Quantum Criticality: Competing Ground States in Low Dimensions

Physical Review B, 2012

We use the renormalization group method to study normal state properties of quasi-onedimensional superconductors nearby a spin-density-wave instability. On the basis of one-loop scattering amplitudes for the quasi-one-dimensional electron gas, the integration of the renormalization group equations for the two-loop single particle Matsubara self-energy leads to a nonFermi-liquid temperature downturn of the momentum-resolved quasi-particle weight over most part of the Fermi surface. The amplitude of the downturn correlates with the entire instability line for superconductivity, defining an extended quantum critical region of the phase diagram as a function of nesting deviations of the Fermi surface. One also extracts the downward renormalization of interchain hopping amplitudes at arbitrary low temperature in the normal phase. By means of analytical continuation of the Matsubara self-energy, one-particle spectral functions are obtained with respect to both energy and temperature and their anomalous features analyzed in connection with the sequence of instability lines of the phase diagram. The quasi-particle scattering rate is found to develop an unusual temperature dependence, which is best described by the superimposition of a linear and quadratic T dependences. The nonFermi-liquid linear-T component correlates with the temperature scale Tc of the superconducting instability over an extended range of nesting deviations, whereas its anisotropy along the Fermi surface is predicted to parallel the momentum profile of a d-wave pairing gap on the Fermi surface. We examine the implications of our results for low dimensional unconventional superconductors, in particular the Bechgaard salts series of quasi-one-dimensional organic conductors, but also the pnictide and cuprate superconductors where several common features are observed.

Physical Review B, 2007

A microscopic analysis of the superconducting quantum critical point realized via a pair-breaking quantum phase transition is presented. Finite temperature crossovers are derived for the electrical conductivity, which is a key probe of superconducting fluctuations. By using the diagrammatic formalism for disordered systems, we are able to incorporate the interplay between fluctuating Cooper pairs and electrons, that is outside the scope of a time-dependent Ginzburg Landau or effective bosonic action formalism. It is essential to go beyond the standard approximation in order to capture the zero temperature correction which results purely from the (dynamic) quantum fluctuations and dictates the behavior of the conductivity in an entire low temperature quantum regime. All dynamic contributions are of the same order and conspire to add up to a negative total, thereby inhibiting the conductivity as a result of superconducting fluctuations. On the contrary, the classical and the intermediate regimes are dominated by the positive bosonic channel. Our theory is applicable in one, two and three dimensions and is relevant for experiments on superconducting nanowires, doubly-connected cylinders, thin films and bulk in the presence of magnetic impurities, magnetic field or other pair-breakers. A window of non-monotonic behavior is predicted to exist as either the temperature or the pair-breaking parameter is swept.

Physical Review B, 2015

We study the 𝐶𝑟 !!! 𝑅𝑒 ! phase diagram finding that its phase transition temperature towards an antiferromagnetic order 𝑇 ! follows a quantum 𝑥 ! -𝑥 /𝑥 ! ! law, with 𝜓 = 1/2, from the quantum critical point (QCP) at 𝑥 ! = 0.25 up to 𝑇 ! ≈ 600𝐾. We compare this system to others in order to understand why this elemental material is affected by the QCP up to such unusually high temperatures. We determine a general criterion for the crossover, as function of an external parameter such as concentration, from the region controlled solely by thermal fluctuations to that where quantum effects become observable. The properties of materials with low coherence lengths will thus be altered far away from the QCP.

Physical Review Letters, 2012

Science, 2004

The theory of second order phase transitions is one of the foundations of modern statistical mechanics and condensed matter theory. A central concept is the observable `order parameter', whose non-zero average value characterizes one or more phases and usually breaks a symmetry of the Hamiltonian. At large distances and long times, fluctuations of the order parameter(s) are described by a continuum field theory, and these dominate the physics near such phase transitions. In this paper we show that near second order quantum phase transitions, subtle quantum interference effects can invalidate this paradigm. We present a theory of quantum critical points in a variety of experimentally relevant two-dimensional antiferromagnets. The critical points separate phases characterized by conventional `confining' order parameters. Nevertheless, the critical theory contains a new emergent gauge field, and `deconfined' degrees of freedom associated with fractionalization of the order parameters. We suggest that this new paradigm for quantum criticality may be the key to resolving a number of experimental puzzles in correlated electron systems.

Physical Review B, 2009

The electrical transport and thermoelectric properties of K x Sr 1-x Fe 2 As 2 are investigated for 0 Յ x Յ 1. The resistivity ͑T͒ shows a crossover from Fermi-liquid-like temperature dependence at small x to linear ϳ T dependence at x c Ӎ 0.4. With further increasing of x, ͑T͒ becomes nonlinear again. The thermoelectric power S͑T͒ exhibits a similar crossover with increasing x with a logarithmic T dependence, S / T ϳ ln͑T͒, near the critical doping x c . These results provide evidence for a quantum critical behavior due to the coupling of low-energy conduction electrons to two-dimensional spin fluctuations.

2015

Superconductivity in strongly correlated systems is a remarkable phenomenon that attracts a huge interest. The study of this problem is relevant for materials as the high Tc oxides, pnictides and heavy fermions. In this work we study a realistic model that includes the relevant physics of superconductivity in the presence of strong Coulomb correlations. We consider a two-band model, since most of these correlated systems have electrons from at least two different atomic orbitals coexisting at their Fermi surface. The Coulomb repulsion is taken into account through a local repulsive interaction. Pairing is considered among quasi- particles in neighbouring sites and we allow for different symmetries of the order parameter. In order to deal with the strong local correlations, we use the well known slave boson approach that has proved very successful for this problem. Here we are interested in obtaining the zero temperature properties of the model, specifically its phase diagram and the existence and nature of superconducting quantum critical points. We show that these can arise by increasing the mixing between the two bands. Since this can be controlled by external pressure or doping, our results have a direct relation with experiments. We show that the superconductor-to-normal transition can be either to a metal, a correlated metal or to an insulator. Also we compare the relative stability of s and d-wave paired states for different regions of parameter space and investigate the BCS- BEC crossover in the two-band lattice model as function of the strength of the pairing interaction.

Physical Review B, 2012

In multi-band systems, electrons from different orbitals coexist at the Fermi surface. An attractive interaction among these quasi-particles gives rise to inter-band or hybrid pairs which eventually condense in a superconducting state. These quasi-particles have a natural mismatch of their Fermi wave-vectors, δkF , which depends on the strength of the hybridization between their orbitals. The existence of this natural scale suggests the possibility of inhomogeneous superconducting ground states in these systems, even in the absence of an applied magnetic field. Furthermore, since hybridization V depends on pressure, this provides an external parameter to control the wave-vectors mismatch at the Fermi surface. In this work, we study the phase diagram of a two-dimensional, twoband metal with inter-band pairing. We show that as the mismatch between the Fermi wave-vectors of the two hybrid bands is reduced, the system presents a normal-to-inhomogeneous superconductor quantum phase transition at a critical value of the hybridization Vc = ∆0. The superconducting ground state for V < Vc is characterized by a wave-vector with magnitude |qc| = qc = 2∆0/v f . Here ∆0 is the superconducting gap in the homogeneous state andv f the average Fermi velocity. We discuss the nature of the quantum critical point (QCP) at Vc and obtain the associated quantum critical exponents.

2012

The heavy fermion system CeNi9Ge4 exhibits a paramagnetic ground state with remarkable features such as: a record value of the electronic specific heat coefficient in systems with a paramagnetic ground state, γ = C/T 5.5 J/mol K 2 at 80 mK, a temperature-dependent Sommerfeld-Wilson ratio, R = χ/γ, below 1 K and an approximate single ion scaling of the 4f-magnetic specific heat and susceptibility. These features are related to a rather small Kondo energy scale of a few Kelvin in combination with a quasi-quartet crystal field ground state. Tuning the system towards long range magnetic order is accomplished by replacing a few at.% of Ni by Cu or Co. Specific heat, susceptibility and resistivity studies reveal TN ∼ 0.2 K for CeNi8CuGe4 and TN ∼ 1 K for CeNi8CoGe4. To gain insight whether the transition from the paramagnetic NFL state to the magnetically ordered ground state is connected with a heavy fermion quantum critical point we performed specific heat and ac susceptibility studies and utilized the µSR technique and quasi-elastic neutron scattering. 1

New Journal of Physics, 2011

Critical behavior developed near a quantum phase transition, interesting in its own right, offers exciting opportunities to explore the universality of stronglycorrelated systems near the ground state. Cold atoms in optical lattices, in particular, represent a paradigmatic system, for which the quantum phase transition between the superfluid and Mott insulator states can be externally induced by tuning the microscopic parameters. In this paper, we describe our approach to study quantum criticality of cesium atoms in a two-dimensional lattice based on in situ density measurements. Our research agenda involves testing critical scaling of thermodynamic observables and extracting transport properties in the quantum critical regime. We present and discuss experimental progress on both fronts. In particular, the thermodynamic measurement suggests that the equation of state near the critical point follows the predicted scaling law at low temperatures.