We evaluate the dynamic structure factor S(q, ω) of interacting one-dimensional spinless fermions with a nonlinear dispersion relation. The combined effect of the nonlinear dispersion and of the interactions leads to new universal features of S(q, ω). The sharp peak S(q, ω) ∝ qδ(ω − uq), characteristic for the Tomonaga-Luttinger model, broadens up; S(q, ω) for a fixed q becomes finite at arbitrarily large ω. The main spectral weight, however, is confined to a narrow frequency interval of the width δω ∼ q 2 /m. At the boundaries of this interval the structure factor exhibits power-law singularities with exponents depending on the interaction strength and on the wave number q.PACS numbers: 71.10.Pm, 72.15.Nj Low-energy properties of fermionic systems are sensitive to interactions between fermions. The effect of interactions is the strongest in one dimension (1D), where single-particle correlation functions exhibit power-law singularities, in a striking departure from the behavior in higher dimensions. Much of our current understanding of 1D fermions is based on the Tomonaga-Luttinger (TL) model [1]. The crucial ingredient of the model is the assumption of a strictly linear fermionic dispersion relation. The TL model, often used in conjunction with a powerful bosonization technique [2], allows one to evaluate various correlation functions, such as momentum-resolved [3,4] and local [5] single-particle densities of states.Unlike the single-particle correlation functions, the two-particle correlation functions of the TL model exhibit behavior rather compatible with that expected for a Fermi liquid with the linear spectrum of quasiparticles. For example, the dynamic structure factor (the densitydensity correlation function)at small q takes the form [3] S TL (q, ω) ∝ qδ(ω − uq). It means that the quanta of density waves propagating with plasma velocity u are true eigenstates of the TL model; these bosonic excitations have an infinite lifetime. Below we show that such a simple behavior is an artefact of the linear spectrum approximation. In reality, the spectrum of fermions always has some nonlinearity,where the upper/lower sign corresponds to the right/left movers (R/L), and k = p ∓ p F are momenta measured from the Fermi points ± p F . (For Galilean-invariant systems the expansion (2) terminates at k 2 .) The finite curvature (1/m = 0) affects drastically the functional form of S(q, ω). In a clear deviation from the results of TL model, power-law singularities now arise not only in the single-particle correlation functions, but in the structure factor as well. We show that the singularities in these two very different objects have a common origin, proliferation of low-energy particle-hole pairs, and evaluate the corresponding exponents.Because of the success of the bosonization technique [2], it is tempting to treat the spectrum nonlinearity as a weak interaction between the TL bosons. Indeed, the nonlinearity gives rise to a three-boson interaction with the coupling constant ∝ 1/m [6]. However, attempts to treat this ...

Magnetism and nematic order are the two nonsuperconducting 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 (RG) analysis. We analyze the RG flow of the couplings and argue that the same magnetic fluctuations, which are known to promote s þ− superconductivity, also promote an attraction in the orbital channel, even if the bare orbital interaction is repulsive. We next analyze the RG flow of the susceptibilities and show that, if all Fermi pockets are small, the system first develops a spontaneous orbital order, then s þ− superconductivity, and magnetic order does not develop down to T ¼ 0. We argue that this scenario applies to FeSe. In systems with larger pockets, such as BaFe 2 As 2 and LaFeAsO, we find that the leading instability is either towards a spindensity wave or superconductivity. We argue that in this situation nematic order is caused by composite spin fluctuations and is vestigial to stripe magnetism. Our results provide a unifying description of different ironbased materials.

We evaluate the spectral function of interacting fermions in one dimension. Contrary to the Tomonaga-Luttinger model, our treatment accounts for the nonlinearity of the free fermion spectrum. In a striking departure from the Luttinger liquid theory, the spectrum nonlinearity restores the main feature of the Fermi liquid: a Lorentzian peak in the spectral function on the particle mass-shell. At the same time, the spectral function displays a power-law singularity on the hole mass-shell, similar to that in the Luttinger liquid.

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.

The linear dispersion of the low-energy electronic structure of monolayer graphene supports chiral quasiparticles that obey the relativistic Dirac equation and have a Berry phase of π (refs 1,2). In bilayer graphene 3 , the shape of the energy bands is quadratic, and its quasiparticles have a chiral degree, l = 2, and a Berry phase of 2π. These characteristics are usually determined from quantum Hall effect (QHE) measurements in which the Berry phase causes shifts in Shubnikov-de Haas (SdH) resistance oscillations. The QHE in graphene also exhibits an unconventional sequence of plateaux of Hall conductivity, σ xy , with quantized steps of 4e 2 /h, except for the first plateau, where it is governed by the Berry phase. Here, we report magnetotransport measurements in ABC-stacked trilayer graphene, and their variation with carrier density, magnetic field and temperature. Our results provide the first evidence of the presence of l = 3 chiral quasiparticles with cubic dispersion, predicted to occur in ABC-stacked trilayer graphene [4][5][6][7][8][9][10][11][12] . The SdH oscillations we observe suggest Landau levels with four-fold degeneracy, a Berry phase of 3π, and the marked increase of cyclotron mass near charge neutrality. We also observe the predicted unconventional sequence of QHE plateaux, σ xy = ±6e 2 /h, ±10e 2 /h, and so on. Despite significant interest in studying layered graphene systems with more than two layers, experimental progress has been limited [13][14][15][16][17][18] . Low-energy electronic properties depend crucially on the stacking order of graphene layers [4][5][6][7][8][9][10][11][12]18 , and therefore such studies require samples with a well-defined stacking sequence. In a bilayer, two honeycomb nets of carbon atoms are positioned with half of the atoms of the top layer (B) right above the atoms of the bottom layer (A) and the other half at the centres of the hexagonal voids in the bottom layer. The third carbon net in a trilayer can either be placed with its atoms above the atoms of the bottom layer A, as in the Bernal structure of crystalline graphite 19 , or with its voids above the lined-up atom pairs in layers A and B, thus breaking the reflection symmetry (Fig. 1a). The latter, ABC stacking, is found in the metastable rhombohedral modification of graphite 19 . The electronic structure of graphene multilayers is derived from the hybridization of monolayer states through interlayer hopping. Its main features are captured already by only considering hopping between the nearest-neighbour carbons, which are stacked above each other in two adjacent layers, γ 1 ∼ 0.1γ 0 , as shown in Fig. 1a (γ 0 ≈ 3.16 eV is the intralayer hopping, in bulk graphite γ 1 ≈ 0.4 eV, and there are also further-neighbour hoppings, γ 2 -γ 5 , which are not shown) [9][10][11][12] . In a bilayer, low-energy electronic states retain is the velocity of linear dispersion in the monolayer, p = (p x ,p y ) = p(cosϕ p ,sinϕ p ) is the 2D momentum, π = p x + iξ p y ,σ x,y are the pseudo-spin Pauli matrices, and ξ = ±1 is ...

The multiband nature of iron pnictides gives rise to a rich temperature-doping phase diagram of competing orders and a plethora of collective phenomena. At low dopings, the tetragonal-to-orthorhombic structural transition is closely followed by a spin density wave transition both being in close proximity to the superconducting phase. A key question is the nature of high-Tc superconductivity and its relation to orbital ordering and magnetism. Here we study the NaFe1−xCoxAs superconductor using polarization-resolved Raman spectroscopy. The Raman susceptibility displays critical enhancement of non-symmetric charge fluctuations across the entire phase diagram which are precursors to a d-wave Pomeranchuk instability at temperature θ(x). The charge fluctuations are interpreted in terms of quadrupole inter-orbital excitations in which the electron and hole Fermi surfaces breathe in-phase. Below Tc, the critical fluctuations acquire coherence and undergo a metamorphosis into a coherent ingap mode of extraordinary strength.

Tunnel junctions, an established platform for high resolution spectroscopy of superconductors, require defect-free insulating barriers; however, oxides, the most common barrier, can only grow on a limited selection of materials. We show that van der Waals tunnel barriers, fabricated by exfoliation and transfer of layered semiconductors, sustain stable currents with strong suppression of sub-gap tunneling. This allows us to measure the spectra of bulk (20 nm) and ultrathin (3- and 4-layer) NbSe2 devices at 70 mK. These exhibit two distinct superconducting gaps, the larger of which decreases monotonically with thickness and critical temperature. The spectra are analyzed using a two-band model incorporating depairing. In the bulk, the smaller gap exhibits strong depairing in in-plane magnetic fields, consistent with high out-of-plane Fermi velocity. In the few-layer devices, the large gap exhibits negligible depairing, consistent with out-of-plane spin locking due to Ising spin–orbit coupling. In the 3-layer device, the large gap persists beyond the Pauli limit.

We propose to use the lateral interface between two regions with different strengths of the spin-orbit interaction(s) to spin polarize the electrons in gated two-dimensional semiconductor heterostructures. For a beam with a nonzero angle of incidence, the transmitted electrons will split into two spin polarization components propagating at different angles. We analyze the refraction at such an interface and outline the basic schemes for filtration and control of the electron spin.