Bernd Schuh

Lifshitz-point behaviour of ferromagnetic superconductors

The critical behaviour of the electromagnetically coupled superconductor magnet system is investigated by means of a generalized mean field theory and a renormalization group analysis.We show that in the presence of a genuine anisotropy in systems with an additional pressure-like parameter (like concentration in pseudo-ternary ferromagnetic superconductors (FMS), e.g. Er1−xHoxRh4B4) the indirect coupling between superconducting and magnetic order parameters (i.e. gauge coupling) can lead to a peculiar kind of critical behaviour characterized by Lifshitz points (LP). These points (quite generally) occur as merging points of three phases: a (magnetically) disordered phase, a homogeneously ordered phase and a modulated phase. In FMS the latter phase may result from exchange screening by supercurrents.This unusual critical behaviour is found in two varieties:1.a regular LP which may occur on the lower transition line of a reentrant FMS2.a similar but slightly different critical point which we term modified Lifshitz point (MLP), and which is to be expected at the merging point of the upper and lower superconducting transition lines with the magnetic order disorder transition lines in the (x, T) phase diagrams of FMSs.

Influence of exchange fields in hybrid pairing superconductors, I: Ground states

Hybrid pairing superconductors with two bands of localized and delocalized states in the presence of uniform molecular fields and a finite displacement of the bands at the Fermi level are analyzed in mean field theory.At zero temperature, in addition to the usual BCS like ground state, agapless superconducting state withfinite spin polarization can be realized. The appearance of this state is somewhat analogous to the occurrence of the Fulde Ferrell state in a single band superconductor with an exchange field.We comment on the relevance of this model for heavy-fermion superconductors.

Influence of exchange fields in hybrid pairing superconductors II. Selfconsistent ground states

A previously investigated model of a two band superconductor with hybrid pairing and molecular fields is enlarged by exchange interactions generating those fields. The fields are calculated selfconsistently in molecular field approximation at zero temperature. They turn out to stabilise the previously found new state of gapless superconductivity and non vanishing spin polarization for a wide range of exchange couplings, in particular for zero external field.

Renormalization group treatment of phase transitions in ferromagnetic superconductors

We investigate the nature of the phase transition from the superconducting to the uniformly ordered magnetic phase in ferromagnetic superconductors by renormalization group methods. For this purpose Halperin, Lubensky, Mas application of theε-expansion to pure superconductors is extended to include the influence of magnetic order as well. Our treatment shows that in the vicinity of the ferromagnetic to superconducting phase-boundary critical fluctuations of the magnetization are absorbed into fluctuations of the magnetic field. As a consequence the transition always is first order. An additional indication to the dominance of electromagnetic effects is the irrelevance of the coupling corresponding to spin flip scattering.

Kondo-lattice: Kondo-effect?

The periodics-d-model is investigated by Green function methods. We find that the lnT-divergence appearing in third order perturbation theory for the electron selfenergy is smoothed out but still shows up in a characteristic decrease (exchange couplingγ<0) or increase (γ>0) of lifetime of electrons at the fermi level asT→0 and a corresponding structure in the specific heat. However, in contrast to the single impurity case, the corresponding characteristic temperature does not vary like exp[−1/|γ|] but always is of orderγ2. From a mean field theory of the model, one finds a critical temperature for a transition into a magnetically ordered stateTc0 which varies precisely likeγ2. Thus an interesting competition between Kondo-effect and long-range magnetic order can be expected in this model.

Remarks on exotic superconductivity mechanisms

A generalization of a recent theory of the superconductingTc for non-phonon interaction mechanisms is presented; it incorporates strong coupling effects in a simple way. In addition it is pointed out that the solution of the integral equation for the kernel of the new gap equation to all orders in the interaction is necessary, feasible, and significant (with regards to highTc) in certain cases; this is illustrated by an approximate solution for a simple model of a typical exotic interaction mechanism.

Unusual critical behaviour of ferromagnetic superconductors

Abstract Electromagnetic effects are believed to play an important role in ferromagnetic superconductors (FMS). As an, to date, unobserved consequence of the electromagnetic coupling of the superconducting and the magnetic order parameter, we predict the possibility of Lifshitz point critical behaviour in FMS. In particular we present a detailed mean field investigation of the ( T, x )-phase diagram of Er 1− x Ho x Rh 4 B 4 in the neighbourhood of the “modified Lifshitz point”, which separates the normal paramagnetic, the superconducting paramagnetic and the normal ferromagnetic phases.

Self-consistent theory of pairbreaking in kondo superconductors

A theory is presented for the calculation of equilibrium properties of superconductors containing magnetic impuritiesof finite concentration. The theory is based on the Nagaoka-Suhl approach to thes — d model and treats finite impurity concentrations within a self-consistentT-matrix-approximation. An integral equation is derived for the pairbreaking parameter which describes de-pairing of Cooper pairs by spin flip scattering. Numerical solutions of this equation are used to compute the phase diagram in the temperature-concentration-plane and the transition-temperature-dependence of the upper critical field. These calculations are in good agreement with experimental data on LaCeAl2-samples. In addition, the recent discovery of three normal superconducting transitions in LaCeY is discussed quantitatively.

Two-dimensional quantum oscillations in crossed fields

Abstract The de Haas-van Alphen oscillations in magnetization M and chemical potential μ are calculated analytically at zero temperature for a two-dimensional gas of free electrons in crossed electric (voltage U ) and magnetic (cyclotron frequency ω c ) fields. An interesting feature emerges: both M and μ develop a smooth minimum in the range ħω c ≳ eU .

Electron dynamics in the Kondo-lattice

Abstract The single-ion Kondo-effect is shown to be self-limiting in the Kondo-lattice. An integral equation for the band-electron self-energy is established which can serve as a starting point for the calculation of electronic properties. As an example preliminary results for the additional specific heat are presented.