Although the existence of nematic order in iron-based superconductors is now a well-established experimental fact, its origin remains controversial. Nematic order breaks the discrete lattice ...rotational symmetry by making the x and y directions in the iron plane non-equivalent. This can happen because of a regular structural transition or as the result of an electronically driven instability -- in particular, orbital order or spin-driven Ising-nematic order. The latter is a magnetic state that breaks rotational symmetry but preserves time-reversal symmetry. Symmetry dictates that the development of one of these orders immediately induces the other two, making the origin of nematicity a physics realization of the 'chicken and egg problem'. In this Review, we argue that the evidence strongly points to an electronic mechanism of nematicity, placing nematic order in the class of correlation-driven electronic instabilities, like superconductivity and density-wave transitions. We discuss different microscopic models for nematicity and link them to the properties of the magnetic and superconducting states, providing a unified perspective on the phase diagram of the iron pnictides.
Chiral superconductivity, which breaks time-reversal symmetry, can exhibit a wealth of fascinating properties that are highly sought after for nanoscience applications. We identify doped graphene ...monolayer as a system where chiral superconductivity can be realized. In this material, a unique situation arises at a doping where the Fermi surface is nested and the density of states is singular. In this regime, d-wave superconductivity can emerge from repulsive electron-electron interactions. Using a renormalization group method, we argue that superconductivity dominates over all competing orders for generic weak repulsive interactions. Superconductivity develops simultaneously in two degenerate d-wave pairing channels. We argue that the resulting superconducting state is of chiral type, with the phase of the superconducting order parameter winding by 4π around the Fermi surface. Realization of this state in doped graphene will prove that superconductivity can emerge from electron-electron repulsion, and will open the door to applications of chiral superconductivity. PUBLICATION ABSTRACT
We analyze the pairing symmetry in Fe-based superconductors AFe2Se2 (A=K, Rb, Cs) which contain only electron pockets. We argue that the pairing condensate in such systems contains not only ...intrapocket component but also interpocket component, made of fermions belonging to different electron pockets. We analyze the interplay between intrapocket and interpocket pairing, depending on the ellipticity of electron pockets and the strength of their hybridization. We show that with increasing hybridization, the system undergoes a transition from a d-wave state to an s+- state, in which the gap changes sign between hybridized pockets. This s+- state has the full gap and at the same time supports spin resonance, in agreement with the data. Near the boundary between d and s+- states, we found a long-sought s+id state which breaks time-reversal symmetry.
We analyze antiferromagnetism and superconductivity in novel Fe-based superconductors within the weak-coupling, itinerant model of electron and hole pockets near (0,
0) and (
π,
π) in the folded ...Brillouin zone. We discuss the interaction Hamiltonian, the nesting, the RG flow of the couplings at energies above and below the Fermi energy, and the interplay between SDW magnetism, superconductivity and charge orbital order. We argue that SDW antiferromagnetism wins at zero doping but looses to superconductivity upon doping. We show that the most likely symmetry of the superconducting gap is
A
1
g
in the folded zone. This gap has no nodes on the Fermi surface but changes sign between hole and electron pockets. We also argue that at weak coupling, this pairing predominantly comes not from spin fluctuation exchange but from a direct pair hopping between hole and electron pockets.
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 ω
sf
below which the system behaves as a Fermi liquid. The ratio of the two determines the dimensionless coupling constant for spin-fermion interaction λ
2
∝ g¯/ω
sf
. 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.
We consider pairing of itinerant fermions in a metal near a quantum-critical point (QCP) towards some form of particle-hole order (nematic, spin-density-wave, charge-density-wave, etc.). At a QCP, ...the dominant interaction between fermions comes from exchanging massless fluctuations of a critical order parameter. At low energies, this physics can be described by an effective model with the dynamical electron-electron interaction
V
(Ω
m
) ∝ 1/|Ω
m
|
γ
, up to some upper cutoff Λ. The case γ = 0 corresponds to BCS theory, and can be solved by summing up geometric series of Cooper logarithms. We show that for a finite γ, the pairing problem is still marginal (i.e., perturbation series are logarithmic), but one needs to go beyond logarithmic approximation to find the pairing instability. We discuss specifics of the pairing at γ > 0 in some detail and also analyze the marginal case γ = 0+, when
V
(Ω
m
) = λlog(Λ/|Ω
m
|). We show that in this case the summation of Cooper logarithms does yield the pairing instability at λlog
2
(Λ/
T
c
) =
O
(1), but the logarithmic series are not geometrical. We reformulate the pairing problem in terms of a renormalization group (RG) flow of the coupling, and show that the RG equation is different in the cases γ = 0, γ = 0+, and γ > 0.
Recent measurements of the doping dependence of the London penetration depth λ(x) at low T in clean samples of isovalent BaFe2(As(1-x)P(x))2 at T≪T(c) Hashimoto et al., Science 336, 1554 (2012) ...revealed a peak in λ(x) near optimal doping x=0.3. The observation of the peak at T≪T(c), points to the existence of a quantum critical point beneath the superconducting dome. We associate such a quantum critical point with the onset of a spin-density-wave order and show that the renormalization of λ(x) by critical magnetic fluctuations gives rise to the observed feature. We argue that the case of pnictides is conceptually different from a one-component Galilean invariant Fermi liquid, for which correlation effects do not cause the renormalization of the London penetration depth at T=0.
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. Here we report the observation by neutron powder diffraction of an additional fourfold-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.
PDF
