arXiv subjects

Andrey V. Chubukov

Publications and source records attributed to Andrey V. Chubukov.

At least 127 records · Page 7Linked to original sources

arXiv2014

Non-Landau damping of magnetic excitations in systems with localized and itinerant electrons

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 $Ω/Γ(q)$ with $Γ(q) \propto q$ (the Landau damping). However, the experiments on uranium metallic compounds UGe$_2$ and UCoGe showed that $Γ(q)$ tends to a constant value at vanishing $q$. A non-zero $Γ(0)$ is impossible in systems with one type of carriers (either localized or itinerant) because it would violate the spin conservation. It has been conjectured recently that a non-zero $Γ(q)$ in UGe$_2$ 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 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 self-energy and vertex correction insertions into the spin polarization bubble and discuss the special role of the Aslamazov-Larkin processes. We show that $Γ(0)$ increases with $T$ both in the paramagnetic and ferromagnetic regions, but in-between it has a peak at $T_c$. We compare our theory with the available experimental data.

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arXiv2014

Phases of triangular lattice antiferromagnet near saturation

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 possess rich phase diagram in field/anisotropy plane due to competition between classical and quantum orders: an incommensurate non-coplanar spiral state, which is favored classically, and a commensurate co-planar state, which is stabilized by quantum fluctuations. We show that the transformation between these two states is highly non-trivial and involves two intermediate phases -- the phase with co-planar incommensurate spin order and the one with non-coplanar double-${\bf Q}$ spiral order. The transition between the two co-planar 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 Ba3CoSb2O9.

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arXiv2014

Antiferromagnetism in Iron-Based Superconductors: Selection of Magnetic Order and Quasiparticle Interference

The recent discovery of superconductivity in the iron-based layered pnictides with T_c ranging between 26 and 56K generated enormous interest in the physics of these materials. Here, we review some of the peculiarities of the antiferromagnetic order in the iron pnictides, including the selection of the stripe magnetic order and the formation of the Ising-nematic state in the unfolded BZ within an itinerant description. In addition we analyze the properties of the quasiparticle interference spectrum in the parent antiferromagnetic phase.

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arXiv2014

Superconductivity from weak repulsion in hexagonal lattice systems

We analyze the pairing instabilities for fermions on hexagonal lattices (both honeycomb and triangular ones) in a wide range of fermionic densities. We argue that for a generic doping in this range, superconductivity at weak coupling is of Kohn-Luttinger type, and, due to the presence of electronic interactions beyond on-site repulsion, is a threshold phenomenon, with superconductivity emerging only if the attraction generated by the Kohn-Luttinger mechanism exceeds the bare repulsion in some channel. For disconnected Fermi pockets, we predict that Kohn-Luttinger superconductivity, if it occurs, is likely to be $f$-wave. While the Kohn-Luttinger analysis is adequate over most of the doping range, a more sophisticated analysis is needed near Van Hove doping. We treat Van Hove doping using a parquet renormalization group, the equations for which we derive and analyze. Near this doping level, superconductivity is a universal phenomenon, arising from any choice of bare repulsive interactions. The strongest pairing instability is into a chiral $d-$wave state ($d+id$). At a truly weak coupling, the strongest competitor is a spin-density-wave instability, however, $d-$wave superconductivity still wins. Moreover, the feedback of the spin density fluctuations into the Cooper channel significantly enhances the critical temperature over the estimates of the Kohn Luttinger theory. We analyze renormalization group equations at stronger couplings and find that the main competitor to $d-$wave supoerconductivity away from weak coupling is actually ferromagnetism. We also discuss the effect of the edge fermions and show that they are unimportant in the asymptotic weak coupling limit, but may give rise to, e.g., a charge-density-wave order at moderate coupling strengths.

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arXiv2014

Optical conductivity of a two-dimensional metal at the onset of spin-density-wave order

We consider the optical conductivity of a clean two-dimensional metal near a quantum spin-density-wave transition. Critical magnetic fluctuations are known to destroy fermionic coherence at "hot spots" of the Fermi surface but coherent quasiparticles survive in the rest of the Fermi surface. A large part of the Fermi surface is not really "cold" but rather "lukewarm" in a sense that coherent quasiparticles in that part survive but are strongly renormalized compared to the non-interacting case. We discuss the self-energy of lukewarm fermions and their contribution to the optical conductivity, $σ(Ω)$, focusing specifically on scattering off composite bosons made of two critical magnetic fluctuations. Recent study [S.A. Hartnoll et al., Phys. Rev. B {\bf 84}, 125115 (2011)] found that composite scattering gives the strongest contribution to the self-energy of lukewarm fermions and suggested that this may give rise to non-Fermi liquid behavior of the optical conductivity at the lowest frequencies. We show that the most singular term in the conductivity coming from self-energy insertions into the conductivity bubble, $σ'(Ω)\propto \ln^3Ω/Ω^{1/3}$, is canceled out by the vertex-correction and Aslamazov-Larkin diagrams. However, the cancelation does not hold beyond logarithmic accuracy, and the remaining conductivity still diverges as $1/Ω^{1/3}$. We further argue that the $1/Ω^{1/3}$ behavior holds only at asymptotically low frequencies, well inside the frequency range affected by superconductivity. At larger $Ω$, up to frequencies above the Fermi energy, $σ'(Ω)$ scales as $1/Ω$, which is reminiscent of the behavior observed in the superconducting cuprates.

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arXiv2013

Spin-current order in anisotropic triangular antiferromagnets

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 large-S approximation, that near the end point of the plateau, the collinear state becomes unstable due to condensation of two-magnon bound pairs rather than single magnons. The two-magnon instability leads to a novel 2D 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.

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arXiv2013

How many quantum phase transitions exist inside the superconducting dome of the iron pnictides?

Recent experiments on two iron-pnictide families suggest the existence of a single quantum phase transition (QPT) 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 $T_{\mathrm{merge}}<T_{c}$, the two transitions merge and continue down to T=0 as a single simultaneous first-order nematic/magnetic transition. We show that superconductivity has a profound effect on the character of this first-order transition, rendering it weakly first-order and allowing strong fluctuations to exist near the QPT.

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arXiv2013

Superconductivity from repulsive interaction

The BCS theory of superconductivity named electron-phonon interaction as a glue that overcomes Coulomb repulsion and binds fermions into pairs which then condense and superconduct. We review recent and not so recent works aiming to understand whether a nominally repulsive Coulomb interaction can by itself give rise to a superconductivity. We first discuss a generic scenario of the pairing by electron-electron interaction, put forward by Kohn and Luttinger back in 1965, and then turn to modern studies of the electronic mechanism of superconductivity in the lattice models for the cuprates, the Fe-pnictides, and the doped graphene. We show that the pairing in all three classes of materials can be viewed as lattice version of Kohn-Luttinger physics, despite that the pairing symmetries are different. We discuss under what conditions the pairing occurs and rationalize the need to do parquet renormalization-group analysis. We also discuss the interplay between superconductivity and density-instabilities.

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arXiv2013

Superconductivity at the onset of spin-density-wave order in a metal

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 non-trivial because the system at criticality displays a non-Fermi liquid behavior and because the effective coupling constant λfor the pairing is generally of order one, even when the actual interaction is smaller than fermionic bandwidth. Previous study [M. A. Metlitski, 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), like in color superconductivity. We analyze the full gap equation and argue that, for QCP problem, 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 the coupling is set to be small, because subleading logarithmical renormalizations diverge and give rise to BCS-like \log(1/T_c) \propto 1/λ. We argue that the analogy with BCS is not accidental as at small coupling superconductivity at a QCP predominantly comes from fermions which retain Fermi liquid behavior at criticality. We computed T_c for the actual λ\sim 1, and found that both Fermi-liquid and non-Fermi liquid fermions contribute to the pairing. The value of T_c agrees well with the numerical results.

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arXiv2013

s+is State with Broken Time Reversal Symmetry in Fe-Based Superconductors

We analyze the evolution of the superconducting gap structure in strongly hole doped Ba_{1-x}K_xFe_2As_2 between x=1 and x ~ 0.4 (optimal doping). In the latter case, the pairing state is most likely s+-, with different gap signs on hole and electron pockets, but with the same signs of the gap on the two Gamma-centered hole pockets (a ++ state on hole pockets). In a pure KFe_2As_2 (x=1), which has only hole pockets, laser ARPES data suggested another s+- state, in which the gap changes sign between hole pockets (a +- state). We analyze how ++ gap transforms into a +- gap as x -> 1. We found that this transformation occurs via an intermediate s+is, state in which the gaps on the two hole pockets differ in phase by `phi', which gradually involves from `phi' = pi (the +- state) to phi =0 (the ++ state). This state breaks time-reversal symmetry and has huge potential for applications. We compute the dispersion of collective excitations and show that two different Leggett-type phase modes soften at the two end points of TRSB state.

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arXiv2012

First-Matsubara-frequency rule in a Fermi liquid. Part I: Fermionic self-energy

We analyze in detail the fermionic self-energy Σ(ω, T) in a Fermi liquid (FL) at finite temperature T and frequency ω. We consider both canonical FLs -- systems in spatial dimension D >2, where the leading term in the fermionic self-energy is analytic [the retarded ImΣ^R(ω,T) = C(ω^2 +π^2 T^2)], and non-canonical FLs in 1 1 the next term after O(T) in Σ^R(iπT,T) is of order T^D (T^3\ln T in D=3). This T^D term comes from only forward- and backward scattering, and is expressed in terms of fully renormalized amplitudes for these processes. The overall prefactor of the T^D term vanishes in the "local approximation", when the interaction can be approximated by its value for the initial and final fermionic states right on the Fermi surface. The local approximation is justified near a Pomeranchuk instability, even if the vertex corrections are non-negligible. We show that the strength of the first-Matsubara-frequency rule is amplified in the local approximation, where it states that not only the T^D term vanishes but also that Σ^R(iπT,T) does not contain any terms beyond O(T). This rule imposes two constraints on the scaling form of the self-energy: upon replacing ωby iπT, ImΣ^R(ω,T) must vanish and ReΣ^R (ω, T) must reduce to O(T). These two constraints should be taken into consideration in extracting scaling forms of Σ^R(ω,T) from experimental and numerical data.

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arXiv2012

Broken translational symmetry in an emergent paramagnetic phase of graphene

We show that the spin-density wave state on the partially filled honeycomb and triangular lattices is preempted by a paramagnetic phase that breaks an emergent Z_4 symmetry of the system, associated with the four inequivalent arrangements of spins in the quadrupled unit cell. Unlike other emergent paramagnetic phases in itinerant and localized-spin systems, this state preserves the rotational symmetry of the lattice but breaks its translational symmetry, giving rise to a super-lattice structure that can be detected by scanning tunneling microscopy. This emergent phase also has distinctive signatures in the magnetic spectrum that can be probed experimentally.

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arXiv2012

Interplay of superconductivity and spin density wave order in doped graphene

We study the interplay between superconductivity and spin density wave order in graphene doped to 3/8 or 5/8 filling (a Van Hove doping). At this doping level, the system is known to exhibit weak coupling instabilities to both chiral d + id superconductivity and to a uniaxial spin density wave. Right at van Hove doping, the superconducting instability is strongest and emerges at the highest Tc, but slightly away from van-Hove doping a spin-density-wave likely emerges first. We investigate whether at some lower temperature superconductivity and spin-density-waves co-exist. We derive the Landau-Ginzburg functional describing interplay of the two order parameters. Our calculations show that superconductivity and spin density wave order do not co-exist and are separated by first-order transitions, either as a function of doping or as a function of T.

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arXiv2012

Itinerant half-metal spin-density-wave state on the hexagonal lattice

We consider electrons on a honeycomb or triangular lattice doped to the saddle point of the bandstructure. We assume 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 $O(3) \times Z_4$ symmetry and corresponds to an eight site unit cell with non-uniform spin moments on different sites. This state is a half-metal -- it preserves 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 nano-science.

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arXiv2011

Relation between 2Delta/Tc and nodes in Fe-based superconductors

We analyze the interplay between the absence or presence of the nodes in the superconducting gap along electron Fermi surfaces (FSs) in Fe-pnictides, and 2Delta/T_c along hole FSs, measured by ARPES. We solve the set of coupled gap equations for 4-band and 5-band models of Fe-pnictides and relate the presence of the nodes to 2Δ/T_c being below a certain threshold. Using ARPES data for 2Δ/T_c, we find that optimally doped (BaK)Fe_2As_2 and Ba(FeCo)_2As_2 and likely nodeless, but iso-valent BaFe_2(AsP)_2 likely has nodes.

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arXiv2011

Resistivity of a non-Galilean--invariant Fermi Liquid near Pomeranchuk Quantum Criticality

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 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 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.

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arXiv2011

Renormalization group flow, competing phases, and the structure of superconducting gap in multi-band models of Iron based superconductors

We perform an analytical renormalization group (RG) study to address the role of Coulomb repulsion, the competition between extended s-wave superconducting order (s+-) and the spin-density wave (SDW) order and the angular dependence of the superconducting gap in multi-pocket models of Iron based superconductors. Previous analytic RG studies considered a toy model of one hole and one electron pocket. We consider more realistic models of two electron pockets and either two or three hole pockets, and also incorporate the angular dependence of interaction. We neglect for simplicity one of the two hole pockets centered at k=0, which is less nested with electron pockets, i.e., consider 3-pocket and 4-pocket models. In a toy 2-pocket model, SDW order always wins over s+- order at perfect nesting, and s+- order only appears at a finite doping, and only if RG flow extends long enough to overcome intra-pocket Coulomb repulsion. For multi-pocket models, we find two new effects. First, there always exists an attractive component of the interaction in s+- channel, such that the system necessary becomes a superconductor once it overcomes the competition from the SDW state. Second, in 3-pocket case (but not in 4-pocket case), there are situations when s+- order wins over SDW order even for perfect nesting, suggesting that SDW order is not a necessary pre-condition for the s+- order. Our results are in good agreement with recent numerical functional RG studies by Thomale et al. [arXiv:1002.3599]

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arXiv2010

Self-consistent Eliashberg theory, Tc, and the gap function in electron-doped cuprates

We consider normal state properties, the pairing instability temperature, and the structure of the pairing gap in electron-doped cuprates. We assume that the pairing is mediated by collective spin excitations, with antiferromagnetism emerging with the appearance of hot spots. We use a low-energy spin-fermion model and Eliashberg theory up to two-loop order. We justify ignoring vertex corrections by extending the model to N >>1 fermionic flavors, with 1/N playing the role of a small Eliashberg parameter. We argue, however, that it is still necessary to solve coupled integral equations for the frequency dependent fermionic and bosonic self-energies, both in the normal and superconducting state. Using the solution of the coupled equations, we find an onset of d-wave pairing at Tc ~ 30 K, roughly three times larger than the one obtained previously [P. Krotkov and A. Chubukov, Phys. Rev. B 74, 014509 (2006)], where it was assumed that the equations for fermionic and bosonic self-energies decouple in the normal state. To obtain the momentum and frequency dependent d-wave superconducting gap D(k,w), we derive and solve the non-linear gap equation together with the modified equation for the bosonic self energy which below Tc depends on the pairing gap. We find that the gap is a non-monotonic function of momentum along the Fermi surface, with its node along the zone diagonal and its maximum some distance away from it. We obtain 2D/Tc ~ 4. We argue that the value of Tc, the non-monotonicity of the gap, and 2D/Tc ratio are all in good agreement with the experimental data on electron-doped cuprates.

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