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On the Cuprate Pseudogap

Exploring the relationship between pseudogap, charge and spin orders in cuprate superconductors, and the role of composite order in the unconventional behavior of these materials.

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On the Cuprate Pseudogap

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  1. On the Cuprate Pseudogap

  2. Intra-unit-cell ordersin the PG phase orbital loop-current (軌道ループ電流秩序) electronic nematic (ネマテック電子秩序) 300 Strange Metal（奇妙な金属） Pseudogap（擬ギャップ） T* 200 TN Tcon 温度T (K) TCon Tc 電荷秩序 charge order 100 正常金属（フェルミ液体） スピン秩序 spin order TCDW AF d-SCd波超伝導 TSonset FL TSDW 0 0.1 0.2 正孔ドーピング量　Hole dopingp B. Keimer, S.A. Kivelson, M.R. Norman, S.Uchida, J. Zaanen, Nature 518, 179 (2015).

  3. Intra-unit-cell magnetic order:Orbital loop current q = 0 novel magnetic order Spin-PolarizedNeutron Loop orbital-current order Hg1201, YBCO Bi2212& LSCO Varma current CuO2 unit cell Electron loop current O Cu Cu O O Cu Cu O Magnetic moment No evidence from NMR and mSR B. Fauque, Y. Sidis, V. Hinkov, S. Pailhes, C.T. Lin, X. Chaud, and P. Bourges, Phys. Rev. Lett. 96, 197001 (2006).

  4. Rotational Symmetry Breaking: Intra-Unit-Cell Electronic Nematicity M.J. Lawler, K. Fujita, SU, J.C. Daviset al., Nature 466, 374 (2010). Lattice preserves C4 symmetry. Different intensity between Qx and Qy spots Oy Ox Cu However, intra-unit-cell order cannot open a gap !!

  5. Recently Proposed Scenarios 1. Composite Order (CDW-dSC) Intertwinedorders E. Fradkin, S.A. Kivelson: Rev. Mod. Phys. 87, 457 (2015). J.C. Davis, D.-H. Lee: PNAS 110, 17623 (2013). Compositeorder L.E. Hayward, S. Sachdev: Science 343, 1336 (2014). Emergent SU(2) SymmetryT. Kloss,C. Pepin: arXiv.1512.03801. 2. PDW Y. Wang, D.F. Agterberg, A. Chubukov: PRL 114, 197001 (2015). Amperian PairingP.A. Lee: Phys. Rev. X 4, 031017 (2014). Fermi Arcs and Leggett Mode Y.-H. Liu, T.M. Rice, F.-C. Zhang: Nature Commun. 7:10378 (2016). 5

  6. CDW and SC fluctuations in the PG phase 300 Strange Metal（奇妙な金属） Pseudogap（擬ギャップ） T* 200 TN 温度T (K) Tcon TCon Tc 電荷秩序 charge order 100 正常金属（フェルミ液体） スピン秩序 spin order TCDW AF d-SCd波超伝導 TSonset FL TSDW 0 0.1 0.2 正孔ドーピング量　Hole dopingp B. Keimer, S.A. Kivelson, M.R. Norman, S.Uchida, J. Zaanen, Nature 518, 179 (2015).

  7. Why is CDW/d-SC the key to PG ?

  8. (a) New findings: CDW with d-symmetry form factor (d-CDW) Sublattice Phase-Resolved Imaging of the Electronic Structure of the CuO2 Plane K. Fujita, M.H. Hamidian, Y. Kohsaka, H. Takagi, H. Eisaki, S. Uchida, M.J. Lawler, E.-A. Kim, S. Sachdev, J.C. Seamus Davis et al., PNAS 111, E3026 (2014).

  9. (b) Phonon Anomaly at CDW Wavevector E. Blackburn et al., Phys. Rev. B88, 054506 (2013). M. Le Tacon et al., Nature Phys. 10, 52 (2014). Giant Phonon Anomaly (GPA): Increased damping as T  Tc from above, and abrupt changes to a dispersion anomaly (softening) with vanishing damping below Tc. YBCO6.6Tc = 61 K qCDW Conventional CDW-soft phonon is unlikely.

  10. Recently Proposed Scenarios 1. Composite Order (CDW-dSC) Intertwinedorders E. Fradkin, S.A. Kivelson: Rev. Mod. Phys. 87, 457 (2015). J.C. Davis, D.-H. Lee: PNAS 110, 17623 (2013). Compositeorder L.E. Hayward, S. Sachdev: Science 343, 1336 (2014). Emergent SU(2) SymmetryT. Kloss,C. Pepin: arXiv.1512.03801. 2. PDW Y. Wang, D.F. Agterberg, A. Chubukov: PRL 114, 197001 (2015).E. Fradkin, S.A. Kivelson: Rev. Mod. Phys. 87, 457 (2015). Amperian PairingP.A. Lee: Phys. Rev. X 4, 031017 (2014). Fermi Arcs and Leggett Mode Y.-H. Liu, T.M. Rice, F.-C. Zhang: Nature Commun. 7:10378 (2016). 10

  11. CDW & SC are both sides of a coin and crucial ingredients of PG. 1. Composite Order (CDW-dSC) Intertwinedorders E. Fradkin, S.A. Kivelson: Rev. Mod. Phys. 87, 457 (2015). J.C. Davis, D.-H. Lee: PNAS110, 17623 (2013). Compositeorder L.E. Hayward, S. Sachdev: Science 343, 1336 (2014). Emergent SU(2) SymmetryT. Kloss,C. Pepin: arXiv.1512.03801. Experimental indications: (1) – (7)

  12. (1) Charge and SC fluctuations are of the same order of magnitude. 400 300 PG T* TemperatureT (K) 200 TSCon TCDWon 100 Tc FL AF d-SC 0 0.3 0 0.1 0.2 Hole dopingp QCP ?

  13. (2) CDW and d-SC orders are intertwined. x-rays (REXS) (a) Tonset ~ 150 K (Tc = 61 K) YBCO6.6 J. Chang et al., Nat. Phys. 8, 871 (2012). G. Ghiringhelli et al., Science 337, 821 (2012). (b) Tc

  14. (3) A sudden flop between CDW and d-SC by magnetic field D. LeBoeuf et al., Nature Phys. 9, 79 (2013).

  15. (4) Interconversion of d-SC and CDW induced by magnetic field M.H. Hamidian et al., arXiv:1508.00620 T. Machida, T. Hanaguri et al., Nature Commun. 7:11747 (2016). Bogoliubov QPI around a vortex dFF-DW induced around a vortex

  16. (4) Interconversion of d-SC and CDW induced by magnetic field Interconversion occurs at the eight k-space regions (near arc edges) indicated by black open circles. Region of k-space generating dFF-DW (CDW) around vortices Bogoliubov QPs

  17. (5) CDW emerges at the Fermi-arc edges R. Comin et al., Science 343, 390 (2014). M.H. Hamidian et al., Nature Phys. 12, 150 (2016). da Silva Neto et al., Science 343, 393 (2014).

  18. (6) The energy scale of CDW is the PG energy scale. PG SC

  19. (6) The energy scale of CDW is the PG energy scale, and is dominated by a d-symmetry form factor. PG SC K. Fujita, M.H. Hamidian, Y. Kohsaka, H. Takagi, H. Eisaki, S. Uchida, M.J. Lawler, E.-A. Kim, S. Sachdev, J.C. Seamus Davis et al., PNAS 111, E3026 (2014). M.H. Hamidian, J.C. Davis, A.P. Mackenzie, H. Eisaki, S. Uchida, M.J. Lawler, E.-A. Kim, S. Sachdev, K. Fujita et al.,Nature Phys. 12, 150 (2016).

  20. (7) Giant Proximity Effect heavily underdoped cuprate d- d- Current density (KA/cm2) d = 13 – 200 Å d ≥ 100 nm Voltage (meV) La2CuO4+d (Tc = 25 K) I. Bozovic et al., Phys. Rev. Lett. 93, 157002 (2004). For YBCO, R.S. Decca et al., Phys. Rev. Lett. 85, 3708 (2000).

  21. Recently Proposed Scenarios 1. Composite Order (CDW-dSC) Intertwinedorders E. Fradkin, S.A. Kivelson: Rev. Mod. Phys. 87, 457 (2015). J.C. Davis, D.-H. Lee: PNAS110, 17623 (2013). Compositeorder L.E. Hayward, S. Sachdev: Science 343, 1336 (2014). Emergent SU(2) SymmetryT. Kloss,C. Pepin: arXiv.1512.03801. CDW primary, PDW secondary

  22. PG, a supervector representing the combination of SC and CDW order parameters J.C. Seamus Davis & Dung-Hai Lee, PNAS 110, 17623 (2013). d-CDW d-SC composite order gap magnitude

  23. Emergent SU(2) Symmetry T. Kloss, X. Montiel, V.S. de Carvalho, H. Freire, C. Pépin, arXiv: 1512.03801 Emergent symmetry: symmetry that is seen only on large (intermediate) scales RPE (Resonant Peierls Exciton) Antinodal gap & Fermi arc A super “spin-flop” between d-CDW and d-SC cf. Emergent SO(5): A 5-component superspin with 2 d-SC and 3 AF (S.-C. Zhang)

  24. Recently Proposed Scenarios 2. PDW Y. Wang, D.F. Agterberg, A. Chubukov: PRL 114, 197001 (2015). E. Fradkin, S.A. Kivelson: Rev. Mod. Phys. 87, 457 (2015). Amperian PairingP.A. Lee: Phys. Rev. X 4, 031017 ( 2014). Fermi Arcs and Leggett Mode Y.-H. Liu, T.M. Rice, F.-C. Zhang: Nature Commun. 7:10378 (2016). PDW primary, CDW secondary

  25. Amperian Pairing-PDW, primary origin of PG P.A. Lee, Phys. Rev. X 4, 031017 (2014). attractive The pair is made up of two fermions moving in the same direction and the total momentum is K. QPDW = QCDW/2: PDW primary, CDW secondary

  26. (8) Phonon Anomaly due to SC Fluctuations Giant phonon anomaly associated with SC fluctuations in the PG phase Y.-H. Liu, R.M. Konik, T.M. Rice & F.-C. Zhang, Nature Commun. 7:100378 (2016).. Inequivalent Fermi arcs (pockets) formed in the PG phase due possibly to PDW M.Le Tacon et al., Nature Phys. 10, 52 (2014). SC phase fluctuations of the phase difference(q1 - q2) q2 q1 vF vF Collective excitation: Leggett mode

  27. (9) Transient SC-Tc’(p) follows T*(p). S. Kaiser, A.Cavalleri et al.; PRB 89, 184516 (2014). Tc’ Josephson Plasma Tc

  28. (9) Transient Tc’(p) follows T*(p). 400 Tc’ under THz excitation 300 PG T* TemperatureT (K) 200 TCDWon 100 Tc FL AF d-SC 0 0.3 0 0.1 0.2 Hole dopingp QCP ?

  29. (10) CDW gap in ARPES: PDW gap ? ky /p R.-H. He, M. Hashimoto, Z.-X. Shen et al., Science 331, 1579 (2011). • PG opens atkG > kF. • Antinodal gap (PG) closes from below when the cut gets closer to the nodes. can be explained only by a PDW state with particle-hole symmetry P.A.. Lee, Phys. Rev. X 4, 031017 (2014). Y..Wang, D.F. Agterberg, and A. Chubukov, Phys. Rev. B 91, 115103 (2015).

  30. (11) Detection of a PDW State in Bi2Sr2CaCu2O8 Using Scanned Josephson Tunneling M.H. Hamidian, H. Eisaki, S. Uchida, M.J. Lawler, E.-A. Kim, A.P. Mackenzie, K. Fujita, J.C. Seamus Daviset al., Nature 532, 343 (2016). critical current across an SIS junction Bi2212 flake  rs(r) Bi2212 p ~ 0.17

  31. PDW vs CDW Modulations M.H. Hamidianet al., Nature 532, 343 (2016). PDW QPDW~ (0.25(2p/a0), 0) and (0, 0.25 (2p/a0)) s/s’ symmetry Ic(r) |Ĩc (q)| QCDW~QPDW CDW ~ 5% modulation d symmetry |D (q)|

  32. Supplimentary Information

  33. Real-space image of d-CDW K. Fujita et al., PNAS 111, E3026 (2014). M.H. Hamidian etal., Nature Phys. 12, 150 (2016).

  34. d-CDW: p-phase shift between Ox and Oy K. Fujita et al., PNAS 111, E3026 (2014). M.H. Hamidian etal., Nature Phys. 12, 150 (2016).

  35. For a pure CDW order, antinodal gap (PG) closes from above when the cut gets closer to the nodes. P.A. Lee, Phys. Rev. X 4, 031017 (2014).

  36. Real-space images of d-CDW & s’-CDW Cu Ox Oy A.J. Achkar et al., Nature Mater. 15, 616 (2016).

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