Sergey G. Ovchinnikov In collaboration with

1. Effect of quasi-2d dimensionality on the formation of electronic structure and normal properties of HTSC cuprates Sergey G. Ovchinnikov In collaboration with V.Gavrichkov,M.Korshunov, E.Shneyder, I.Makarov, S.Nikolaev, I.Nekrasov, Z.Pchelkina L.V. Kirensky Institute of Physics, Siberian Branch of Russian Academy of Science, Krasnoyarsk 660036, Russia

2. Outline • Strong electron correlations and low dimensionality of cuprates • Microscopically derived t-t’-t”-J* model from ab initio LDA+GTB study of muliband p-d model • Strongly correlated electrons and spin-liquid with short AFM order • Doping evolution of the Fermi surface and two Lifshitz quantum phase transitions between UD and OD regions • Whether ARPES measure the true Fermi surface? By new norm conserving CPT it depends on energy resolution. For typical resolution negative answer

3. What are strong electron correlations? • Е el = Е kin + ЕCoul, • ЕCoul = Е HF + Еcorr • Weak correlations: Еcorr<< Е kin + Е HF Е el = Е kin + Е HF Strong correlations: Еcorr>> Е HF,Е kin No free electron in any mean field There are multielectron terms and electron hopping between them

4. LEHMANN REPRESENTATION:electron in strong correlated system as a superposition of Hubbard-type quasiparticles Single electron GF can be written as (1) where the QP energies are given by and the QP spectral weight is equal to L.V. Kirensky Institute of Physics, SB RAS, Krasnoyarsk, Russia

5. S.G.O. and I.Sandalov, Physica C 1989; V.Gavrichkov etal, JETP 2000

6. Val’kov, Ovchinnikov 2001

7. EF x 1 2 Band structure and density of states of undoped antiferromagnetic La2CuO4 at the energy scale E~U ( Ovchinnikov, PRB 49, 9891,1994) U 0

8. Hybrid LDA+GTB scheme without fitting parameters(in collaboration with prof.V.I.Anisimov group, Ekaterinburg, (Korshunov etal, PRB2005)) • Projection of LDA band structure and construction the Wannier functions forp-d –model • Ab initio calculation of p-d –model parameters • Quasiparticle band structure GTBcalculations in the strongly correlated regime withab initio parameters • Comparison of La2CuO4 and Nd2CuO4 band structure with fitting and LDA+GTB parameters

10. Parameters of the t-t’-t”-J* model from the LDA+GTB calculations • La2CuO4 t=0.93 eV, t’= - 0.12 eV, t”=0.15 eV, J=0.295 eV, J’= 0.003 eV, J”=0.007 eV • Nd2CuO4 t= - 0.50 eV, t’=0.02 eV, t”= - 0.07 eV, J=0.195 eV, J’= 0.001 eV, J”=0.004 eV

11. Short range AFM in CuO2 plane • Undoped La2CuO4 has 3d AFM with TN~J/(lnJ/J’) Where J and J’<<J are in-plane and interplane exchange • Hole doping destroys 3d AFM at x>.03. 2d short AFM correlations persists for all doping with correlation length l~a/x^1/2 (by inelastic neutron scattering). Recent RIXS date for strongly overdoped La1.6Sr0.4CuO4 reveals magnetic excitations (Dean etal, Nat.Mater.12, 1019 (2013) • Isotropic 2d spin liquid model with <Sx>=<Sy>=<Sz>=0 and Nonzero <Sx(i)Sx(j)>=<Sy(i)Sy(j)>=<Sz(i)Sz(j)> (Barabanov et al, 1989-2001)

12. Hole dynamics in SCES at the short range order antiferromagnetic background. SCBA for Self-energy. At low T correlations are static(Barabanov et al, JETP 2001, Valkov and Dzebisashvili, JETP 2005, Plakida and Oudovenko JETP 2007, Korshunov and Ovchinnikov Eur.Phys.J.B, 2007) Correlation functions are calculated follow Valkov and Dzebisashvili, JETP 2005

13. 3 3 1 2 4 4 4 short range magnetic order in spin liquid state up to 9-th neighbor Self consistent spin and charge correlation functions in the t-t’- t”J* model,all parameters from ab-initio LDA+GTB

14. Comparison ARPES and LDA+GTB calculationsKorshunov and Ovchinnikov Eur.Phys.J.B, 2007Ovchinnikov, Korshunov, Shneyder, JETP 2009 ARPES data for Bi2201 Hashimoto etal, PRB77,2008 (left down), and Meng etal, arXiv may 2009 (right down) Bulut and Scalapino PRB1996 Bulut and Scalapino PRB1996

15. X=0.11 X=0.06 X=0.19 X=0.14 Barabanov et al, JETP 119, вып.4 (2001)Spin-polaron approach, Mori-type projection method for spin-fermion model Shadow band intensity is smaller due to spectral weight redisribution. No QP damping

16. Fermi surfacein the p-d Hubbard model,SCBA (non crossing approximation) for the self-energy,S(k,w)=SRe + iSImPlakida, Oudovenko JETP 131, 259 (2007)

17. Effect of short antiferromagnetic order on the electron spectrum(Kuchinskii, Nekrasov, Sadovskii, JETP Lett. 2005, JETP 2006, JETP Lett. 88, 224, 2008) Green function for electron interacting with a random Gaussian spin fluctuation field is given by HereDis the amplitude of the fluctuating AFM order , e(k)is the electron dispersion in the paramagnetic state In the limit of zero Im part the long range AFM (SDW) is restored

18. m1 m2 m3

19. Effective masspredicted by MMK and SGO (2007) and from quantum oscillations measurements:+ YBa2Cu3O6.5(p=0.1)Doiron-Leyraud l Nature,2007* YBa2Cu4O8 (p=0.125) Yelland etal, PRL 100, 2008 x YBa2Cu4O8 Bangura etal, PRL 100, 047004, 2008T Hg1201 Barisic etal, Nature Physics 2013 (m*/m=2.45) * x + Fig. 2. Doping dependent evolution of the chemical potential shift, nodal Fermi velocity, and effective mass. T

20. Balakirev, PRL 2009 Density of states near optimal doping QPT, N(E)=Nreg(E) + Nsing(E)Ovchinnikov etal, arXiv 0908.0576J.Phys.: Condens.Matter 23, 045701 (2011) Critical behavior near xc1=0.15: Fsing ~z^2*Log|z|, Ce/T~Log|z| Nsing(E) ~ Log|z|, z~e-eF~x-xc1~T Sommerfeld parameter Ce/T~Log T, This is a properties of the Lifshitz QPT in the 2d electron systens (Nedorezov JETP 1966) Logz is a tipical van Hove singularity for 2d free electrons (Ziman 1964)

21. DOS near pseudogap critical point x=p*=0.24Ovchinnikov etal, arXiv 0908.0576 J.Phys.: Condens.Matter 23, 045701 (2011)

22. Ovchinnikov, Korshunov, Shneyder, arXiv 0908.0576 J.Phys.: Condens.Matter 23, 045701 (2011) Eg(x)= J(1-x/p*) Kinetic energy Ekin(x)/Ekin(p*) as function of doping. Above p* dependence ~(1+x) is expected for 2D electron gas. Below p* its extrapolation reveals the depletion of kinetic energy due to pseugogap. Black triangles-fitting with Loram-Cooper triangular pseudogap model. Red line – exponential fitting E/E* ~ exp(-4Eg(x)/J)

23. Xc1=0.15 Xc2=0.24 Conclusion: normal state Concentration dependence of the two characteristic energy scales in cuprates: Tc and T* From T.Yoshida etal, PRL137, 037004 (2009), ARPES Theory: Ovchinnikov etal JETP 109, 775 (2009)

24. f 2 3 t t’ 4 1 2D модель Хаббардадля кластера 2X2 Norm conserving Cluster perturbation theory for 2D Hubbard model (S.Nikolaev, S.Ovchinnikov, JETP 111, 634 (2010)

25. Norm conserving CPT1. For 2x2 cluster and 4 local states of the Hubbard model there are 4^4=256 cluster eigenstates.The exact sum rule requires all these states 2. Usually Lanczos method involves only the ground and a few excited eigenstates. Lost spectral weight: f <1 3. It appears that 30 eigenstates is enouph to get f>0.995 We control our CPT to keep f>0.99 and call it the NC CPT 4.Then CPT in X-operator representation

26. Зависимость зонной структуры от f-фактора (Николаев, Овчинников, ЖЭТФ 138б 717 (2010))

27. Ovchinnikov, Nikolaev, JETP Lett 93, 575, 2011 NC CPT reproduces CDMFT+ED method, (Stanescu, Kotliar PRB 74, 125110, 2006, Sakai,Motome, Imada PRL102, 056404 (2009)) ARPES LSCO . Yoshida, et al., Condens Matter 19, 125209 (2007).delta= 0:02 eV, t = 0:25 eV, delta/t=0.08

28. CDMFT+ED (Sakai,Motome, Imada PRL102, 056404 (2009))

29. Isotope effect and critical temperature at different values G/J Shneyder, Ovchinnikov, JETP 109, 1017 (2009)

30. Conclusions • Two quantum phase transition with doping take are required to go from UD to OD Fermi liquid • At optimal doping Xc1=0.15 there are log singularity in DOS which results in maximum Tc • Second QPT at Xc2=0.24 separates at T=0 FL at x>xc2 and pseudogap state at x<xc2.\ • The ARPES with modern resolution does nor show true FS. The order of magnitude improvement of resolution will give the true FS • Magnetic and phonon d-pairing works together and gives aproximately equal contributions in Tc