R. L. Greene Electron-doped Cuprates University of Maryland Center for Superconductivity Research Collaborators: Yoram Dagan---UMd Amlan Biswas-------UMd/UFl Hamza Balci---------UMd Mumtaz Qazilbash--UMd Patrick Fournier----Sherbrooke Girsh Blumberg----Lucent, Bell Labs
OUTLINE Background on Cuprates phase diagram Normal State Properties evidence for a QCP under the SC “dome” pseudogap issues nature of the ground state SC state pairing symmetry as a function of doping
Phase diagram of electron- and hole-doped cuprates (La,Pr,Nd)2-xCexCuO4-y La2-xSrxCuO4-y
Theoretical Phase Diagrams Phase Ordering Quantum Critical TMF Tθ max Quantum critical region T T Pseudogap Ordered (pseudogap) Disordered (Fermi liquid) Tc x QCP x
Transport evidence for a Quantum Phase Transition and QCP For details see Dagan et al., Cond-mat/0310475
Résistivité : ~ T2 ~ T YBCO : J.M. Harris et al., Phys.Rev. B 46, 14293 (92). LSCO : B. Batlogg et al., J. Low Temp. Phys. 95, 23 (94). PCCO : nos travaux sur couches minces...
Resistivity vs doping
= 0 +AT x=0.17
= 0 + AT
ab-plane resistivity for Pr2-xCexCuO4 films with H>Hc2 Fournier et al., PRL 81,4720 (98)
~ T2
Hall vs H X=0.17
Tmin(K)
ARPES Nd2-xCexCuO4 N.P. Armitage et al. PRL 88 257001 (2002).
Linear in T resistivity is expected above a 2D AFM to paramagnetic metal QCP. Other powers of T would be expected at nearby dopings because of fitting the data over a low temperature Fermi Liquid T2 regime and the quantum critical regime at higher temperature. This is exactly the behavior we find! The lowest temperature Hall Coefficient shows a kink at the same doping (within error) as the linear in T resistivity. This is strong confirming evidence of the QCP. ARPES shows a drastic change in the Fermi surface near the same doping.However, the ARPES doping resolution is not as good as our transport data. The doping dependence of the low energy pseudogap ( to be shown in a few slides) is consistent with the QCP scenerio from transport.
Pseudogap High Energy (~100mev)----- optics, Raman, ARPES Low Energy (~5meV) --------tunneling, Raman
Conductivity Y. Onose et al. PRL 87 217001 (2001).
“Break junction” between PCCO (x=0.15) and Ag H=0, Superconducting state H=9 T ( || c-axis), Normal state 2SC Normal state gap (NSG) SC gap clearly seen Not residual SC at interface Not effect of tunnel barrier Biswas et al., PRB 64, 104519 (2001)
Grain Boundary Tunneling Alff et al., Nature 422, 698 (2003)
Nature of the Ground State
Magnetism Kang et al., Nature 423, 522 (2003) Antiferromagnetic Order as the Competing Ground State in electron-doped Nd1.85Ce0.15CuO4 They find TN=37K for H>Hc2 AF order different than for undoped parent NCO Sonier et al., PRL 91, 147002 (2003) Antiferromagnetic order in the vortex cores of Pr1.85Ce0.15CuO4
Violation of Wiedemann-Franz law R.W. Hill et al. NATURE 414 711 (2001). Pr1.85Ce0.15CuO4 Crystal
NMR in PLCCO Fermi Liquid GS No pseudogap Zheng et al., PRL 90, 197005 (2003) Fermi Liquid GS No pseudogap
Pairing Symmetry of Superconducting State
Disagreements even for optimally doped compounds For n-doped cuprates Disagreements even for optimally doped compounds Penetration depth Kokales et al., PRL 85, 3696 (2000), Prozorov et al., PRL 85, 3700 (2000) ARPES Armitage et al., PRL 86, 1126 (2001); Sato et al., Science 291, 1517 (2001) Tricrystal experiment Tsuei et al., PRL 85, 182 (2000) Raman scattering Blumberg et al., PRL 88, 107002 (2002) Specific heat Balci et al., PRB 66, 174510 (2002) d-wave Penetration depth Alff et al., PRL 83, 2644 (1999); Kim et al., PRL 91, 087001 (2003); Skinta et al., Phys. Rev. Lett. 88, 207003 (2002) Tunneling spectroscopy Kashiwaya et al., PRB 57, 8680 (1998) ; Alff et al., PRB 58, 11197 (1998). s-wave
To distinguish between d-wave and s-wave by tunneling spectroscopy d-wave (110) direction Blonder, Tinkham and Klapwijk (BTK) Phys. Rev. B 25, 4515 (1982) Tanaka and Kashiwaya Phys. Rev. Lett. 74, 3451 (1995) N S Z = 0 barrierless contact between N and S Z 1 tunneling limit Barrier strength Z
Evidence for a transition from d-wave to s-wave pairing symmetry in Pr2–xCexCuO4 Tunneling conductance G=dI/dV vs. voltage V A. Biswas, P. Fournier, M. M. Qazilbash, V. N. Smolyaninova, H. Balci, and R. L. Greene, Phys. Rev. Lett. 88, 207004 (2002) Underdoped sample with x=0.13 Zero-bias peak characteristic for d-wave Overdoped sampe with x=0.17 Double peak characteristic for s-wave
How to differentiate s- wave and d-wave Use the different field dependence of Cel in s-wave and d-wave. In the temp and field range of our experiment, if s-wave Þ CelµH d-wave Þ CelµH1/2 in the clean limit G. E. Volovik, Pis’ma Zh. ksp. Teor. Fiz. 58, 457 (1993) [JETP Lett. 58, 469 (1993)]. CelµH log(H) in the dirty limit C. Kubert and P. J. Hirschfeld, Solid State Commun. 105, 459 (1998)
Temperature dependence x= 0.15 Global fitting of the form C/T=+T2 gives: N = 6.7 ± 0.5 mJ/mole K2 (intercept of 10 T data) (0) = 1.4 ± 0.2 mJ/mole K2 (intercept of 0 T data)
Comparison with different theoretical predictions Balci et al. PRB 66, 174510 (02)
s-wave theory: C(H) nTH/Hc2 slope 2.5*2/4=1.3 mJ/mole KT
2D excitation in optimally doped NCCO crystal Tc=22 K G. Blumberg et al, PRL 88, 107002 (2002)
Raman spectra of overdoped NCCO crystal (Tc = 14K)
Isotropic gap in overdoped NCCO crystal
d- to s-wave transition: l-2(T) J.A. Skinta et al. PRL 88 207003 (2002); PRL 88 207005 (2002). l-2(T): T2 -> Exp(-D/T)
ARPES Nd2-xCexCuO4 N.P. Armitage et al. PRL 88 257001 (2002).
Theoretical explanation of a symmetry change in n-doped cuprates +
The antiferromagnetic spin fluctuations (ASF) peaked at the wave vector Q = (,) are responsible for d-wave superconductivity The interaction via ASF has the highest strength at the so-called hot spots, the points on the Fermi surface connected to each other by the vector Q. the interaction via ASF is repulsive in the singlet channel:
- - + + + + - - d-wave symmetry for hole doped
electron-doped case at low doping + + + + - -
electron-doped in the high doping regime + + + + - -
Doping dependence
SUMMARY QCP scenario seems to be valid in n-type Kink in RH and ~ T1 at xc =0.165 d- to s-wave symmetry change near xc Pseudogaps in n- and p-type are different Significance of subtle differences in n- and p-type properties not yet clear