First-order superconducting transition near a ferromagnetic quantum critical point

We address the issue of how triplet superconductivity emerges in an electronic system near a ferromagnetic quantum critical point (FQCP). Previous studies found that the superconducting transition is of second order, and T(c) is strongly reduced near the FQCP due to pair-breaking effects from thermal spin fluctuations. In contrast, we demonstrate that near the FQCP, the system avoids pair-breaking effects by undergoing a first order transition at a much larger T(c). A second order superconducting transition emerges only at some distance from the FQCP.     

Field and pressure response of Yb compounds close to a quantum critical point

YbCu_5−x Al _x provides the possibility to tune ground state properties by a change of the valence due to the Cu/Al substitution, by pressure as well as by the application of a magnetic field. Near to the critical concentration x _cr≈1.5 non-Fermi-liquid properties (NFL) are obvious, obeying hyperscaling. If magnetic order sets in for x>1.5, the application of moderate magnetic fields quenches order and again NFL features become evident. Hyperscaling in this case indicates strongly interacting spin fluctuations.     

Scanning a metallic tip close to a quantum point contact

Low-temperature transport experiments on a quantum point contact under the influence of a scanning gate are reported. The scanning gate is the metallic tip of a scanning force microscope operating at a temperature of 300 mK. In particular, the influence of the scanning tip on conductance resonances observed in the gate-characteristics of the point contact is studied. The strongest conductance resonances appear to be related to the local potential within the channel of the point contact. As a consequence, the point contact with its conductance resonances can be used as a sensor for the local tip-induced potential.     

Virial theorem for localized states of a quantum particle in classical fluids close to the critical point

Localized states of a light quantum particle, thermalized in a dense classical fluid close to the critical point, obey a simple virial identity as a result of the scaling properties of the host medium. This identity may serve as a self-consistency check for coarse-grained theories of localization.     

Localization and critical diffusion of quantum dipoles in two dimensions

We discuss quantum propagation of dipole excitations in two dimensions. This problem differs from the conventional Anderson localization due to the existence of long-range hops. We find that the critical wave functions of the dipoles always exist which manifest themselves by a scale independent diffusion constant. If the system is T invariant the states are critical for all values of the parameters. Otherwise, there can be a "metal-insulator" transition between this "ordinary" diffusion and the Levy flights (the diffusion constant logarithmically increasing with the scale). These results follow from the two-loop analysis of the modified nonlinear supermatrix σ model.     

Quantum transport in randomly diluted quantum percolation clusters in two dimensions

We study the hopping transport of a quantum particle through finite, randomly diluted percolation clusters in two dimensions. We investigate how the transmission coefficient T behaves as a function of the energy E of the particle, the occupation concentration p of the disordered cluster, the size of the underlying lattice, and the type of connection chosen between the cluster and the input and output leads. We investigate both the point-to-point contacts and the busbar type of connection. For highly diluted clusters we find the behavior of the transmission to be independent of the type of connection. As the amount of dilution is decreased we find sharp variations in transmission. These variations are the remnants of the resonances at the ordered, zero-dilution, limit. For particles with energies within 0.25≤E≤1.75 (relative to the hopping integral) and with underlying square lattices of size 20×20, the configurations begin transmitting near p_α=0.60 with T against p curves following a common pattern as the amount of dilution is decreased. Near p_β=0.90 this pattern is broken and the transmission begins to vary with the energy. In the asymptotic limit of very large clusters we find the systems to be totally reflecting in almost all cases. A few clear exceptions we find are when the amount of dilution is very low, when the particle has energy close to a resonance value at the ordered limit, and when the particle has energy at the middle of the band. These three cases, however, may not exhaust all possible exceptions.     

Crossover from non-Fermi liquid to Fermi liquid behavior close to a quantum critical point: A brief review

The nesting of the Fermi surfaces of an electron and a hole pocket separated by a nesting vector Q and the interaction between electrons gives rise to itinerant antiferromagnetism. The order can gradually be suppressed by mismatching the nesting and a quantum critical point is obtained as the Néel temperature tends to zero. We review our results on the specific heat, the quasi-particle linewidth, the electrical resistivity, the amplitudes of de Haas-van Alphen oscillations and the dynamical spin susceptibility.     

Quantum critical scenario from an effective classical renormalization group treatment close to and below four dimensions

We suggest a general procedure to analyze quantum criticality for a wide variety of quantum systems of topical interest, close and below four dimensions. The idea is to apply the Wilsonian renormalization group philosophy to an effective classical functional derived from a general quantum action by averaging over degrees of freedom with non-zero Matsubara frequencies. This allows us to describe, in an unified way, all crossovers expected close to a quantum critical point.     

Quantum matrices in two dimensions

Quantum matrices in two dimensions, admitting left and right quantum spaces, are classified: they fall into two families, the 2-parametric family GL_p,q(2) and a 1-parametric family GL _inf ^sup J(2). Phenomena previously found for GL_p,q(2) hold in this general situation: (a) powers of quantum matrices are again quantum and (b) entries of the logarithm of a two-dimensional quantum matrix form a Lie algebra.     

Quantum censorship in two dimensions

It is pointed out that increasingly attractive interactions, represented by partially concave local potential in the Lagrangian, may lead to the degeneracy of the blocked, renormalized action at the gliding cutoff scale by tree-level renormalization. A quantum counterpart of this mechanism is presented in the two-dimensional sine-Gordon model. The presence of Quantum Censorship is conjectured which makes the loop contributions pile up during the renormalization and thereby realize an approximate semiclassical effect.     

Topological crossovers near a quantum critical point

We study the temperature evolution of the single-particle spectrum ε-(p) and quasiparticle momentum distribution n(p) of homogeneous strongly correlated Fermi systems beyond a point where the necessary condition for stability of the Landau state is violated, and the Fermi surface becomes multi-connected by virtue of a topological crossover. Attention is focused on the different non-Fermi-liquid temperature regimes experienced by a phase exhibiting a single additional hole pocket compared with the conventional Landau state. A critical experiment is proposed to elucidate the origin of NFL behavior in dense films of liquid ³He.     

Quantum critical point in high-temperature superconductors

Recently, in high-Tc superconductors (HTSC), exciting measurements have been performed revealing their physics in superconducting and pseudogap states and in normal one induced by the application of magnetic field, when the transition from non-Fermi liquid to Landau-Fermi liquid behavior occurs. We employ a theory, based on fermion condensation quantum phase transition which is able to explain facts obtained in the measurements. We also show, that in spite of very different microscopic nature of HTSC, heavy-fermion metals and 2D ³He, the physical properties of these three classes of substances are similar to each other.     

Quantum noncommutative gravity in two dimensions

We study quantisation of noncommutative gravity theories in two dimensions (with noncommutativity defined by the Moyal star product). We show that in the case of noncommutative Jackiw–Teitelboim gravity the path integral over gravitational degrees of freedom can be performed exactly even in the presence of a matter field. In the matter sector, we study possible choices of the operators describing quantum fluctuations and define their basic properties (e.g., the Lichnerowicz formula). Then we evaluate two leading terms in the heat kernel expansion, calculate the conformal anomaly and the Polyakov action (as an expansion in the conformal field).