Quantum corrections to the phase diagram of heavy-fermion superconductors

The competition between magnetism and Kondo effect is the main effect determining the phase diagram of heavy fermion systems. It gives rise to a quantum critical point which governs the low temperature properties of these materials. However, experimental results made it clear that a fundamental ingredient is missing in this description, namely superconductivity. In this paper we make a step forward in the direction of incorporating superconductivity and study the mutual effects of this phase and antiferromagnetism in the phase diagram of heavy fermion metals. Our approach is based on a Ginzburg-Landau theory describing superconductivity and antiferromagnetism in a metal with quantum corrections taken into account through an effective potential. The proximity of an antiferromagnetic instability extends the region of superconductivity in the phase diagram and drives this transition into a first order one. On the other hand superconducting quantum fluctuations near a metallic antiferromagnetic quantum critical point gives rise to a first order transition from a low moment to a high moment state in the antiferromagnet. Antiferromagnetism and superconductivity may both collapse at a quantum bicritical point whose properties we calculate.Comment: 10 pages, 6 figure

Universality in Heavy Fermions Revisited

A previous scaling analysis of pressure experiments in heavy fermion is reviewed and enlarged. We show that the critical exponents obtained from this analysis indicate that a one-parameter scaling describes these experiments. We obtain explicitly the enhancemente factors showing that these systems are indeed near criticality and that the scaling approach is appropriate. The physics responsible for the one-parameter scaling and breakdown of hyperscaling is clarified. We discuss a microsocopic theory that is in agreement with the experiments. The scaling theory is generalized for the case the shift and crossover exponents are different. The exponents governing the physical behavior along the non-Fermi liquid trajectory are obtained for this case.Comment: 7 pages, Latex, 3 Postscript figures, to be published in Physical Review

Thermodynamic quantum critical behavior of the Kondo necklace model

We obtain the phase diagram and thermodynamic behavior of the Kondo necklace model for arbitrary dimensions $d$ using a representation for the localized and conduction electrons in terms of local Kondo singlet and triplet operators. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. We show that in $d\geq 3$ there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In 2-d, long range magnetic order occurs only at T=0. The line of Neel transitions for $d>2$ varies with the distance to the quantum critical point QCP $|g|$ as, $T_N \propto |g|^{\psi}$ where the shift exponent $\psi=1/(d-1)$. In the paramagnetic side of the phase diagram, the spin gap behaves as $\Delta\approx \sqrt{|g|}$ for $d \ge 3$ consistent with the value $z=1$ found for the dynamical critical exponent. We also find in this region a power law temperature dependence in the specific heat for $k_BT\gg\Delta$ and along the non-Fermi liquid trajectory. For $k_BT \ll\Delta$, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence.Comment: Submitted to PR

Phase diagram of the random Heisenberg antiferromagnetic spin-1 chain

We present a new perturbative real space renormalization group (RG) to study random quantum spin chains and other one-dimensional disordered quantum systems. The method overcomes problems of the original approach which fails for quantum random chains with spins larger than S=1/2. Since it works even for weak disorder we are able to obtain the zero temperature phase diagram of the random antiferromagnetic Heisenberg spin-1 chain as a function of disorder. We find a random singlet phase for strong disorder and as disorder decreases, the system shows a crossover from a Griffiths to a disordered Haldane phase.Comment: 4 pages, 10 figure

Asymmetric superconductivity in metallic systems

Different types of superfluid ground states have been investigated in systems of two species of fermions with Fermi surfaces that do not match. This study is relevant for cold atomic systems, condensed matter physics and quark matter. In this paper we consider this problem in the case the fermionic quasi-particles can transmute into one another and only their total number is conserved. We use a BCS approximation to study superconductivity in two-band metallic systems with inter and intra-band interactions. Tuning the hybridization between the bands varies the mismatch of the Fermi surfaces and produces different instabilities. For inter-band attractive interactions we find a first order normal-superconductor and a homogeneous metastable phase with gapless excitations. In the case of intra-band interactions, the transition from the superconductor to the normal state as hybridization increases is continuous and associated with a quantum critical point. The case when both interactions are present is also considered.Comment: new enlarged version, new title, 7 pages, 7 figure

Field induced quantum phase transition in the anisotropic Kondo necklace model

The anisotropic Kondo necklace model in 2D and 3D is treated as a genuine model for magnetic to Kondo singlet quantum phase transitions in the heavy fermion (HF) compounds. The variation of the quantum critical point (QCP) with anisotropy parameters has been investigated previously in the zero field case [1]. Here we extend the treatment to finite fields using a generalised bond operator representation including all triplet states. The variation of critical tc with external field H and the associated phase diagram is derived. The influence of anisotropies and the different g-factors for localised and itinerant spins on tc(H) is also investigated. It is found that three different types of behaviour may appear: (i) Destruction of antiferromangetism and appearance of a singlet state above a critical field. (ii) The inverese behaviour, namely field induced antiferromagnetism out of the Kondo singlet phase. (iii) Reentrance behaviour of the Kondo singlet phase as function of field strength.Comment: 12 pages, 5 figure

Fluctuations in a superconducting quantum critical point of multi-band metals

In multi-band metals quasi-particles arising from different atomic orbitals coexist at a common Fermi surface. Superconductivity in these materials may appear due to interactions within a band (intra-band) or among the distinct metallic bands (inter-band). Here we consider the suppression of superconductivity in the intra-band case due to hybridization. The fluctuations at the superconducting quantum critical point (SQCP) are obtained calculating the response of the system to a fictitious space and time dependent field, which couples to the superconducting order parameter. The appearance of superconductivity is related to the divergence of a generalized susceptibility. For a single band superconductor this coincides with the \textit{Thouless criterion}. For fixed chemical potential and large hybridization, the superconducting state has many features in common with breached pair superconductivity with unpaired electrons at the Fermi surface. The T=0 phase transition from the superconductor to the normal state is in the universality class of the density-driven Bose-Einstein condensation. For fixed number of particles and in the strong coupling limit, the system still has an instability to the normal sate with increasing hybridization.Comment: 10 pages, 8 figure