arXiv subjects

Andrey V. Chubukov

Publications and source records attributed to Andrey V. Chubukov.

At least 109 records · Page 6Linked to original sources

arXiv2016

Displacement and annihilation of Dirac gap-nodes in d-wave iron-based superconductors

Several experimental and theoretical arguments have been made in favor of a $d-$wave symmetry for the superconducting state in some Fe-based materials. It is a common belief that a $d-$wave gap in the Fe-based superconductors must have nodes on the Fermi surfaces centered at the $Γ$ point of the Brillouin zone. Here we show that, while this is the case for a single Fermi surface made out of a single orbital, the situation is more complex if there is an even number of Fermi surfaces made out of different orbitals. In particular, we show that for the two $Γ$-centered hole Fermi surfaces made out of $d_{xz}$ and $d_{yz}$ orbitals, the nodal points still exist near $T_{c}$ along the symmetry-imposed directions, but are are displaced to momenta between the two Fermi surfaces. If the two hole pockets are close enough, pairs of nodal points can merge and annihilate at some $T<T_{c}$, making the $d-$wave state completely nodeless. These results imply that photoemission evidence for a nodeless gap on the $d_{xz}/d_{yz}$ Fermi surfaces of KFe$_{2}$As$_{2}$ does not rule out $d-$wave gap symmetry in this material, while a nodeless gap observed on the $d_{xy}$ pocket in K$_{x}$Fe$_{2-y}$Se$_{2}$ is truly inconsistent with the $d-$wave gap symmetry.

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arXiv2016

Low-energy microscopic models for iron-based superconductors: a review

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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arXiv2016

Itinerant scenario for Fe-pnictides: comparison with quantum Monte Carlo

Recent applications of Quantum Monte Carlo (QMC) technique to Fe-based superconductors opened a way to directly verify the applicability of the itinerant scenario for these systems. Fe-based superconductors undergo various instabilities upon lowering temperature (magnetism, superconductivity, nematicity/orbital order), and one can check whether the hierarchy of instabilities obtained within the itinerant approach is the same as in unbiased QMC simulations. In a recent paper [arXiv:1512:08523] the authors considered the simplest two-band model with interaction tailored to favor orbital order. The type of the orbital order found in QMC is different from the one found in earlier itinerant analysis. We report the results of our calculations within the itinerant scenario and argue that they are in perfect agreement with QMC.

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arXiv2016

Magnetism, superconductivity, and spontaneous orbital order in iron-based superconductors: who comes first and why?

Magnetism and nematic order are the two non-superconducting orders observed in iron-based superconductors. To elucidate the interplay between them and ultimately unveil the pairing mechanism, several models have been investigated. In models with quenched orbital degrees of freedom, magnetic fluctuations promote stripe magnetism which induces orbital order. In models with quenched spin degrees of freedom, charge fluctuations promote spontaneous orbital order which induces stripe magnetism. Here we develop an unbiased approach, in which we treat magnetic and orbital fluctuations on equal footing. Key to our approach is the inclusion of the orbital character of the low-energy electronic states into renormalization group analysis. Our results show that in systems with large Fermi energies, such as BaFe2As2, LaFeAsO, and NaFeAs, orbital order is induced by stripe magnetism. However, in systems with small Fermi energies, such as FeSe, the system develops a spontaneous orbital order, while magnetic order does not develop. Our results provide a unifying description of different iron-based materials.

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arXiv2016

Raman resonance in iron-based superconductors: The magnetic scenario

We perform theoretical analysis of polarization-sensitive Raman spectroscopy on NaFe$_{1-x}$Co$_x$As, EuFe$2$As$_2$, SrFe$_2$As$_2$, and Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$, focusing on two features seen in the $B_{1g}$ symmetry channel (in one Fe unit cell notation): the strong temperature dependence of the static, uniform Raman response in the normal state and the existence of a collective mode in the superconducting state. We show that both features can be explained by the coupling of fermions to pairs of magnetic fluctuations via the Aslamazov-Larkin process. We first analyze magnetically-mediated Raman intensity at the leading two-loop order and then include interactions between pairs of magnetic fluctuations. We show that the full Raman intensity in the $B_{1g}$ channel can be viewed as the result of the coupling of light to Ising-nematic susceptibility via Aslamazov-Larkin process. We argue that the singular temperature dependence in the normal state is the combination of the temperature dependencies of the Aslamazov-Larkin vertex and of Ising-nematic susceptibility. We discuss two scenarios for the resonance below $T_c$. In one, the resonance is due to the development of a pole in the fully renormalized Ising-nematic susceptibility. The other is the orbital excitonic scenario, in which spin fluctuations generate an attractive interaction between low-energy fermions.

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arXiv2016

Interplay between uni-directional and bi-directional charge-density-wave orders in underdoped cuprates

We analyze the interplay between charge-density-wave (CDW) orders with axial momenta $(Q, 0)$ and $(0,Q)$ ($Δ_x$ and $Δ_y$ respectively), detected in the underdoped cuprates. The CDW order in real space can be uni-directional (either $Δ_x$ or $Δ_y$ is non-zero) or bi-directional (both $Δ_x$ and $Δ_y$ are non-zero). To understand which of the two orders develop, we adopt the magnetic scenario, in which the CDW order appears due to spin-fluctuation exchange, and derive the Ginzburg-Landau action to the sixth order in $Δ_x$ and $Δ_y$. We argue that, at the mean-field level, the CDW order is bi-directional at the onset, with equal amplitudes of $Δ_x$ and $Δ_y$, but changes to uni-directional inside the CDW phase. This implies that, at a given temperature, CDW order is uni-directional at smaller dopings, but becomes bi-directional at larger dopings. This is consistent with recent x-ray data on YBCO, which detected tendency towards bi-directional order at larger dopings. We discuss the role of discrete symmetry breaking at a higher temperature for the interplay between bi-directional and uni-directional CDW orders and also discuss the role of pair-density-wave (PDW) order, which may appear along with CDW. We argue that PDW with the same momentum as CDW changes the structure of the bi-directional charge order by completely replacing either $Δ_x$ or $Δ_y$ CDW components by PDW. However, if an "Amperean" PDW order, which pairs fermions with approximately the same momenta, is also present, both $Δ_x$ and $Δ_y$ remain non-zero in the bi-directional phase, albeit with non-equal amplitudes. This is again consistent with x-ray experiments, which at larger doping found non-equal $Δ_x$ and $Δ_y$ in every domain.

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arXiv2015

Enhancement of superconductivity at the onset of charge-density-wave order in a metal

We analyze superconductivity in the cuprates near the onset of an incommensurate charge density wave (CDW) order with momentum ${\bf Q} = (Q,0)/(0,Q)$, as observed in the experiments. We first consider a semi-phenomenological charge-fermion model in which hot fermions, separated by ${\bf Q}$, attract each other by exchanging soft CDW fluctuations. We find that in a quantum-critical region near CDW transition, $T_c = A {\bar g}_c$, where ${\bar g}_c$ is charge-fermion coupling and $A$ is the prefactor which we explicitly compute. We then consider the particular microscopic scenario in which CDW order parameter emerges as a composite field made out of primary spin-density-wave fields. We show that charge-fermion coupling ${\bar g}_c$ is of order of spin-fermion coupling ${\bar g}_s$. As the consequence, superconducting $T_c$ is substantially enhanced near the onset of CDW order. Finally we analyze the effect of an external magnetic field $H$. We show that, as $H$ increases, optimal $T_c$ decreases and the superconducting dome becomes progressively more confined to the CDW quantum-critical point. These results are consistent with the experiments.

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arXiv2015

Fluctuating charge order in the cuprates: spatial anisotropy and feedback from superconductivity

We analyze the form of static charge susceptibility $χ(q)$ in underdoped cuprates near axial momenta $(Q,0)$ and $(0,Q)$ at which short-range static charge order has been observed. We show that the momentum dependence of $χ(q)$ is anisotropic, and the correlation length in the longitudinal direction is larger than in the transverse direction. We show that correlation lengths in both directions decrease once the system evolves into a superconductor, as a result of the competition between superconductivity and charge order. These results are in agreement with resonant x-ray scattering data [R. Comin et al., Science 347, 1335 (2015)]. We also argue that density and current components of the charge order parameter are affected differently by superconductivity --- the charge-density component is reduced less than the current component and hence extends deeper into the superconducting state. This gives rise to two distinct charge order transitions at zero temperature.

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arXiv2015

Itinerant electron scenario for Fe-based superconductors

I review works on Fe-based superconductors which depart from a metal with well defined Fermi surfaces and Fermi liquid-type quasiparticles. I consider normal state instabilities -- SDW magnetism and nematic order, and superconductivity, all three as the consequences of the instability of a Fermi surface due to interactions between low-energy fermionic quasiparticles. This approach assumes that renormalizations coming from fermions from high energies, of order bandwidth, modify but do not destroy Fermi liquid behavior in the normal state and can be absorbed into the effective low-energy model of interacting fermions located near hole and electron-type Fermi surfaces. I argue that the interactions between these fermions are responsible for (i) a stripe-type SDW magnetic order (and, in some cases, a checkerboard order), (ii) a preliminary nematic-type instability, in which magnetic fluctuations break $C_4$ lattice rotational symmetry down to $C_2$, but magnetic order does not yet develop, and (iii) a superconductivity, which competes with these two orders. The experimental data on superconductivity show rich behavior with potentially different symmetry of a superconducting state even for different compositions of the same material. I argue that, despite all this, the physics of superconductivity in the itinerant scenario for Fe-based materials is governed by a single underlying pairing mechanism.

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arXiv2015

Gap structure in Fe-based superconductors with accidental nodes: the role of hybridization

We study the effects of hybridization between the two electron pockets in Fe-based superconductors with s-wave gap with accidental nodes. We argue that hybridization reconstructs the Fermi surfaces and also induces an additional inter-pocket pairing component. We analyze how these two effects modify the gap structure by tracing the position of the nodal points of the energy dispersions in the superconducting state. We find three possible outcomes. In the first, the nodes simply shift their positions in the Brillouin zone; in the second, the nodes merge and disappear, in which case the gap function has either equal or opposite signs on the electron pockets; in the third, a new set of nodal points emerges, doubling the original number of nodes.

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arXiv2015

The origin of nematic order in FeSe

The origin of the 90 K nematic transition in the chalcogenide FeSe, which displays no magnetic order down to T=0, remains a major puzzle for a unifying theory for the iron-based superconductors. We analyze this problem in light of recent experimental data which reveal very small Fermi pockets in this material. We show that the smallness of the Fermi energy leads to a near-degeneracy between magnetic fluctuations and fluctuations in the charge-current density-wave channel. While the two fluctuation modes cooperate to promote the same preemptive Ising-nematic order, they compete for primary order. We argue that this explains why in FeSe the nematic order emerges when the magnetic correlation length is smaller than in other Fe-based materials, and why no magnetism is observed. We discuss how pressure lifts this near-degeneracy, resulting in a non-monotonic dependence of the nematic transition with pressure, in agreement with experiments.

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arXiv2015

Magnetically-Driven Suppression of Nematic Order in an Iron-Based Superconductor

A theory of superconductivity in the iron-based materials requires an understanding of the phase diagram of the normal state. In these compounds, superconductivity emerges when stripe spin density wave (SDW) order is suppressed by doping, pressure or atomic disorder. This magnetic order is often pre-empted by nematic order, whose origin is yet to be resolved. One scenario is that nematic order is driven by orbital ordering of the iron 3d-electrons that triggers stripe SDW order. Another is that magnetic interactions produce a spin-nematic phase, which then induces orbital order. In this article, we report the observation by neutron powder diffraction of an additional four- fold-symmetric phase in Ba1-xNaxFe2As2 close to the suppression of SDW order, which is consistent with the predictions of magnetically-driven models of nematic order.

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arXiv2015

Magnetic fluctuations and specific heat in NaxCoO2 near a Lifshitz topological transition

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 $x \geq x_c$. 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 $x \leq x_c$ 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 $\log T$. This behavior extends to progressively lower $T$ as $x$ increases towards a magnetic instability at $x \approx 0.75$.

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arXiv2014

Fe-based superconductors: seven years later

Iron-based superconductors were discovered seven years ago, in 2008. This short review summarizes what we learned about these materials over the last seven years, what are open questions, and what new physics we expect to extract from studies of this new class of high-temperature superconductors.

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arXiv2014

Polar Kerr effect from chiral-nematic charge order

We analyze the polar Kerr effect in an itinerant electron system on a square lattice in the presence of a composite charge order proposed for the pseudogap state in underdoped cuprates. This composite charge order preserves discrete translational symmetries, and is "chiral-nematic" in the sense that it breaks time-reversal symmetry, mirror symmetries in $x$ and $y$ directions, and $C_4$ lattice rotation symmetry. The Kerr angle $θ_K$ in $C_4$-symmetric system is proportional to the antisymmetric component of the anomalous Hall conductivity $σ_{xy}-σ_{yx}$. We show that this result holds when $C_4$ symmetry is broken. We show that in order for $σ_{xy}$ and $σ_{yx}$ to be non-zero the mirror symmetries in $x$ and $y$ directions have to be broken, and that for $σ_{xy}-σ_{yx}$ to be non-zero time-reversal symmetry has to be broken. The chiral-nematic charge order satisfies all these conditions, such that a non-zero signal in a polar Kerr effect experiment is symmetry allowed. We further show that to get a non-zero $θ_K$ in a one-band spin-fluctuation scenario, in the absence of disorder, one has to extend the spin-mediated interaction to momenta away from $(π,π)$ and has to include particle-hole asymmetry. Alternatively, in the presence of disorder one can get a non-zero $θ_K$ from impurity scattering: either due to skew scattering (with non-Gaussian disorder) or due to particle-hole asymmetry in case of Gaussian disorder. The impurity analysis in our case is similar to that in earlier works on Kerr effect in $p_x+ip_y$ superconductor, however in our case the magnitude of $θ_K$ is enhanced by the flattening of the Fermi surface in the "hot" regions which mostly contribute to charge order.

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arXiv2014

Effect of pairing fluctuations on the spin resonance in Fe-based superconductors

The spin resonance observed in the inelastic neutron scattering data on Fe-based superconductors has played a prominent role in the quest for determining the symmetry of the order parameter in these compounds. Most theoretical studies of the resonance employ an RPA-type approach in the particle-hole channel and associate the resonance in the spin susceptibility $χ_S (\mathbf{q}, ω)$ at momentum ${\bf Q} = (π,π)$ with the spin-exciton of an $s^{+-}$ superconductor, pulled below $2Δ$ by residual attraction associated with the sign change of the gap between Fermi points connected by ${\bf Q}$. Here we explore the effect of fluctuations in the particle-particle channel on the spin resonance. Particle-particle and particle-hole channels are coupled in a superconductor and to what extent the spin resonance can be viewed as a particle-hole exciton needs to be addressed. In the case of purely repulsive interactions we find that the particle-particle channel at total momentum ${\bf Q}$ (the $π$channel) contributes little to the resonance. However, if the interband density-density interaction is attractive and the $π-$resonance is possible on its own, along with the spin-exciton, we find a much stronger shift of the resonance frequency from the position of the would-be spin-exciton resonance. We also show that the expected double-peak structure in this situation does not appear because of the strong coupling between particle-hole and particle-particle channels, and $\mathrm{Im} χ_S ({\bf Q}, ω)$ displays only a single peak.

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arXiv2014

Charge-density-wave order with momentum $(2Q, 0)$ and $(0, 2Q)$ within the spin-fermion model: continuous and discrete symmetry breaking, preemptive composite order, and relation to pseudogap in hole-doped cuprates

We analyze charge order within the the spin-fermion model. We show that magnetically-mediated interaction gives rise to charge order $Δ_k^Q = \langle c^\dagger_{{\bf k}+{\bf Q}} c_{{\bf k}-{\bf Q}}\rangle$ with momenta ${\bf Q}=Q_x =(2Q,0)$ and ${\bf Q}=Q_y =(0,2Q)$, if the magnetic correlation length $ξ$ exceeds some critical value. We argue that $Δ_k^Q$ and $Δ_{-k}^Q$ are not equivalent, and their symmetric and antisymmetric combinations describe density modulations and bond current. We derive GL functional for four-component $U(1)$ order parameters $Δ^Q_{\pm k}$ with ${\bf Q} = Q_x$ or $Q_y$. Within mean-field we find two types of CDW states, I and II, depending on system parameters. In state I density and current modulations emerge with the same ${\bf Q} = Q_x$ or $Q_y$, breaking $Z_2$ lattice rotational symmetry, and differ in phase by $\pmπ/2$. The selection of $π/2$ or $-π/2$ additionally breaks $Z_2$ time-reversal symmetry, such that the total order parameter manifold is $U(1) \times Z_2 \times Z_2$. In state II density and current modulations emerge with different $\bf Q$ and the order parameter manifold is $U(1) \times U (1) \times Z_2$. We go beyond mean-field and show that discrete symmetries get broken before long-range charge order sets in. For state I, the system first breaks $Z_2$ lattice rotational symmetry ($C_4 \to C_2$) at $T= T_n$ and develops a nematic order, then breaks $Z_2$ time-reversal symmetry at $T_t < T_n$, and finally breaks $U(1)$ symmetry of a common phase of even and odd components of $Δ^Q_{k}$ at $T= T_{\rm cdw} < T_t < T_n$ and develops a true charge order. We argue that the preemptive orders lift $T_{\rm cdw}$ and reduces $T_{\rm sc}$ such that at large $ξ$ charge order may develop prior to superconductivity. We obtain the phase diagram and present quantitative comparison with ARPES data for hole-doped cuprates.

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arXiv2014

Time-reversal symmetry breaking superconductivity in the coexistence phase with magnetism in Fe-pnictides

We argue that superconductivity in the coexistence region with spin-density-wave (SDW) order in weakly doped Fe-pnictides differs qualitatively from the ordinary $s^{+-}$ state outside the coexistence region, as it develops an additional gap component which is a mixture of intra-pocket singlet ($s^{++}$) and inter-pocket 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 than $0$ or $π$, manifesting explicitly the breaking of the time-reversal symmetry promoted by long-range SDW order. We show that this exotic state emerges already in the simplest model of Fe-pnictides, with one hole pocketand two symmetry-related electron pockets. We argue that in some parameter range time-reversal gets broken even before long-range superconducting order develops.

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