A. Kallio

Spectator fermion binding of bosons

We consider a two-component mixture of charged fermions on neutralizing background with all sign combinations and arbitrarily small mass ratios. In the two-impurity limit for the heavier component we show that the pair forms a bound state for all charge combinations. In the lowest order approximation we derive a closed-form expression for Veff(r), the binding potential which has short-range repulsion followed by attraction. In the classical limit, when the mass of embedded particles is large, m2 a m, we can calculate from Veff(r) also the cohesive energy E and the bond length R of a metallic crystal such as lithium. For lithium metal the lowest-order result is R = 3.1 A, E = −1.8 eV, while the corresponding experimental values are 3.4 A and −1.6 eV. The same interaction for two holes on a parabolic band with m2 > m gives the quantum mechanical bound state which one may interpret as a boson or local pair in the case of high-Tc and heavy-fermion superconductors.

Exponent relations for superfluids with pair breaking

Abstract We show that near T=0 there exists a simple power law connection between the superfluid density n2(T) and the pair breaking function ƒ(T) . This relation can be used to classify the superfluids. The power law behaviour of the specific heat is different for different classes. Also an exact connection between ns(T) and ƒ(T) is derived, which gives 4He and BCS as special cases. Some experimental evidence is presented in the case of high-Tc for NMR Knight shifts and for heavy fermion superconductors for specific heat, ultrasound attenuation, and pressure dependence, which support the theoretical results. These power laws are obtained assuming that the order parameter is of 1S0-type. Many of the results obtained are independent of the exact nature of boson binding. Both 3D and 2D cases are discussed C.N. Yang, Rev. Mod. Phys. 34 (1962) 694.

Boson localization and universality in YBa2Cu3 − xMxO7 − δ

Abstract We show that for compounds of the type YBa2Cu3 − xMxO7 − δ one can understand most of the experimental results for the superconducting and normal states with a single temperature dependent boson breaking function f(T) for each impurity content x. Within the electron hole liquid model f(T) determines the density of bosons to be nB(T) = n0f(T) and the density of pairing fermions (= holes) nh(T) = 2n0 [1 − f (T)]. In the normal state f(T) turns out to be a linear, universal function, independent of the impurity content x and the oxygen content δ. We predict with universality a depression in Tc(x) with slight down bending in agreement with experiment. In the superconducting state we use an f(T) with a constant activation gap combined with power law behaviours. As a natural consequence of the model the bosons become localized slightly above Tc due to the Wigner crystallization, enhanced with lattice local field minima. The holes remain delocalized with a linearly increasing concentration in the normal state, thus explaining the rising Hall density. The boson localization temperature TL shows up as a minimum in the Hall density R-1ab.

Explicit scaling function for low temperature specific heat in magnetic field

Abstract We apply the boson–fermion chemical equilibrium model to derive an expression for the electronic specific heat at zero field and calculate also the magnetic field dependence of the specific heat coefficient γ ( T , H )= C ( T , H )/ T in external magnetic field H . The carrier densities for bosons ( B ++ ) and fermions ( h + ) are determined by the treatment of the equilibrium reaction B ++ ⇌2 h + , in a magnetic field. The densities for bosons and fermions, n B ( t , h ) and n h ( t , h ) determined in terms of a single, universal function f ( t , h ), where the scaled variables are defined by t = T / T * and h = H / H * . For zero field we show that the electronic specific heat coefficient γ ( t ,0) comes out to be in semiquantitative agreement with experiment at all temperatures. The main contribution comes from localized bosons forming stripes of localized charge in addition to the fermion contribution. The model predicts the specific heat step at T c to come from localized bosons with spin unity, which are 3D-paramagnetic below T c and 2D-antiferromagnetic above T c . Because the boson density increases with doping we predict the peak value to be larger for overdoped compounds. The main test for the theory is the derivation of the scaling function at low temperatures γ ( T , H )/ H 1/2 ∼(1+( z / z 0 ) 2 ) 1/2 , with z = T / H 1/2 .

The spectator fermion superfluid model for high-Tc and heavy fermion superconductors: The pressure effect

Abstract We show that the pressure dependence of T c for the high- T c and heavy fermion superconductors can be explained within a generalized electron-hole liquid model called the spectator fermion superfluid model. We assign the structure (e - , B ++ ) for the hole-doped and (e - , B -- ) for the electron-doped superconductors. This classification explains in a natural way the observed pressure asymmetry. In both cases, the experimental pressure gradients of T c are fitted well if the spectator component has a much smaller effective mass than the bosons. The pressure gradient of T c is predicted to be smallest near the maximum T c point, in agreement with experiments. The theory predicts an increase of the specific heat linear term with pressure for all four spectator categories. The pressure dependences of T c and c p ( T c ) for the HFS-compounds UBe 13 and UPt 3 are brought into agreement with experiment if we assign the structure (h + , B ++ ) to them. We show that the pressure dependences of the Hall coefficient and the Hall resistance agree with experiments for HTS-compounds for T > T c .

Spectator Fermion Binding of Bosons

Abstract We propose a simple molecular binding model for the bosons by considering two heavy charges Ze with mass M2 embedded into electron gas with mass m. In the lowest order approximation we derive a closed form expression Veff(r) for the binding potential which has short-range repulsion followed by attraction. In the classical limit M2 ⪢ m, we calculate the bond length R and cohesive energy E for the lithium metal to be R = 3.1 A , E = −.9 eV. The same interaction for two holes in a parabolic band with M2 ⪢ m gives quantum mechanical bound state which one may interprete as a boson appearing in high-Tc superconductors such as 123.

Acoustic plasmon velocity from Raman scattering lineshapes

Abstract The temperature dependence of the 120 and 340 cm −1 phonons and the low frequency Raman background continuum in YBa 2 Cu 3 O 7 are interpreted in terms of an acoustic plasmon with temperature-dependent sound velocity. We argue that the observed phonon lineshapes and positions together with the intensity redistribution in the Raman background cannot be fully explained in terms of an energy gap. We find the gap interpretation unsatisfactory, because even though the energy gap can explain some Raman results below T c , the normal state Raman properties, which are very similar to the ones in the superconducting state, remain unexplained. We propose that the observed T -dependence of the Raman background continuum, the Raman shifts and linewidths of the optical phonons are due to the high-velocity acoustic plasmon predicted by the SFS-model of high- T c superconductivity. The T -dependence of the acoustic plasmon velocity is deduced from both the Raman background and from the peak position of the 340 cm −1 phonon measured by several groups. We find the sound velocities deduced from the two different experiments to be in good qualitative agreement. We show also that the linewidths of the 120 and 340 cm −1 phonons can be explained with the same T -dependent acoustic plasmon velocity. This temperature dependence can be explained with boson localization above a temperature T L > T c .

Pressure dependence of Tc from chemical equilibrium

Abstract Chemical equilibrium theory analogous with dissociation of molecules is applied to high-Tc superconductors. The starting point are preformed pairs, which exist in the normal state and can be treated as Coulomb bosons with charge 2e. Above Tc the pairs (B2+) decay into fermions (h+) according to the equilibrium reaction B 2+ ⇌ 2h + . Using an approximate chemical equilibrium constant proportional to pressure P, we derive for the pressurized optimum transition temperature a universal two-parameter expression TcMAX(P)/TcMAX(0)=(1+β1P)1/2(1−β2P)2, where β1(>0) and β2 are parameters. We have applied this formula to the mercury compounds, where we obtain β 1 =0.093 ( GPa ) −1 . This then shows that in an interesting pressure range P>10 GPa , the expansion in powers of pressure diverges, due to the square root. One can also derive a more general doping formula Tc(x,P)=A(1+β1P)1/2[x−x1(P)][x2(P)−x].

New magnetic field scaling of NMR in cuprates

Abstract The magnetic field dependence of the low temperature specific heat coefficient γ ( T , H )= C ( T , H )/ T has been shown experimentally and theoretically to obey the scaling relation γ(T,H)=γ 0 T 2 +Ah , where h =| H |/1 T and the coefficient A depends upon field direction. This suggests that also other quantities such as the NMR Knight shifts K α ( T , h ) ( α = c , ab ) and the relaxation rates w α ( T , h )=( T 1 T ) −1 may be expressed in terms of the scaled variable T = T 2 +A α h in the form K α (T,h)=K 0 ( T ) and w α (T,h)=w 0 ( T ) , where the presence of vortices in the mixed state simply rises the effective temperature T . We have tested this idea using the recent NMR rate data on TlSr 2 CaCu 2 O 6.8 by Zheng et al. with H ∥ c . The theoretical curve for w ( T ,0) consists of a Fermion part with added stripe contribution due to the localized triplet bosons. The data points for various field collapse to the curve w ( T ,0), with A =80 K 2 .

Stripes and a two-component interpretation of NMR in cuprates

Abstract Based on the experimental fact that the susceptibilities χ i ( T ) and the corresponding Knight shifts K i ( T ) ( i = c , ab ) are linearly related above certain temperature T χ * (> T c ), one normally draws a conclusion that a single Fermi component is operative. We show that this may not be generally valid. As a counter example we propose a two-component system were the susceptibilities are determined by a universal function f ( T ). The model consist of a Fermi component h + and a Bose component B ++ with triplet spin localized in CuO 5 sites, in chemical equilibrium with respect to reaction B ++ ⇌2 h + , where f ( T ) gives fraction of bosons and 1− f ( T ) the fraction fermions. The susceptibilities above T * χ are given by adding the fermion and boson contributions in the form χ i ( T )= χ i 0 + A i [1− f ( T )]+ B i f ( T ), where χ i 0 , A i and B i are T -independent. Clearly then χ c ( T ) and χ ab ( T ) are linearly dependent. If the bosons are localized within the CuO 6 octahedra or CuO 5 pyramids in the ab planes, rows of such tilted sites can explain the occurrence of stripes of localized charge and antiferromagnetic fluctuations in 2D CuO 2 planes.