Dirac point degenerate with massive bands at a topological quantum critical point

The quasilinear bands in the topologically trivial skutterudite insulator CoSb(3) are studied under adiabatic, symmetry-conserving displacement of the Sb sublattice. In this cubic, time-reversal and inversion symmetric system, a transition from trivial insulator to topological point Fermi surface system occurs through a critical point in which massless (Dirac) bands appear, and moreover are degenerate with massive bands. Spin-orbit coupling, while small due to the type of band character, coupled with tetragonal strain opens the gap required to give the topological insulator. The mineral skutterudite (CoSb(3)) is very near the critical point in its natural state.     

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.     

Undercompensated kondo impurity with quantum critical point

The low-temperature properties of a magnetic impurity of spin S interacting with an electron gas via anisotropic spin exchange are studied via Bethe's ansatz. For S>1/2 the impurity is only partially compensated at T = 0, leaving an effective spin that is neither integer nor half integer. The entropy has an essential singularity at H = T = 0, and the susceptibility and the specific heat follow power laws of H and T with nonuniversal exponents, which are the consequence of a quantum critical point. The results for the generalization to an arbitrary number of channels are also reported.     

Optimal nonlinear passage through a quantum critical point

We analyze the problem of optimal adiabatic passage through a quantum critical point. We show that to minimize the number of defects the tuning parameter should be changed as a power law in time. The optimal power is proportional to the logarithm of the total passage time multiplied by universal critical exponents characterizing the phase transition. We support our results by the general scaling analysis and by explicit calculations for the transverse-field Ising model.     

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.     

Energy scales and magnetoresistance at a quantum critical point

The magnetoresistance (MR) of CeCoIn₅ is notably different from that in many conventional metals. We show that a pronounced crossover from negative to positive MR at elevated temperatures and fixed magnetic fields is determined by the scaling behavior of quasiparticle effective mass. At a quantum critical point (QCP) this dependence generates kinks (crossover points from fast to slow growth) in thermodynamic characteristics (like specific heat, magnetization, etc.) at some temperatures when a strongly correlated electron system transits from the magnetic field induced Landau-Fermi liquid (LFL) regime to the non-Fermi liquid (NFL) one taking place at rising temperatures. We show that the above kink-like peculiarity separates two distinct energy scales in QCP vicinity - low temperature LFL scale and high temperature one related to NFL regime. Our comprehensive theoretical analysis of experimental data permits to reveal for the first time new MR and kinks scaling behavior as well as to identify the physical reasons for above energy scales.     

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.     

Two scenarios of the quantum critical point

Two different scenarios of the quantum critical point (QCP), a zero-temperature instability of the Landau state related to the divergence of the effective mass, are investigated. Flaws of the standard scenario of the QCP, where this divergence is attributed to the occurrence of some second-order phase transition, are demonstrated. Salient features of a different topological scenario of the QCP, associated with the emergence of bifurcation points in the equation ∈(p) = μ that ordinarily determines the Fermi momentum, are analyzed. The topological scenario of the QCP is applied to three-dimensional (3D) Fermi liquids with an attractive current-current interaction. The text was submitted by the author in English.     

Two scenarios of the quantum critical point

Two different scenarios of the quantum critical point (QCP), a zero-temperature instability of the Landau state related to the divergence of the effective mass, are investigated. Flaws of the standard scenario of the QCP, where this divergence is attributed to the occurrence of some second-order phase transition, are demonstrated. Salient features of a different topological scenario of the QCP, associated with the emergence of bifurcation points in the equation ∈(p) = μ that ordinarily determines the Fermi momentum, are analyzed. The topological scenario of the QCP is applied to three-dimensional (3D) Fermi liquids with an attractive current-current interaction.     

Note on the quantum displacement of the critical point

The quantum corrections to the law of corresponding states are studied by calculating the critical pressure, temperature, and density to first order in Planck's constanth on an exactly soluble model. The ratio of the critical parameters to the corresponding classical values are found to be (p _c/p _c ⁰)^1/2=_c/_c ⁰ = T_c/T_c ⁰ = 1–0.67, with=h _c ^1/3(mkT _c)^–1/2. The critical ratio is independent ofh to first order. The results are compared with critical data for noble gases and hydrogen isotopes.     

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.     

Breakdown of weak-field magnetotransport at a metallic quantum critical point

We show how the collapse of an energy scale in a quantum critical metal can lead to physics beyond the weak-field limit usually used to compute transport quantities. For a density-wave transition we show that the presence of a finite magnetic field at the critical point leads to discontinuities in the transport coefficients as temperature tends to zero. The origin of these discontinuities lies in the breakdown of the weak-field Jones-Zener expansion which has previously been used to argue that magnetotransport coefficients are continuous at simple quantum critical points. The presence of potential scattering and magnetic breakdown rounds the discontinuities over a window determined by tauDelta < 1 where Delta is the order parameter and tau is the quasiparticle elastic lifetime.     

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.     

Defect production in nonlinear quench across a quantum critical point

We show that the defect density n, for a slow nonlinear power-law quench with a rate tau(-1) and an exponent alpha>0, which takes the system through a critical point characterized by correlation length and dynamical critical exponents nu and z, scales as n approximately tau(-alphanud/(alphaznu+1)) [n approximately (alphag((alpha-1)/alpha)/tau)(nud/(znu+1))] if the quench takes the system across the critical point at time t=0 [t=t(0) not = 0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a linear quench (alpha=1) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.     

Reentrant hidden order at a metamagnetic quantum critical end point

Magnetization measurements of URu2Si2 in pulsed magnetic fields of 44 T reveal that the hidden order phase is destroyed before appearing in the form of a reentrant phase between approximately 36 and 39 T. Evidence for conventional itinerant electron metamagnetism at higher temperatures suggests that the reentrant phase is created in the vicinity of a quantum critical end point.     

Transport anomalies and marginal-fermi-liquid effects at a quantum critical point

The conductivity and the tunneling density of states of disordered itinerant electrons in the vicinity of a ferromagnetic transition at low temperature are discussed. Critical fluctuations lead to nonanalytic frequency and temperature dependencies that are distinct from the usual long-time tail effects in a disordered Fermi liquid. The crossover between these two types of behavior is proposed as an experimental check of recent theories of the quantum ferromagnetic critical behavior. In addition, the quasiparticle properties at criticality are shown to be those of a marginal Fermi liquid.     

Geometric frustration and dimensional reduction at a quantum critical point

We show that the spatial dimensionality of the quantum critical point associated with Bose-Einstein condensation at T=0 is reduced when the underlying lattice comprises layers coupled by a frustrating interaction. Our theoretical predictions for the critical behavior correspond very well with recent measurements in BaCuSi(2)O(6) [ S. E. Sebastian et al., Nature (London) 441, 617 (2006)].