1. Competing Orders, Quantum Criticality, Pseudogap & Magnetic Field-Induced Quantum Fluctuations in Cuprate Superconductors Nai-Chang Yeh, California Institute of Technology, DMR 0405088 The samples studied: YBa 2 Cu 3 O 7 (Y-123) Bi 2 Sr 2 CaCu 3 O x (Bi-2212) Pr 1.85 Ce 0.15 Cu 4 O x (PCCO) Sr 0.9 La 0.1 CuO 2 (La-112) HgBa 2 Ca 2 Cu 3 O x (Hg-1223) HgBa 2 Ca 3 Cu 4 O x (Hg-1234) HgBa 2 Ca 4 Cu 5 O x (Hg-1245) Fig.1: Main panel – Universal h*-vs.-  in logarithmic plot for different cuprates, with decreasing  representing increasing quantum fluctuations. The lines are fitting curves h*(  ) = 3.5 (  c ) 0.5 to experimental data, with different fitting values of quantum criticality  c = 0, 10 , and 2  10  from left to right. Intellectual Merit: Using both macroscopic and microscopic experimental techniques, we find that the physical origin for the extreme type-II nature and the associated strong fluctuations in high-T c cuprates is the result of close proximity to quantum criticality: [1] From macroscopic measurements of magnetization, we find universal field-induced quantum fluctuations among cuprates of different microscopic variables such as the doping level (  ), the electronic anisotropy (  ), the number of CuO 2 layers per unit cell (n), and the charge imbalance between the inner- and outer-layer doping levels (  i and  o ). This manifestation is given by the much suppressed zero-temperature in-plane irreversibility field H*  H irr ab (0) relative to the upper critical field H c2 ab (0), and h*  H*/H c2 ab (0) for all cuprates follows a universal trend h*(  ) ~ (  c ) 0.5 as shown in Fig. 1 if we define a material parameter     (  o /  i ) n  for n  3 and     for n  2. [2] From microscopic studies of the quasiparticle (QP) spectra at H = 0 and H > 0: the spectral features are consistent with coexisting competing order and superconductivity. Publications emanated from this support in 2007: C.-T. Chen et al, Solid State Communications 143, Fast Communications 447 – 452 (2007). N.-C. Yeh et al, Chinese J. Phys. 45, 263 (2007). A. D. Beyer et al, to appear in Phys. Rev. B; cond-mat/0612380 A. D. Beyer et al, submitted to Physica C; cond-mat/0610855. Fig.2: Preliminary studies of the spatial-resolved tunneling spectra on various cuprates in zero and finite fields exhibit results different from expected for pure SC. Below are contrasting spectra taken on the same area of La-112 at 9 K under H = 0 and 6 Tesla along one direction, w/  ab ~ 4.8nm. Inset: Linear plot of the main panel H = 0H = 6 T

2. Fig.4: Unified doping (  )- dependent phase diagram of the normalized SC gap (  SC /  SC 0 ), CO energy (V CO /V CO 0 ) and (T c /T c 0 ) for hole- and electron-type cuprates. (The superscript 0 refers to optimal doping.) Broader Impact: The consideration of two energy scales V CO and  SC associated with coexisting competing order (CO) and superconductivity (SC) in the cuprates not only accounts for the physical origin of strong quantum fluctuations (Fig.1) and the proximity to quantum criticality, but also explains the satellite features at T T c (Fig. 3b inset) in the QP spectra, as well as the observation of unconventional low-energy QP excitations such as the dichotomy in the QP coherence (Fig. 3a) and the anomalous vortex core spectra (Fig. 2b). By associating the presence (absence) of PG with V CO >  SC (V CO <  SC ), we are able to provide for the first time unified phenomenology for all known empirical facts of the cuprates (e.g. Fig. 4), which should be important to to the ultimate development of microscopic theory of cuprate superconductivity. (Please refer to our publications for more details). Education: Trainees involved in this research Graduate students: Andrew D. Beyer, Marcus Teague Undergraduate students: Huan Yang, Michael Grinolds, Janet Ramos Honors received by students under the NSF support Intel Graduate Fellowship: Andrew D. Beyer. Caltech Upper Class Merit Scholarship: Michael Grinolds The George W. Housner Prize: Huan Yang Competing Orders, Quantum Criticality, Pseudogap & Magnetic Field-Induced Quantum Fluctuations in Cuprate Superconductors Nai-Chang Yeh, California Institute of Technology, DMR 0405088 C.-T.Chen et al, Solid State Comm. 143 (2007) Y-123 Bi-2212 From fitting Fig.3: (a) Calculated QP lifetime (   ) of a d-wave hole-type cuprate SC coexisting with SDW. Clear dichotomy in the QP coherence is observed for QP momentum along ( ,  ) and (0,  ) directions under sufficiently small quantum fluctuations (represented by the parameter  ). (b) Main panel: Calculated QP spectra at T = 0 for d-wave SC/SDW with the same  SC but different V CO values, showing the satellite features only if V CO >  SC. Inset: Evolution of the satellite feature at T = 0 to the PG feature at T > T C in the mean-field limit (  = 0). Beyer et al, (2007)