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Abstract:We report that (Ba,K)Fe 2 As 2 superconductor (a transition temperature, T c ~ 38 K) has inverse iron isotope coefficient α Fe = -0.18(3) (where T c ~ M -αFe and M is the iron isotope mass), i.e. the sample containing the larger iron isotope mass depicts higher T c . Systematic inverse shifts in T c were clearly observed between the samples using three types of Fe-isotopes ( Polycrystalline samples of (Ba,K)Fe 2 As 2 were prepared by high-pressure synthesis method [14]. The sample synthesized from a stoichiometric starting composition of (Ba 1-x K x )Fe 2 As 2 includes a FeAs impurity phase probably because K -4-and Ba exclude from the samples during heat treatment. This difficulty was overcome by using the 50% excess of Ba and K for the starting composition i.e.(Ba 0.5 K 0.5 ) 1.5 Fe 2 As 2 . Precursors of BaAs, KAs and As powder were mixed homogeneously and divided into two equal weights, then mixed with the two different iron isotopes in order to rule out K concentration difference between the two samples which can be a factor to change T c . The materials were ground by an agate mortar in a glove box. The mixed powders were pressed into pellets. Two pellets were put into a BN crucible as shown in the inset of Fig.1; to rule out difference in synthesis temperature and pressure, which also can affect in a variation in the T c between the samples. The samples were simultaneously heated at about 900°C under a pressure of about 1 GPa for 1 h. 54 Fe and n Fe were tested for sample preparation to ensure systematic behavior of T c .We obtained 7 sets of samples (S1-S7) synthesized in the same conditions except for the iron isotope mass.Powder X-ray diffraction (XRD) patterns of the samples were measured by using CuK a radiation. The dc magnetic susceptibility was measured by using a SQUID magnetometer (Quantum Design MPMS) under a magnetic field of 5 Oe. The resistivity of the two isotope containing samples was measured simultaneously by a four-probe method (Quantum Design PPMS).All the samples are an almost single-phase and difference in lattice parameters between the two samples synthesized simultaneously was small (negligible). The XRD patterns of the sample set S2 synthesized using 54 Fe and 57 Fe isotopic powders, S2( 54 Fe) and S2( 57 Fe) are represented in Fig. 1 is almost constant against x, which is suitable for verification of the isotope effect. We also confirmed the homogeneity of the samples by using scanning electron microscope with energy dispersive x-ray spectroscopy (SEM-EDX) analysis, and we detected the x = 0.40(2) throughout the pellet. (ΔT c(χ) ) and α Fe of the sample sets S1-S7 are listed in Table 1.In Fig. 3 the temperature dependent normalized resistivity of the samples S2( 57 Fe) and S2( 54 Fe) are shown. It should be noted that the normal state in the normalized resistivity plot is almost overlapped each other except the region of T c, assuring the same quality of the samples. T c(ρ) is determined by the definition as shown in the inset of Fig. 3. This result also clearly sho...

Ž .Ž . The possibility of superconductivity SC in the ground state of the two-dimensional 2D Hubbard model was investigated by means of the variational Monte Carlo method. The energy gain of the d-wave SC state, obtained as the difference of the minimum energy with a finite gap and that with zero gap, was examined with respect to dependences on U, electron density r and next nearest neighbor transfer t X mainly on the 10 = 10 lattice. It was found to be maximized around Ž .X U s 8 the energy unit is nearest neighbor transfer t . It was shown to sharply increase for negative values of t and have a broad peak for t X ; y0.10. For these value of t X the energy gain was a smooth increasing function of r almost independent of the shell structure in the region starting from ; 0.76 up to the upper bound of investigation 0.92. This clearly indicates that the result is already close to the value in the bulk limit. For t X s 0, the energy gain depended on the electronic shell state. This suggests the 10 = 10 lattice is not sufficiently large for this case, although it is highly plausible that the bulk limit value is finite. Competition between the SC and the commensurate SDW states was also investigated. When t X s 0, the ground state is SDW in the range of r G; 0.84. The SC region slightly extends up to ; 0.87 for t X ; y0.10. Consequently the present results strongly support an assertion that the 2D Hubbard model with t X ; y0.1 drives SC by itself in the r region from ; 0.76 to ; 0.87. The above features are in a fair agreement with the phase diagram of the optimally and overly hole-doped cuprates. The energy gain in the SC state with suitable parameters is found to be in reasonable agreement with the condensation energy in the SC state of YBa Cu O . The corresponding t-J model proves to give an 2 3 7order-of-magnitude larger energy gain, which questions its validity. q 1998 Elsevier Science B.V. All rights reserved.

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We propose a Monte Carlo method, which is a hybrid method of the quantum Monte Carlo method and variational Monte Carlo theory, to study the Hubbard model. The theory is based on the off-diagonal and the Gutzwiller type correlation factors which are taken into account by a Monte Carlo algorithm. In the 4×4 system our method is able to reproduce the exact results obtained by the diagonalization. An application is given to investigate the half-filled band case of two-dimensional square lattice. The energy is favorably compared with quantum Monte Carlo data.

We investigate some significant properties of multi-band superconductors. They are time-reversal symmetry breaking, chirality and fractional quantum flux vortices in three-band superconductors. The BCS (Bardeen-Cooper-Schrieffer) gap equation has a solution with time-reversal symmetry breaking in some cases. We derive the Ginzburg-Landau free energy from the BCS microscopic theory. The frustrating pairing interaction among Fermi surfaces leads to a state with broken timereversal symmetry, that is, a chiral solution. The Ginzburg-Landau equation for three-component superconductors leads to a double sine-Gordon model. A kink solution exists to this equation as in the conventional sine-Gordon model. In the chiral region of the double sine-Gordon model, an inequality of Bogomol'nyi type holds, and fractional-π kink solutions exist with the topological charge Q. This yields multi-vortex bound states in three-band superconductors.

The ground state of the two-dimensional (2D) Hubbard model is investigated by adopting improved wave functions that take into account intersite electron correlation beyond the Gutzwiller ansatz. The ground-state energy is lowered considerably, giving the best estimate of the groundstate energy for the 2D Hubbard model. There is a crossover from weakly to strongly correlated regions as the on-site Coulomb interaction U increases. The antiferromagnetic correlation induced by U is reduced for hole doping when U is large, being greater than the bandwidth, thus increasing the kinetic energy gain. The spin and charge fluctuations are induced in the strongly correlated region. These antiferromagnetic and kinetic charge fluctuations induce electron pairings, which result in high-temperature superconductivity.