Inhomogeneous spin and charge densities in d-wave superconductors

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1 Inhomogeneous spin and charge densities in d-wave superconductors Arno P. Kampf Paris, June 2009 Collaborative Research Center SFB 484 Cooperative Phenomena in Solids: Metal-Insulator-Transitions and Ordering of Microscopic Degrees of Freedom

2 Outline Resonances in d-wave superconductors Impurities & field-induced antiferromagnetism common origin Coexistence of superconductivity and charge order Stripe patterns and finite momentum pairing

3 Collaborators d-wave superconductivity and antiferromagnetism Markus Schmid Peter Hirschfeld Brian Andersen University of Augsburg University of Florida, Gainesville Niels Bohr Institute, Copenhagen d-wave superconductivity and charge order Florian Loder Thilo Kopp University of Augsburg University of Augsburg

4 Insights & Puzzles from STM Spectra of Cuprate Superconductors sharp conductance peaks near Zn impurities close to zero bias gap inhomogeneities and negative coherence peak height to gap value correlation split bound states in d-wave vortex cores 4-unit cell checkerboard charge density modulations J.C. Davis (Cornell), A. Yazdani (Princeton), Kapitulnik (Stanford) Theory issues: τ 1 versus τ 3 impurities quasiparticle interference patterns spatial LDOS structure nucleation of spin and charge order P. Hirschfeld, C.S. Ting, A. Balatsky, T. Devereaux, P. Lee,...

5 Imaging Zn impurity atoms on BSCCO S. H. Pan et al., Nature 403, 746 (2000)

6 Gap Inhomogeneity in BSCCO A. C. Fang et al., PRL 96, (2006)

7 Local density of states in the vortex core of YBCO I. Maggio-Aprile et al., Y. Wang & A. H. MacDonald, PRL 75, 2754 (1995) PRB 52, R3876 (1995)

8 STM spectra of the vortex core in BSCCO S. H. Pan et al., PRL 85, (2000)

9 Signatures for the coexistence of antiferromagnetism and superconductivity µ-on spin rotation in underdoped YBCO Miller et al and in LSCO Panagopoulos et al evidence for antiferromagnetic vortex cores in Tl 2 Ba 2 CuO 6 from NMR relaxation rate Kakuyanagi et al elastic neutron scattering with (π δ, π) incommensurate antiferromagnetism in superconducting LSCO Wakimoto et al Zn impurities induced inhomogeneous antiferromagnetic order in optimally doped LSCO Kimura et al field-induced antiferromagnetism in superconducting underdoped LSCO from neutron diffraction Lake et al. 2002

10 Field-induced antiferromagnetic order in underdoped LSCO B. Lake et al., Nature 415, 299 (2002)

11 Focus issues Impurity versus field-induced antiferromagnetism Role of impurity resonances & vortex bound states for the nucleation of antiferromagnetism Temperature dependence of the staggered magnetization

12 Model and Calculational Tools Pairing Hamiltonian in an external magnetic field: H = ij σ + iσ t ij exp [ i π φ 0 j i A dl ( ) Un i, σ + V imp i µ ] ĉ iσĉjσ + ij ĉ iσĉiσ ( ij ĉ i ĉ j + H.c. ) d-wave pairing potential: ij = V d ĉ i ĉ j self-consistent Bogoliubov-de Gennes (BdG) equations j [ Hij,σ ij ij H ij, σ ] ( ujn v jn ) = E n ( uin v in supercell method & magnetic Bloch theorem )

13 Impurity-Induced Antiferromagnetism Charge Density Order Parameter Magnetization doping = 10%, V imp = 60t, H = 0T LDOS (next to impurity) LDOS Energy [t] U = 0t U = 2.2t U>U c : impurity induces short-range AF order Origin: spin splitting of the (near) zero-energy resonance

14 Field-induced Antiferromagnetism Charge Density Order Parameter Magnetization doping = 10%, V imp = 0, Φ = 2Φ 0 U = 2.2t (magnetized) U = 0 (unmagnetized) vortex core LDOS LDOS 2.0 AF vortex core for U>U c Energy [t] Origin: spin splitting of the vortex bound state

15 Field-Induced Antiferromagnetism T Dependence Structure Factor LDOS at the vortex center doping 10%, B = 59.2 Tesla, V imp = 0 doping = 10%, V imp = 0, Φ = 2Φ 0 M(q) 2 (integrated) 0.02 U=2.5t U=2.6t U=2.7t U=2.8t U=2.9t LDOS T = 0.175t, unmagnetized vc T = 0.150t, magnetized vc T = 0.125t, magnetized vc T c Temperature [t] Magnetization Energy [t] M(q) 2 (T) negative curvature, order parameter like no domain walls simultaneous onset of bound-1state splitting & magnetization

16 Two Strong Non-magnetic Impurities Charge density Magnetization M(q) 2 (integrated) Structure factor doping = 10%, V imp =10t, B = 0 T c Temperature [t] negative curvature of M(q) 2 (T) T dependence as for field induced antiferromagnetism possible reason: absence of domain walls 16

17 Finite Density of Non-magnetic Impurities La 2 x Sr x CuO 4 Out-of-plane Sr atoms act as weak potential scatterers on the in-plane electrons. impurity concentration = doping

18 Combined Disorder & Field-Induced Antiferromagnetism Charge Density Φ=0 Φ = 2Φ0 Order Parameter Magnetization

19 Structure Factor for Different Impurity Configurations Φ = 0 Φ = 2Φ 0

20 Φ = 0 Averaged Structure Factor Lake s experiment Φ = 2Φ 0 incommensurate AF order Q = (π ± δ, π)

21 M(q) 2 (integrated) 0.02 T-Dependence of the Structure Factor Theory U=2.9t, doping=10%=imp. conc., V imp =1.3t 0.04 H = 59T H = 0T T c Lake s experiment Temperature [t] zero-field signal rises linearly upon cooling field-induced signal increases order parameter like origin for different curvatures: antiphase domain walls

22 More results and details on the poster: Impurity and field-induced antiferromagnetism in cuprate superconductors by Markus Schmid, Brian Andersen, Peter Hirschfeld, and A.P.K. 22