Johannes Knolle

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

Dynamics of a Two-Dimensional Quantum Spin Liquid: Signatures of Emergent Majorana Fermions and Fluxes

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Fermionic response from fractionalization in an insulating two-dimensional magnet

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.

Effect of fermi surface nesting on resonant spin excitations in Ba 1-xKxFe2As2

We provide a complete and exact theoretical study of the dynamical structure factor of a twodimensional quantum spin liquid in gapless and gapped phases, as realized in Kitaev’s honeycomb model. We show that there are direct signatures—qualitative and quantitative—of the Majorana fermions and gauge fluxes emerging in this model. These include counterintuitive manifestations of quantum number fractionalization, such as a neutron scattering response with a gap even in the presence of gapless excitations, and a sharp component despite the fractionalization of electron spin. Our analysis identifies new varieties of the venerable x-ray edge problem and explores connections to the physics of quantum quenches.

Theory of itinerant magnetic excitations in the spin-density-wave phase of iron-based superconductors

An intriguing state of matter known as a quantum spin liquid has been predicted to host Majorana fermions. A detailed theoretical and numerical analysis re-interprets existing Raman data for α-RuCl3 and uncovers direct evidence of a fermionic response.

Dynamics of fractionalization in quantum spin liquids

We report inelastic neutron scattering measurements of the resonant spin excitations in Ba(1-x)K(x)Fe(2)As(2) over a broad range of electron band filling. The fall in the superconducting transition temperature with hole doping coincides with the magnetic excitations splitting into two incommensurate peaks because of the growing mismatch in the hole and electron Fermi surface volumes, as confirmed by a tight-binding model with s(±)-symmetry pairing. The reduction in Fermi surface nesting is accompanied by a collapse of the resonance binding energy and its spectral weight, caused by the weakening of electron-electron correlations.

Quasiparticle interference in the spin-density wave phase of iron-based superconductors.

We argue that salient experimental features of the magnetic excitations in the spin-density-wave phase of iron-based superconductors can be understood within an itinerant model. We identify a minimal model and use a multiband random-phase approximation treatment of the dynamical spin susceptibility. Weakly damped spin waves are found near the ordering momentum and it is shown how they dissolve into the particle-hole continuum. We show that ellipticity of the electron bands accounts for the anisotropy of the spin waves along different crystallographic directions and the spectral gap at the momentum conjugated to the ordering one. We argue that our theory agrees well with the existing neutron scattering data.

Neutron scattering in the proximate quantum spin liquid α-RuCl3

We present the theory of dynamical spin response for the Kitaev honeycomb model, obtaining exact results for the structure factor (SF) in gapped and gapless, Abelian and non-Abelian quantum spin-liquid (QSL) phases. We also describe the advances in methodology necessary to compute these results. The structure factor shows signatures of spin fractionalization into emergent quasiparticles: Majorana fermions and fluxes of Z2 gauge field. In addition to a broad continuum from spin fractionalization, we find sharp (δ-function) features in the response. These arise in two distinct ways: from excited states containing only (static) fluxes and no (mobile) fermions, and from excited states in which fermions are bound to fluxes. The SF is markedly different in Abelian and non-Abelian QSLs, and bound fermion-flux composites appear only in the non-Abelian phase.

Superconductivity from repulsion in LiFeAs: novel s-wave symmetry and potential time-reversal symmetry breaking

We propose an explanation for the electronic nematic state observed recently in parent iron-based superconductors [T.-M. Chuang, Science 327, 181 (2010)10.1126/science.1181083]. We argue that the quasi-one-dimensional nanostructure identified in the quasiparticle interference (QPI) is a consequence of the interplay of the magnetic (π, 0) spin-density wave (SDW) order with the underlying electronic structure. We show that the evolution of the QPI peaks largely reflects quasiparticle scattering between bands involved in the SDW formation. Because of the ellipticity of the electron pocket and the fact that only one of the electron pockets is involved in the SDW, the resulting QPI has a pronounced one-dimensional structure. We further predict that the QPI crosses over to two dimensionality on an energy scale, set by the SDW gap.

Excitations in the field-induced quantum spin liquid state of α-RuCl3

Quantum matter provides an effective vacuum out of which arise emergent particles not corresponding to any experimentally detected elementary particle. Topological quantum materials in particular have become a focus of intense research in part because of the remarkable possibility to realize Majorana fermions, with their potential for new, decoherence-free quantum computing architectures. In this paper we undertake a study on high-quality single crystal of -RuCl3 which has been identified as a material realizing a proximate Kitaev state, a topological quantum state with magnetic Majorana fermions. Four-dimensional tomographic reconstruction of dynamical correlations measured using neutrons is uniquely powerful for probing such magnetic states. We discover unusual signals, including an unprecedented column of scattering over a large energy interval around the Brillouin zone center which is remarkably stable with temperature. This is straightforwardly accounted for in terms of the Majorana excitations present in Kitaevs topological quantum spin liquid. Other, more delicate, features in the scattering can be transparently associated with perturbations to an ideal model. This opens a window on emergent magnetic Majorana fermions in correlated materials.Sighting of magnetic Majorana fermions? Quantum spin liquids—materials whose magnetic spins do not settle into order even at absolute zero temperature—have long captured the interest of physicists. A particularly lofty goal is finding a material that can be described by the so-called Kitaev spin model, a network of spins on a honeycomb lattice that harbors Majorana fermions as its excitations. Banerjee et al. present a comprehensive inelastic neutron scattering study of single crystals of the material α-RuCl3, which has been predicted to a host a Kitaev spin liquid. The unusual dependence of the data on energy, momentum, and temperature is consistent with the Kitaev model. Science, this issue p. 1055 Unusual inelastic neutron scattering signal is consistent with predictions of the Kitaev spin model. The Kitaev quantum spin liquid (KQSL) is an exotic emergent state of matter exhibiting Majorana fermion and gauge flux excitations. The magnetic insulator α-RuCl3 is thought to realize a proximate KQSL. We used neutron scattering on single crystals of α-RuCl3 to reconstruct dynamical correlations in energy-momentum space. We discovered highly unusual signals, including a column of scattering over a large energy interval around the Brillouin zone center, which is very stable with temperature. This finding is consistent with scattering from the Majorana excitations of a KQSL. Other, more delicate experimental features can be transparently associated with perturbations to an ideal model. Our results encourage further study of this prototypical material and may open a window into investigating emergent magnetic Majorana fermions in correlated materials.