Andrey V. Chubukov

What drives nematic order in iron-based superconductors?

Although the existence of nematic order in iron-based superconductors is now a wellestablished experimental fact, its origin remains controversial. Nematic order breaks the discrete lattice rotational symmetry by making the x and y directions in the Fe plane non-equivalent. This can happen because of (i) a tetragonal to orthorhombic structural transition, (ii) a spontaneous breaking of an orbital symmetry, or (iii) a spontaneous development of an Ising-type spin-nematic order – a magnetic state that breaks rotational symmetry but preserves time-reversal symmetry. The Landau theory of phase transitions dictates that the development of one of these orders should immediately induce the other two, making the origin of nematicity a physics realization of a “chicken and egg problem”. The three scenarios are, however, quite different from a microscopic perspective. While in the structural scenario lattice vibrations (phonons) play the dominant role, in the other two scenarios electronic correlations are responsible for the nematic order. In this review, we argue that experimental and theoretical evidence strongly points to the electronic rather than phononic mechanism, placing the nematic order in the class of correlation-driven electronic instabilities, like superconductivity and density-wave transitions. We discuss different microscopic models for nematicity in the iron pnictides, and link nematicity to other ordered states of the global phase diagram of these materials – magnetism and superconductivity. In the magnetic model nematic order pre-empts stripe-type magnetic order, and the same interaction which favors nematicity also gives rise to an unconventional s superconductivity. In the charge/orbital model magnetism appears as a secondary effect of ferro-orbital order, and the interaction which favors nematicity gives rise to a conventional s superconductivity. We explain the existing data in terms of the magnetic scenario, for which quantitative results have been obtained theoretically, including the phase diagram, transport properties of the nematic phase, scaling of nematic fluctuations, and the feedback of the nematic order on magnetic and electronic spectra.

Magnetism, superconductivity, and pairing symmetry in iron-based superconductors

We analyze antiferromagnetism and superconductivity in novel Fe-based superconductors within the itinerant model of small electron and hole pockets near 0,0 and ,. We argue that the effective interactions in both channels logarithmically flow toward the same values at low energies; i.e., antiferromagnetism and superconductivity must be treated on equal footing. The magnetic instability comes first for equal sizes of the two pockets, but loses to superconductivity upon doping. The superconducting gap has no nodes, but changes sign between the two Fermi surfaces extended s-wave symmetry. We argue that the T dependencies of the spin susceptibility and NMR relaxation rate for such a state are exponential only at very low T, and can be well fitted by power laws over a wide T range below Tc.

Chiral superconductivity from repulsive interactions in doped graphene

Chiral superconducting states are expected to support a variety of exotic and potentially useful phenomena. Theoretical analysis suggests that just such a state could emerge in a doped graphene monolayer.

Quantum-critical theory of the spin-fermion model and its application to cuprates: normal state analysis

We present the full analysis of the normal state properties of the spin-fermion model near the antiferromagnetic instability in two dimensions. The model describes low-energy fermions interacting with their own collective spin fluctuations, which soften at the antiferromagnetic transition. We argue that in 2D, the system has two typical energies—an effective spin-fermion interaction g¯ and an energy ωsf below which the system behaves as a Fermi liquid. The ratio of the two determines the dimensionless coupling constant for spin-fermion interaction λ2 ∝ g¯/ωsf. We show that λ scales with the spin correlation length and diverges at criticality. This divergence implies that the conventional perturbative expansion breaks down. We develop a novel approach to the problem—the expansion in either the inverse number of hot spots in the Brillouin zone, or the inverse number of fermionic flavours—which allows us to explicitly account for all terms which diverge as powers of λ, and treat the remaining, O(log λ) terms in the RG formalism. We apply this technique to study the properties of the spin-fermion model in various frequency and temperature regimes. We present the results for the fermionic spectral function, spin susceptibility, optical conductivity and other observables. We compare our results in detail with the normal state data for the cuprates, and argue that the spin-fermion model is capable of explaining the anomalous normal state properties of the high T c materials. We also show that the conventional {4 theory of the quantum-critical behaviour is inapplicable in 2D due to the singularity of the {4 vertex.

Preemptive nematic order, pseudogap, and orbital order in the iron pnictides

Starting from a microscopic itinerant model, we derive and analyze the effective low-energy model for collective magnetic excitations in the iron pnictides. We show that the stripe magnetic order is generally preempted by an Ising-nematic order which breaks

A Relation between the Resonance Neutron Peak and ARPES Data in Cuprates

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On the quantum effects in helimagnets

lattice symmetry but preserves O(3) spin-rotational symmetry. This leads to a rich phase diagram as function of doping, pressure, and elastic moduli, displaying split magnetic and nematic tri-critical points. The nematic transition may instantly bring the system to the verge of a magnetic transition, or it may occur first, being followed by a magnetic transition at a lower temperature. In the latter case, the preemptive nematic transition is accompanied by either a jump or a rapid increase of the magnetic correlation length, triggering a pseudogap behavior associated with magnetic precursors. Furthermore, due to the distinct orbital character of each Fermi pocket, the nematic transition also induces orbital order. We compare our results to various experiments, showing that they correctly address the changes in the character of the magneto-structural transition across the phase diagrams of different compounds, as well as the relationship between the orthorhombic and magnetic order parameters.

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 argue that the resonant peak observed in neutron scattering experiments on superconducting cuprates and the peak/dip/hump features observed in ARPES measurements are byproducts of the same physical phenomenon. We argue that both are due to feedback effects on the damping of spin fluctuations in a

Novel neutron resonance mode in d x 2 y 2-wave superconductors

d-

Evolution of the superconducting state of Fe-based compounds with doping.

wave superconductor. We consider the spin-fermion model at strong coupling, solve a set of coupled integral equations for fermionic and bosonic propagators and show that the dynamical spin susceptibility below