RESUMEN

We analyze the validity of a quasiparticle description of a superconducting state above a metallic quantum-critical point (QCP). A normal state at a QCP is a non-Fermi liquid with no coherent quasiparticles. A superconducting order gaps out low-energy excitations, except for a sliver of states for non-s-wave gap symmetry, and at a first glance, restores coherent quasiparticle behavior. We argue that this does not necessarily hold as the fermionic self-energy may remain singular above the gap edge. This singularity gives rise to markedly non-BCS behavior of the density of states and to the appearance of a nondispersing mode at the gap edge in the spectral function. We analyze the set of quantum-critical models with an effective dynamical four-fermion interaction V(Ω)∝1/Ω^{γ}, where Ω is a frequency of a boson, which mediates the interaction. We show that coherent quasiparticle behavior in a superconducting state holds for γ<1/2, but breaks down for larger γ. We discuss signatures of quasiparticle breakdown and compare our results with the photoemission data for Bi2201 and Bi2212.

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We study symmetry-broken phases in twisted bilayer graphene at small filling above charge neutrality and at van Hove filling. We argue that the Landau functionals for the particle-hole order parameters at these fillings both have an approximate SU(4) symmetry, but differ in the sign of quartic terms. We determine the order parameter manifold of the ground state and analyze its excitations. For small fillings, we find a strong first-order transition to an SU(3)⊗U(1) manifold of orders that break spin-valley symmetry and induce a 3-1 splitting of fermionic excitations. For van Hove filling, we find a weak first-order transition to an SU(2)⊗SU(2)⊗U(1) manifold of orders that preserves the twofold band degeneracy. We discuss the effect of particle-hole orders on superconductivity and compare with strong-coupling approaches.

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The origin of the pseudogap behavior, found in many high-Tc superconductors, remains one of the greatest puzzles in condensed matter physics. One possible mechanism is fermionic incoherence, which near a quantum critical point allows pair formation but suppresses superconductivity. Employing quantum Monte Carlo simulations of a model of itinerant fermions coupled to ferromagnetic spin fluctuations, represented by a quantum rotor, we report numerical evidence of pseudogap behavior, emerging from pairing fluctuations in a quantum-critical non-Fermi liquid. Specifically, we observe enhanced pairing fluctuations and a partial gap opening in the fermionic spectrum. However, the system remains non-superconducting until reaching a much lower temperature. In the pseudogap regime the system displays a "gap-filling" rather than "gap-closing" behavior, similar to the one observed in cuprate superconductors. Our results present direct evidence of the pseudogap state, driven by superconducting fluctuations.

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We analyze the scattering rate for 2D fermions interacting via soft nematic fluctuations. The ground state is an s-wave superconductor, but other pairing channels are almost equally attractive. This strongly alters the scattering rate: At energies beyond the pairing gap Δ, it is renormalized by contributions from all pairing channels. At energies of order Δ, it is determined by the competition between scattering into a gapped continuum and dispersing nematic resonance. The outcome is a "peak-peak-dip-hump" spectrum, similar, but not identical, to the "peak-dip-hump" structure in the cuprates.

RESUMEN

Raman experiments on bulk FeSe revealed that the low-frequency part of the B_{1g} Raman response R_{B1g}(Ω), which probes nematic fluctuations, rapidly decreases below the nematic transition at T_{n}∼85 K. Such behavior is expected when a gap opens up and at a first glance is inconsistent with the fact that FeSe remains a metal below T_{n}. We argue that the drop of R_{B1g}(Ω) can be ascribed to the fact that the nematic order drastically changes the orbital content of low-energy excitations near hole and electron pockets, making them nearly mono-orbital. In this situation, the B_{1g} Raman response gets reduced by the same vertex corrections that enforce charge conservation in the symmetric Raman channel. The reduction holds at low frequencies and gives rise to gaplike behavior of R_{B1g}(Ω). We also show that the enhancement of the B_{1g} Raman response near T_{n} is consistent with the sign change of the nematic order parameter between hole and electron pockets.

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In ferromagnetic superconductors, like URhGe, superconductivity coexists with magnetism near zero field, but then reappears in a finite field range, where the system also displays mass enhancement in the normal state. We present the theoretical understanding of this nonmonotonic behavior. We explore the multiband nature of URhGe and associate reentrant superconductivity and mass enhancement with the topological transition (Lifshitz) in one of the bands in a finite magnetic field. We find excellent agreement between our theory and a number of experimental results for URhGe, such as weakly first-order reentrant transition, the dependence of superconducting T_{c} on a magnetic field, and the field dependence of the effective mass, the specific heat, and the resistivity in the normal state. Our theory can be applied to other ferromagnetic multiband superconductors.

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We present a novel mechanism of s-wave pairing in Fe-based superconductors. The mechanism involves holes near d_{xz}/d_{yz} pockets only and is applicable primarily to strongly hole doped materials. We argue that as long as the renormalized Hund's coupling J exceeds the renormalized interorbital Hubbard repulsion U^{'}, any finite spin-orbit coupling gives rise to s-wave superconductivity. This holds even at weak coupling and regardless of the strength of the intraorbital Hubbard repulsion U. The transition temperature grows as the hole density decreases. The pairing gaps are fourfold symmetric, but anisotropic, with the possibility of eight accidental nodes along the larger pocket. The resulting state is consistent with the experiments on KFe_{2}As_{2}.

RESUMEN

We report the results of the parquet renormalization group (RG) analysis of the phase diagram of the most general 5-pocket model for Fe-based superconductors. We use as an input the orbital structure of excitations near the five pockets made out of d_{xz}, d_{yz}, and d_{xy} orbitals and argue that there are 40 different interactions between low-energy fermions in the orbital basis. All interactions flow under the RG, as one progressively integrates out fermions with higher energies. We find that the low-energy behavior is amazingly simple, despite the large number of interactions. Namely, at low energies the full 5-pocket model effectively reduces either to a 3-pocket model made of one d_{xy} hole pocket and two electron pockets or a 4-pocket model made of two d_{xz}/d_{yz} hole pockets and two electron pockets. The leading instability in the effective 4-pocket model is a spontaneous orbital (nematic) order, followed by s^{+-} superconductivity. In the effective 3-pocket model, orbital fluctuations are weaker, and the system develops either s^{+-} superconductivity or a stripe spin-density wave. In the latter case, nematicity is induced by composite spin fluctuations.

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The development of sensible microscopic models is essential to elucidate the normal-state and superconducting properties of the iron-based superconductors. Because these materials are mostly metallic, a good starting point is an effective low-energy model that captures the electronic states near the Fermi level and their interactions. However, in contrast to cuprates, iron-based high-T c compounds are multi-orbital systems with Hubbard and Hund interactions, resulting in a rather involved 10-orbital lattice model. Here we review different minimal models that have been proposed to unveil the universal features of these systems. We first review minimal models defined solely in the orbital basis, which focus on a particular subspace of orbitals, or solely in the band basis, which rely only on the geometry of the Fermi surface. The former, while providing important qualitative insight into the role of the orbital degrees of freedom, do not distinguish between high-energy and low-energy sectors and, for this reason, generally do not go beyond mean-field. The latter allow one to go beyond mean-field and investigate the interplay between superconducting and magnetic orders as well as Ising-nematic order. However, they cannot capture orbital-dependent features like spontaneous orbital order. We then review recent proposals for a minimal model that operates in the band basis but fully incorporates the orbital composition and symmetries of the low-energy excitations. We discuss the results of the renormalization group study of such a model, particularly of the interplay between superconductivity, magnetism, and spontaneous orbital order, and compare theoretical predictions with experiments on iron pnictides and chalcogenides. We also discuss the impact of the glide-plane symmetry on the low-energy models, highlighting the key role played by the spin-orbit coupling.

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Recent progress in experimental techniques has made it possible to extract detailed information on dynamics of carriers in a correlated electron material from its optical conductivity, [Formula: see text]. This review consists of three parts, addressing the following three aspects of optical response: (1) the role of momentum relaxation; (2) [Formula: see text] scaling of the optical conductivity of a Fermi-liquid metal, and (3) the optical conductivity of non-Fermi-liquid metals. In the first part (section 2), we analyze the interplay between the contributions to the conductivity from normal and umklapp electron-electron scattering. As a concrete example, we consider a two-band metal and show that although its optical conductivity is finite it does not obey the Drude formula. In the second part (sections 3 and 4), we re-visit the Gurzhi formula for the optical scattering rate, [Formula: see text], and show that a factor of [Formula: see text] is the manifestation of the 'first-Matsubara-frequency rule' for boson response, which states that [Formula: see text] must vanish upon analytic continuation to the first boson Matsubara frequency. However, recent experiments show that the coefficient b in the Gurzhi-like form, [Formula: see text], differs significantly from b = 4 in most of the cases. We suggest that the deviations from Gurzhi scaling may be due to the presence of elastic but energy-dependent scattering, which decreases the value of b below 4, with b = 1 corresponding to purely elastic scattering. In the third part (section 5), we consider the optical conductivity of metals near quantum phase transitions to nematic and spin-density-wave states. In the last case, we focus on 'composite' scattering processes, which give rise to a non-Fermi-liquid behavior of the optical conductivity at T = 0: [Formula: see text] at low frequencies and [Formula: see text] at higher frequencies. We also discuss [Formula: see text] scaling of the conductivity and show that [Formula: see text] in the same model scales in a non-Fermi-liquid way, as [Formula: see text].

RESUMEN

Near a quantum-critical point in a metal strong fermion-fermion interaction mediated by a soft collective boson gives rise to incoherent, non-Fermi liquid behavior. It also often gives rise to superconductivity which masks the non-Fermi liquid behavior. We analyze the interplay between the tendency to pairing and fermionic incoherence for a set of quantum-critical models with effective dynamical interaction between low-energy fermions. We argue that superconducting T_{c} is nonzero even for strong incoherence and/or weak interaction due to the fact that the self-energy from dynamic critical fluctuations vanishes for the two lowest fermionic Matsubara frequencies ω_{m}=±πT. We obtain the analytic formula for T_{c}, which reproduces well earlier numerical results for the electron-phonon model at vanishing Debye frequency.

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We analyze the temperature and doping dependence of the specific heat C(T) in Na(x)CoO(2). This material was conjectured to undergo a Lifshitz-type topological transition at x=x(c)=0.62, in which a new electron Fermi pocket emerges at the Γ point, in addition to the existing hole pocket with large k(F). The data show that near x=x(c), the temperature dependence of C(T)/T at low T gets stronger as x approaches x(c) from below and then reverses the trend and changes sign at x≥x(c). We argue that this behavior can be quantitatively explained within the spin-fluctuation theory. We show that magnetic fluctuations are enhanced near x(c) at momenta around k(F), and their dynamics changes between x≤x(c) and x>x(c), when the new pocket forms. We demonstrate that this explains the temperature dependence of C(T)/T. We show that at larger x (x>0.65) the system enters a magnetic quantum critical regime where C(T)/T roughly scales as logT. This behavior extends to progressively lower T as x increases towards a magnetic instability at x≈0.75.

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We argue that superconductivity in the coexistence region with spin-density-wave (SDW) order in weakly doped Fe pnictides erdiffers qualitatively from the ordinary s(+-) state outside the coexistence region as it develops an additional gap component which is a mixture of intrapocket singlet (s(++)) and interpocket spin-triplet pairings (the t state). The coupling constant for the t channel is proportional to the SDW order and involves interactions that do not contribute to superconductivity outside of the SDW region. We argue that the s(+-)- and t-type superconducting orders coexist at low temperatures, and the relative phase between the two is, in general, different from 0 or π, manifesting explicitly the breaking of the time-reversal symmetry promoted by long-range SDW order. We argue that time reversal may get broken even before true superconductivity develops.

Asunto(s)

RESUMEN

We consider 2D Heisenberg antiferromagnets on a triangular lattice with spatially anisotropic interactions in a high magnetic field close to the saturation. We show that this system possesses a rich phase diagram in a field or anisotropy plane due to competition between classical and quantum orders: an incommensurate noncoplanar spiral state, which is favored classically, and a commensurate coplanar state, which is stabilized by quantum fluctuations. We show that the transformation between these two states is highly nontrivial and involves two intermediate phases--the phase with coplanar incommensurate spin order and the one with noncoplanar double-Q spiral order. The transition between the two coplanar states is of commensurate-incommensurate type, not accompanied by softening of spin-wave excitations. We show that a different sequence of transitions holds in triangular antiferromagnets with exchange anisotropy, such as Ba(3)CoSb(2)O(9).

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We discuss the form of the damping of magnetic excitations in a metal near a ferromagnetic instability. The paramagnon theory predicts that the damping term should have the form γ(q,Ω)∝Ω/Γ(q), with Γ(q)∝q (the Landau damping). However, the experiments on uranium metallic compounds UGe2 and UCoGe showed that Γ(q) is essentially independent of q. A nonzero γ(q=0,Ω) is impossible in systems with one type of carrier (either localized or itinerant) because it would violate the spin conservation. It has been conjectured recently that a near-constant Γ(q) in UGe2 and UCoGe may be due to the presence of both localized and itinerant electrons in these materials, with ferromagnetism involving predominantly localized spins. We present the microscopic analysis of the damping of near-critical localized excitations due to interaction with itinerant carriers. We show explicitly how the presence of two types of electrons breaks the cancellation between the contributions to Γ(0) from the self-energy and vertex correction insertions into the spin polarization bubble. We compare our theory with the available experimental data.

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Recent experiments on two iron-pnictide families suggest the existence of a single quantum phase transition inside the superconducting dome despite the fact that two separate transition lines--magnetic and nematic-cross the superconducting dome at T(c). Here we argue that these two observations are actually consistent. We show, using a microscopic model, that each order coexists with superconductivity for a wide range of parameters, and both transition lines continue into the superconducting dome below T(c). However, at some T(merge)

RESUMEN

We analyze instabilities of the collinear up-up-down state of a two-dimensional quantum spin-S spatially anisotropic triangular lattice antiferromagnet in a magnetic field. We find, within the large-S approximation, that near the end point of the plateau, the collinear state becomes unstable due to the condensation of two-magnon bound pairs rather than single magnons. The two-magnon instability leads to a novel two-dimensional vector chiral phase with alternating spin currents but no magnetic order in the direction transverse to the field. This phase breaks a discrete Z(2) symmetry but preserves a continuous U(1) one of rotations about the field axis. It possesses orbital antiferromagnetism and displays a magnetoelectric effect.

RESUMEN

We revisit the issue of superconductivity at the quantum-critical point (QCP) between a 2D paramagnet and a spin-density-wave metal with ordering momentum (π, π). This problem is highly nontrivial because the system at criticality displays a non-Fermi-liquid behavior and because the effective coupling constant λ for the pairing is generally of order one, even when the actual interaction is smaller than fermionic bandwidth. Previous study [M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, 075128 (2010)] has found that the renormalizations of the pairing vertex are stronger than in BCS theory and hold in powers of log(2)(1/T). We analyze the full gap equation and argue that summing up of the leading logarithms does not lead to a pairing instability. Yet, we show that superconductivity has no threshold and appears even if λ is set to be small, because subleading logarithmical renormalizations diverge and give rise to a BCS-like result log1/T(c) ∝ 1/λ. We argue that the analogy with BCS is not accidental as at small λ superconductivity at a QCP predominantly comes from fermions that retain Fermi-liquid behavior at criticality. We compute T(c) for the actual λ ∼ O(1), and find that both Fermi-liquid and non-Fermi-liquid fermions contribute to the pairing.

RESUMEN

We consider electrons on a honeycomb or triangular lattice doped to the saddle point of the band structure. We assume the system parameters are such that spin density wave (SDW) order emerges below a temperature T(N) and investigate the nature of the SDW phase. We argue that at T≤T(N), the system develops a uniaxial SDW phase whose ordering pattern breaks O(3)×Z(4) symmetry and corresponds to an eight-site unit cell with nonuniform spin moments on different sites. This state is a half-metal--it preserves the full original Fermi surface, but has gapless charged excitations in one spin branch only. It allows for electrical control of spin currents and is desirable for nanoscience.

RESUMEN

We analyze the effect of the electron-electron interaction on the resistivity of a metal near a Pomeranchuk quantum phase transition (QPT). We show that umklapp processes are not effective near a QPT, and one must consider both interactions and disorder to obtain a finite and T dependent resistivity. By power counting, the correction to the residual resistivity at low T scales as AT((D+2)/3) near a Z=3 QPT. We show, however, that A=0 for a simply connected, convex Fermi surface in 2D, due to the hidden integrability of the electron motion. We argue that A>0 in a two-band (s-d) model and propose this model as an explanation for the observed T((D+2)/3) behavior.