Impact of charge order on the electronic properties of underdoped cuprates Cyril PROUST

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1 Impact of charge order on the electronic properties of underdoped cuprates Cyril PROUST Laboratoire National des Champs Magnétiques Intenses Toulouse, France

2 Collaborations F. Laliberté W. Tabis D. Vignolles B. Vignolle M-H. Julien D. LeBoeuf L. Taillefer N. Doiron-Leyraud D. Bonn B. Ramshaw R. Liang W. Hardy S. Badoux S. Lepault B. Keimer M. Greven A. Carrington M. Le Tacon N. Barisic N. Hussey T. Loew M. K. Chan

3 Quantum oscillations in hole-doped cuprate Topological change in Fermi surface underdoped YBa 2 Cu 3 O 6.5 overdoped Tl 2 Ba 2 CuO 6+δ 2 F = 530 T 4 F = T R (mω) 0 B Aimantation (u.a.) % 65 % / B (T -1 ) N. Doiron-Leyraud et al, Nature 07 φ 2π 0 F = 2 A k / B (T -1 ) B. Vignolle et al, Nature 08

4 Ubiquity: Quantum Oscillations Quantum oscillation in YBa 2 Cu 3 O y : Observedin manyprobes: electrical/ thermal transport, magnetization, ultrasound, TDO, thermoelectricity Observedin the doping range between9 % and 15 % Quantum oscillations in single layer HgBa 2 CuO 4+δ : F = 840 ±30 T and m * =2.45 ±0.15 m e N. Barisic et al, Nature Physics (2013)

5 Ubiquity: Hall effect YBa 2 Cu 3 O y HgBa 2 CuO 4+δ D. LeBoeuf et al, Nature 07 N. Doiron-Leyraud et al, PRX 13 Electron pocket! Reconstruction of the FS into electron (and hole) pockets below a critical doping p *

6 Broken symmetry = charge order High field NMR in underdoped YBCO (M-H. Julien, LNCMI-Grenoble) High energy x-ray diffraction in underdoped YBCO 2D charge fluctuations up to T=150 K with an incommensurate periodicity T. Wu et al, Nature 11 Broken translational symmetry by charge order No spin order! T. Wu et al, Nature Commun. 13 Threshold field J. Chang et al, Nature Physics 12 G. Ghiringhelli et al, Science 12 A. Achkar et al, PRL 13 Charge orderdetectedbetween8 % < p < 16 % But alsox-ray in Hg1201 (Q 0.28) W. Tabis et al, Nature Commun. 14

7 Link between QO and CDW Can wereconcilequantum oscillations and the transport properties in YBCO with the Fermi surface reconstructed by a biaxialcharge order?

8 Fermi surface reconstruction Qualitative FSR by biaxial charger order Other pockets? S. E. Sebastian et al, RPP 12

9 Discovery of a new frequency in YBCO Thermopower(Taillefer s group) Tallahassee c-axis resistivity Toulouse 40 dr / db (mω / T) K 15 K 20 K 25 K p = / B (T -1 ) p = 0.11 N. Doiron-Leyraud et al, Nature Commun. 15

10 Effective mass / angle dependence Temperature dependence Angle dependence R (mω) 10 0 p = K 15K 20K 25K 30K 40K R (mω) p = 0.11 Amplitude (%) / B (T -1 ) m * = 0.45 ±0.1 m e T (K) Frequency (T) (a) (b) N. Doiron-Leyraud et al, Nature Commun / B cos(θ) (T -1 ) p = θ (deg) (=0) cos

11 Connecting QO with FSR by charge order Fermi surface reconstruction by a bond density wave Anisotropic biaxial CDW hole Magnetic Breakdown electron 2 2 F electron / F hole 5 p = 0.11 A. Allais et al, Nature Commun. 14 hole Q 1, Q 2 measuredby x-ray Q 1, Q 2 Q anti-nodal AND Q 1, Q 2 Q hotspot B. Vignolle et al, CRAS12 two-step processfor the Fermi surface reconstruction: Pseudogap+ CDW

12 The case for an extra hole pocket Doping dependenceof Thermopower in YBCO F. Laliberté et al, Nat. Comm 11 1 () () () Two band model = F h = 95 T m h* =0.45 Needfor a twoband model to explainthe doping dependenceof Seebeck N. Doiron-Leyraud et al, Nature Commun. 15

13 The Thermodynamic police Electronic coefficient of the specific heat: m* electron = 1.7 ± 0.2 m 0 and m* hole = 0.45 ± 0.1 m 0 γ theo = 7.6 ± 0.8 mj.mol -1.K -2 for 1 electron + 2 hole pockets (+ bilayer) S. Riggs et al, Nature Physics 11 Recent measurements in Grenoble: (C. Marcenat, T. Klein et al) YBCO p = 0.11 : γ el (B=30 T, T 0) = 7 ±1.5 mjk -2 mol -1 YBCO (p~0.11): γ el (B=45 T, T 0) ~ 5.0 ±1mJmol -1 K -2

14 Sound velocity measurements Where does the thermodynamic phase transition take place?

15 High fields sound velocity in YBCO c 11 YBCO Sound velocity: thermodynamic quantity related to the elastic constants of a solid c 2 2 ij F vs = where c = ρ ij ε ε Directional probe: propagation / polarization i j Melting of the vortex lattice B co thermodynamic signature of phase transition Comparison with NMR charge order Simple group theory argument: D. LeBoeuf et al, Nature Physics 13 Charge modulation both along aand b-axis

16 Threshold field Comparaison c 66 -NMR Field dependenceof c 66 p=0.104 T c = 59.6K p=0.108 T c = 60.7 K p=0.109 T c = 61.5 K

17 Conclusion / open questions Fermi surface reconstruction by biaxial charge order electron + hole pockets Reconciliationof quantum oscillation and transport propertieswithx-ray resultsif pseudogap effect on the Fermi surface is taken into account Phase transition detectedby ultrasoundatlowt and abovea thresholdfieldbothin the field and temperature dependences of the sound velocity Analogywithstripe? Fermi surface reconstruction produces electron pocket in criss-crossed stripe model CDW correlation length measured by x-ray versus cyclotron orbit of quantum oscillations