 ferro-type (F) stacking ky 1 0 -1 -2 -3 -3 -2 -1 0 kx 1 2 3 antiferrotype (AF) stacking self-masking 3 2 ky η<0 η<0 η>0 1 0 -1 -2 -3 -3 -2 -1 0 kx 1 2 3 competing order Sr3Ru2O7 high-Tc cuprates 2DEG in field graphene dipolar fermi gas 14 Ph.D. positions in NIMS in Tsukuba nims yamase Google 検索 I'm Feeling Lucky ウェブ全体から検索 検索オプション 表示設定 言語ツール 日本語のページを検索 Studio Ghibli ...からテーマを変更 | コンテンツを追加 » Tsukuba Tokyo Narita Airport 15
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