Field-induced quantum critical point in CeCoIn5

The resistivity of the heavy-fermion superconductor CeCoIn5 was measured as a function of temperature, down to 25 mK and in magnetic fields of up to 16 T applied perpendicular to the basal plane. With increasing field, we observe a suppression of the non-Fermi liquid behavior, rho approximately T, and the development of a Fermi liquid state, with its characteristic rho=rho(0)+AT2 dependence. The field dependence of the T2 coefficient shows critical behavior with an exponent of 1.37. This is evidence for a field-induced quantum critical point (QCP), occurring at a critical field which coincides, within experimental accuracy, with the superconducting critical field H(c2). We discuss the relation of this field-tuned QCP to a change in the magnetic state, seen as a change in magnetoresistance from positive to negative, at a crossover line that has a common border with the superconducting region below approximately 1 K.     

Nonvanishing energy scales at the quantum critical point of CeCoIn5

Heat and charge transport were used to probe the magnetic field-tuned quantum critical point in the heavy-fermion metal CeCoIn5. A comparison of electrical and thermal resistivities reveals three characteristic energy scales. A Fermi-liquid regime is observed below T(FL), with both transport coefficients diverging in parallel and T(FL) -->0 as H --> Hc, the critical field. The characteristic temperature of antiferromagnetic spin fluctuations, T(SF), is tuned to a minimum but finite value at Hc, which coincides with the end of the T-linear regime in the electrical resistivity. A third temperature scale, T(QP), signals the formation of quasiparticles, as fermions of charge e obeying the Wiedemann-Franz law. Unlike T(FL), it remains finite at Hc, so that the integrity of quasiparticles is preserved, even though the standard signature of Fermi-liquid theory fails.     

Avoided antiferromagnetic order and quantum critical point in CeCoIn5

We measured the specific heat and resistivity of heavy fermion CeCoIn5 between the superconducting critical field H(c2)=5 T and 9 T, with the field in the [001] direction, and at temperatures down to 50 mK. At 5 T the data show a non-Fermi liquid (NFL) behavior down to the lowest temperatures. At the field above 8 T the data exhibit a crossover from the Fermi liquid to a non-Fermi liquid behavior. We analyzed the scaling properties of the specific heat and compared both the resistivity and the specific heat with the predictions of a spin-fluctuation theory. Our analysis leads us to suggest that the NFL behavior is due to incipient antiferromagnetism (AFM) in CeCoIn5 with the quantum critical point in the vicinity of H(c2). Below H(c2) the AFM phase which competes with the paramagnetic ground state is superseded by the superconducting transition.     

Interacting antiferromagnetic droplets in quantum critical CeCoIn5

The heavy fermion superconductor CeCoIn5 can be tuned between superconducting and antiferromagnetic ground states by hole doping with Cd. Nuclear magnetic resonance data indicate that these two orders coexist microscopically with an ordered moment approximately 0.7 microB. As the ground state evolves, there is no change in the low-frequency spin dynamics in the disordered state. These results suggest that the magnetism emerges locally in the vicinity of the Cd dopants.     

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.     

Dimensional crossover of quantum critical behavior in CeCoIn5

The nature of quantum criticality in CeCoIn5 is studied by low-temperature thermal expansion alpha(T). At the field-induced quantum critical point at H = 5 T a crossover scale T* approximately 0.3 K is observed, separating alpha(T)/T proportional, variant T(-1) from a weaker T(-1/2) divergence. We ascribe this change to a crossover in the dimensionality of the critical fluctuations which may be coupled to a change from unconventional to conventional quantum criticality. Disorder, whose effect on quantum criticality is studied in CeCoIn(5-x)Sn(x) (0 < or = x < or = 0.18), shifts T* towards higher temperatures.     

Magnetic excitations of stripes near a quantum critical point

We calculate the dynamical spin structure factor of spin waves for weakly coupled stripes. At low energy, the spin-wave cone intensity is strongly peaked on the inner branches. As energy is increased, there is a saddlepoint followed by a square-shaped continuum rotated 45 degrees from the low energy peaks. This is reminiscent of recent high energy neutron scattering data on the cuprates. The similarity at high energy between this semiclassical treatment and quantum fluctuations in spin ladders may be attributed to the proximity of a quantum critical point with a small critical exponent eta.     

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.     

Probing the quantum critical behavior of CeCoIn5 via Hall effect measurements

We present highly sensitive Hall effect measurements of the heavy fermion compound CeCoIn5 down to temperatures of 55 mK. A pronounced dip in the differential Hall coefficient | partial differential rho(xy)/ partial differential H| at low temperature and above the upper critical field of superconductivity, H(c2), is attributed to critical spin fluctuations associated with the departure from Landau Fermi liquid behavior. This identification is strongly supported by a systematic suppression of this feature at elevated pressures. The resulting crossover line in the field-temperature phase diagram favors a field induced quantum critical point at mu(0)H(qc) approximately 4.1 T below H(c2)(T=0) suggesting related, yet separate, critical fields.     

Universal behavior of heavy-fermion metals near a quantum critical point

The behavior of the electronic system of heavy-fermion metals is considered. We show that there exist at least two main types of the behavior when the system is near quantum critical point, which can be identified as the fermion condensation quantum phase transition (FCQPT). We show that the first type is represented by the behavior of a highly correlated Fermi liquid, while the second type is depicted by the behavior of a strongly correlated Fermi liquid. If the system approaches FCQPT from the disordered phase, it can be viewed as a highly correlated Fermi liquid which at low temperatures exhibits the behavior of Landau Fermi liquid (LFL). At higher temperatures T, it demonstrates the non-Fermi liquid (NFL) behavior which can be converted into the LFL behavior by the application of magnetic fields B. If the system has undergone FCQPT, it can be considered as a strongly correlated Fermi liquid which demonstrates the NFL behavior even at low temperatures. It can be turned into LFL by applying magnetic fields B. We show that the effective mass M* diverges at the very point that the Neél temperature goes to zero. The B-T phase diagrams of both liquids are studied. We demonstrate that these B-T phase diagrams have a strong impact on the main properties of heavy-fermion metals, such as the magnetoresistance, resistivity, specific heat, magnetization, and volume thermal expansion.     

Nonperturbative microscopic theory of superconducting fluctuations near a quantum critical point

We consider an anisotropic gap superconductor in the vicinity of the disorder-driven quantum critical point. Starting with the BCS Hamiltonian, we derive the Ginzburg-Landau action, which is a critical theory with the dynamic critical exponent, z=2. This allows us to use the parquet method to calculate the nonperturbative effect of quantum superconducting fluctuations on thermodynamics. We derive a general expression for the fluctuation magnetic susceptibility, which exhibits a crossover from the logarithmic dependence, chi proportional, variantlndeltan, valid beyond the Ginzburg region to chi proportional, variantln(1/5)deltan valid in the immediate vicinity of the transition (where deltan is the deviation from the critical disorder concentration). These nonperturbative results may describe the quantum critical behavior of overdoped high-temperature cuprates, disordered p-wave superconductors, and conventional superconducting films with magnetic impurities.     

Undressing the Kondo effect near the antiferromagnetic quantum critical point

The problem of a spin-1/2 magnetic impurity near an antiferromagnetic transition of the host lattice is shown to transform to a multichannel problem. A variety of fixed points is discovered asymptotically near the antiferromagnetic critical point. Among these is a new variety of stable fixed point of a multichannel Kondo problem which does not require channel isotropy. At this point Kondo screening disappears but coupling to spin fluctuations remains. In addition to its intrinsic interest, the problem is an essential ingredient in the problem of quantum critical points in heavy fermions.     

Hall effect in nested antiferromagnets near the quantum critical point

We investigate the behavior of the Hall coefficient in the case of antiferromagnetism driven by Fermi-surface nesting, and find that the Hall coefficient should abruptly increase with the onset of magnetism, as recently observed in vanadium doped chromium. This effect is due to the sudden removal of flat portions of the Fermi surface upon magnetic ordering. Within this picture, the Hall coefficient should scale as the square of the residual resistivity divided by the impurity concentration, which is consistent with available data.     

Spin-fermion model near the quantum critical point: one-loop renormalization group results

We consider spin and electronic properties of itinerant electron systems, described by the spin-fermion model, near the antiferromagnetic critical point. We expand in the inverse number of hot spots in the Brillouin zone, N, and present the results beyond the previously studied N = infinity limit. We found two new effects: (i) Fermi surface becomes nested at hot spots, and (ii) vertex corrections give rise to anomalous spin dynamics and change the dynamical critical exponent from z = 2 to z>2. To first order in 1/N we found z = 2N/(N-2) which for a physical N = 8 yields z approximately 2.67.     

Superconductivity and quantum criticality in CeCoIn5

Electrical resistivity measurements on a single crystal of the heavy-fermion superconductor CeCoIn5 at pressures to 4.2 GPa reveal a strong crossover in transport properties near P(*) approximately 1.6 GPa, where T(c) is a maximum. The temperature-pressure phase diagram constructed from these data provides a natural connection to cuprate physics, including the possible existence of a pseudogap.     

Non-Fermi-liquid behavior and d-wave superconductivity near the charge-density-wave quantum critical point

A scenario is presented, in which the presence of a quantum critical point due to formation of incommensurate charge density waves accounts for the basic features of the high temperature superconducting cuprates, both in the normal and in the superconducting states. Specifically, the singular interaction arising close to this charge-driven quantum critical point gives rise to the non-Fermi liquid behavior universally found at optimal doping. This interaction is also responsible for d-wave Cooper pair formation with a superconducting critical temperature strongly dependent on doping in the overdoped region and with a plateau in the optimally doped region. In the underdoped region a temperature dependent pairing potential favors local pair formation without superconducting coherence, with a peculiar temperature dependence of the pseudogap and a non-trivial relation between the pairing temperature and the gap itself. This last property is in good qualitative agreement with so far unexplained features of the experiments.     

Equation of motion and nonlinear response near the critical point

For a one-component (Ising-like) Ginzburg-Landau field we have derived an equation of motion which governs the behaviour of the order parameter nearT _c . We present this equation in a general scaling form dictated by the renormalization group, and calculate the form explicitly to first order in=4–d. There is a memory term in the result which in order contains the full nonlinear response of the order parameter. As a special case we obtain the linear response function for a nonvanishing external field.     

Single-gap s-Wave superconductivity near the charge-density-wave quantum critical point in CuxTiSe2

The in-plane thermal conductivity kappa of the layered superconductor CuxTiSe2 was measured down to temperatures as low as Tc/40, at x=0.06 near where the charge-density-wave order vanishes. The absence of a residual linear term at T-->0 is strong evidence for conventional s-wave superconductivity in this system. This is further supported by the slow magnetic field dependence, also consistent with a single gap, of uniform magnitude across the Fermi surface. Comparison with the closely related material NbSe2, where the superconducting gap is 3 times larger on the Nb 4d band than on the Se 4p band, suggests that in Cu0.06TiSe2 the Se 4p band is below the Fermi level and Cu doping into the Ti 3d band is responsible for the superconductivity.