We study quasiparticle interference (QPI) in the Kitaev quantum spin liquid (QSL) for electrons tunneling into the QSL. The local tunneling conductance around a spin vacancy or localized vison reveals unique features associated with fractionalized Majorana fermions, chargons, and visons. In certain parameter regimes, the single-spinon density of states and momentum dispersion can both be directly extracted from the tunneling conductance. Our results suggest that QPI is a promising tool for identifying the Kitaev QSL and its fractionalized excitations.
We study the stability of Kitaev quasiparticles in the presence of a perturbing Heisenberg interaction as a Fock space localization phenomenon. We identify parameter regimes where Kitaev states are localized, fractal or delocalized in the Fock space of exact eigenstates, with the first two implying quasiparticle stability. Finite temperature calculations show that a vison gap, and a nonzero plaquette Wilson loop at low temperatures, both characteristic of the deconfined Kitaev spin liquid phase, persist far into the neighboring phase that has a concomitant stripy spin-density wave (SDW) order.…
We explore with exact diagonalization the propagation of a single hole in four magnetic phases of the t-J-like Kitaev-Heisenberg model on a honeycomb lattice: the Neel antiferromagnetic, stripe, zigzag and Kitaev spin-liquid phase. We find coherent propagation of spin-polaron quasiparticles in the antiferromagnetic phase by a similar mechanism as in the $t$-$J$ model for high-$T_c$ cuprates. In the stripe and zigzag phases clear quasiparticles features appear in spectral functions of those propagators where holes are created and annihilated on one sublattice, while they remain largely {\it hid…
We investigate the real-time spin response of the $S=1$ Kitaev model upon stimuli of a pulsed magnetic field in one of the edges using the exact diagonalization method. It is found that the pulsed magnetic field has no effect on the appearance of the spin moments in the quantum spin liquid region, but induces the spin oscillations in the other edge region with a small magnetic field. This is understood by the existence of the itinerant quasiparticles, which carry the spin excitations without the spin polarization in the quantum spin liquid state. This suggests that the spin fractionalizations …
We investigate the dynamic structure factor of the antiferromagnetic Kitaev honeycomb model in a magnetic field by applying perturbative continuous unitary transformations about the high-field limit. One- and two-quasiparticle properties of the dressed elementary spin-flip excitations of the high-field polarized phase are calculated which account for most of the spectral weight in the dynamic structure factor. We discuss the evolution of spectral features in these quasiparticle sectors in terms of one-quasiparticle dispersions, two-quasiparticle continua, the formation of antibound states, and…
We study the low frequency spectra of complex Sachdev-Ye-Kitaev (SYK) models at general densities. The analysis applies also to SU($M$) magnets with random exchange at large $M$. The spectral densities are computed by numerical analysis of the saddle point equations on the real frequency ($ω$) axis at zero temperature ($T$). The asymptotic low $ω$ behaviors are found to be in excellent agreement with the scaling dimensions of irrelevant operators which perturb the conformally invariant critical states. Of possible experimental interest is our computation of the universal spin spectral weight o…
The pure Kitaev honeycomb model harbors a quantum spin liquid in zero magnetic fields, while applying finite magnetic fields induces a topological spin liquid with non-Abelian anyonic excitations. This latter phase has been much sought after in Kitaev candidate materials, such as $α$-RuCl$_3$. Currently, two competing scenarios exist for the intermediate field phase of this compound ($B=7-10$ T), based on experimental as well as theoretical results: (i) conventional multiparticle magnetic excitations of integer quantum number vs. (ii) Majorana fermionic excitations of possibly non-Abelian natu…
Quantum spin liquid involves fractionalized quasipariticles such as spinons and visons. They are expressed as itinerant Majorana fermions and $Z_2$ fluxes in the Kitaev model with bond-dependent exchange interactions on a honeycomb spin lattice. The observation has recently attracted attention for a candidate material $α$-RuCl$_3$, showing spin liquid behaviour induced by a magnetic field. Since the observable spin excitation is inherently composed of the two quasiparticles, which further admix each other by setting in the magnetic field as well as non-Kitaev interactions, their individual ide…
The honeycomb Kitaev model in a magnetic field is a source of a topological quantum spin liquid with Majorana fermions and gauge flux excitations as fractional quasiparticles. We present experimental results for the thermal Hall effect of the material $α$-RuCl$_{3}$ which recently emerged as a prime candidate for realizing such physics. At temperatures above long-range magnetic ordering $T\gtrsim T_N\approx8$ K, we observe with an applied magnetic field $B$ perpendicular to the honeycomb layers a sizeable positive transversal heat conductivity $κ_{xy}$ which increases linearly with $B$. Upon r…
In this paper, we study the lightly doped Kitaev spin liquid (DKSL) and find it to be a Fermi liquid state. The DKSL has a closed Fermi surface around the center of the Brillouin zone with the quantized volume determined by the Luttinger's theorem. It has well-defined quasiparticles near the Fermi surface and can be detected in the angle-resolved photoemission spectroscopy. The DKSL has the topological Kitaev spin liquid (KSL) as its neutral background. It violates the Wiedemann-Franz law and has a large Wilson ration. These results has the potential experimental test in the iridates upon dopi…
We show that a small number of intentionally introduced defects can be used as a spectroscopic tool to amplify quasiparticle interference in 2H-NbSe$_{2}$, that we measure by scanning tunneling spectroscopic imaging. We show from the momentum and energy dependence of the quasiparticle interference that Fermi surface nesting is inconsequential to charge density wave formation in 2H-NbSe$_{2}$. We demonstrate that by combining quasiparticle interference data with additional knowledge of the quasiparticle band structure from angle resolved photoemission measurements, one can extract the wavevecto…
A Majorana fermion is a fermionic particle that is its own antiparticle. Since the theoretical discovery in 1937, the exotic particle has long been searched in particle physics. In the last few decades, however, it has attracted renewed interest in condensed matter physics, where it can be realized as an elementary excitation (quasiparticle) in quantum states of matter. In this review, we discuss another platform for Majorana fermions, the quantum spin liquid, in which interacting magnetic moments remain disordered down to the lowest temperature under strong quantum fluctuations. They are char…
Evidence for Deconfined Magnetic Order in the Kitaev-$J_3$ Model
School of Physics, Hangzhou Normal University（杭州师范大学物理学院）；School of Physical Science and Technology, Lanzhou University（兰州大学物理科学与技术学院）；Lanzhou Center for Theoretical Physics, Key Laboratory of Quantum Theory and Applications of MoE, Key Laboratory of Theoretical Physics of Gansu Province, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University（兰州大学理论物理中心、量子理论与应用教育部重点实验室、甘肃省理论物理重点实验室、甘肃省量子物理基础学科省级研究中心）
Motivated by recent experiments on the Kitaev honeycomb magnet $α\text{-RuCl}_3$, we introduce time-domain probes of the edge and quasiparticle content of non-Abelian spin liquids. Our scheme exploits ancillary quantum spins that communicate via time-dependent tunneling of energy into and out of the spin liquid's chiral Majorana edge state. We show that the ancillary-spin dynamics reveals the edge-state velocity and, in suitable geometries, detects individual non-Abelian anyons and emergent fermions via a time-domain counterpart of quantum-Hall anyon interferometry. We anticipate applications …
Using a large-N approach, we study the effect of disorder in the Kondo-screened phase of heavy-fermion materials. We demonstrate that the strong feedback between the hybridization and the conduction electron charge density magnifies the effect of disorder, such that already small concentrations of defects strongly disorder the materials' local electronic structure, while only weakly affecting their spatially averaged, thermodynamic properties. Finally, we show that the microscopic nature of defects can be identified through their characteristic signatures in the hybridization and quasiparticle…
We study the self-energy of phonons, magnetoelastically coupled to the two-dimensional Kitaev spin-model on the honeycomb lattice. Fractionalization of magnetic moments into mobile Majorana matter and a static $\mathbb{Z}_{2}$ gauge field lead to a continuum of relaxation processes comprising two channels. Thermal flux excitations, which act as an emergent disorder, strongly affect the phonon renormalization. Above the flux proliferation temperature, the dispersion of a narrow quasiparticle-hole channel is suppressed in favor of broad and only weakly momentum dependent features, covering large…
We investigate the impurity scattering induced quasiparticle interference in the ($π, 0$) spin-density wave phase of the iron pnictides. We use a five orbital tight binding model and our mean field theory in the clean limit captures key features of the Fermi surface observed in angle-resolved photoemission. We use a t-matrix formalism to incorporate the effect of doping induced impurities on this state. The impurities lead to a spatial modulation of the local density of states about the impurity site, with a periodicity of $\sim 8a_{{\rm Fe}-{\rm Fe}}$ along the antiferromagnetic direction. Th…
Resonant X-ray scattering (RXS) has recently become an increasingly important tool for the study of ordering phenomena in correlated electron systems. Yet, the interpretation of the RXS experiments remains theoretically challenging due to the complexity of the RXS cross-section. Central to this debate is the recent proposal that impurity-induced Friedel oscillations, akin to quasiparticle interference signals observed with the scanning tunneling microscope (STM), can lead to scattering peaks in the RXS experiments. The possibility that quasiparticle properties can be probed in RXS measurements…
Quantum spin liquids realize massive entanglement and fractional quasiparticles from localized spins, proposed as an avenue for quantum science and technology. In particular, topological quantum computations are suggested in the non-abelian phase of Kitaev quantum spin liquid with Majorana fermions, and detection of Majorana fermions is one of the most outstanding problems in modern condensed matter physics. Here, we propose a concrete way to identify the non-abelian Kitaev quantum spin liquid by magnetic field angle dependence. Topologically protected critical lines exist on a plane of magnet…
Emergent excitation continua in frustrated magnets are a fingerprint of fractionalization, characteristic of quantum spin-liquid states. Recent evidence from Raman scattering for a coupling between such continua and lattice degrees of freedom in putative Kitaev magnets [1-6] may provide insight into the nature of the fractionalized quasiparticles. Here we study the renormalization of optical phonons coupled to the underlying $\mathbb{Z}_{2}$ quantum spin-liquid. We show that phonon line-shapes acquire an asymmetry, observable in light scattering, and originating from two distinct sources, name…
Fourier transform scanning tunneling spectroscopy (FT-STS) measures the scattering of conduction electrons from impurities and defects, giving information about the electronic structure of both the host material and adsorbed impurities. We interpret such FT-STS measurements in terms of the quasiparticle interference (QPI), investigating the QPI due to magnetic impurities adsorbed on a range of representative non-magnetic host surfaces, and contrasting with the case of a simple scalar impurity or point defect. We demonstrate how the electronic correlations present for magnetic impurities marked…
A fascinating type of symmetry-protected topological states of matter are topological Kondo insulators, where insulating behavior arises from Kondo screening of localized moments via conduction electrons, and non-trivial topology emerges from the structure of the hybridization between the local-moment and conduction bands. Here we study the physics of Kondo holes, i.e., missing local moments, in three-dimensional topological Kondo insulators, using a self-consistent real-space mean-field theory. Such Kondo holes quite generically induce in-gap states which, for Kondo holes at or near the surfa…
Quantum spin liquid is a disordered magnetic state with fractional spin excitations. Its clearest example is found in an exactly solved Kitaev honeycomb model where a spin flip fractionalizes into two types of anyons, quasiparticles that are neither fermions nor bosons: a pair of gauge fluxes and a Majorana fermion. Here we demonstrate this kind of fractionalization in the Kitaev paramagnetic state of the honeycomb magnet $α$-RuCl$_3$. The spin-excitation gap measured by nuclear magnetic resonance consists of the predicted Majorana fermion contribution following the cube of the applied magneti…
We study systems of multiple interacting quantum impurities deposited on a metallic surface in a 3D host. For the real-space two-impurity problem, using numerical renormalization group calculations, a rich range of behavior is shown to arise due to the interplay between Kondo physics and effective RKKY interactions - provided the impurity separation is small. Such calculations allow identification of the minimum impurity separation required for a description in terms of independent impurities, and thereby the onset of the 'dilute impurity limit' in many-impurity systems. A 'dilute cluster' lim…
A bond-directional anisotropic exchange interaction, called the Kitaev interaction, is a promising route to realize quantum spin liquids. The Kitaev interactions were found in Mott insulators with the strong spin-orbit coupling, in the presence of quantum interference between indirect electron transfers. Here we theoretically propose a different scenario by introducing a polar structural asymmetry that unbalances the quantum interference. We show that the imbalance activates additional exchange processes and gives rise to a dominant antiferromagnetic Kitaev interaction, in stark contrast to th…
A microscopic theory is presented for the observed electronic disorder in superconducting Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. The essential phenomenology is shown to be consistent with the existence of two types of interstitial oxygen dopants: those serving primarily as charge reserviors and those close to the apical plane contributing both carriers and electrostatic potential to the CuO$_2$ plane. The nonlinear screening of the latter produces nanoscale variations in the doped hole concentration, leading to electronic inhomogeneity. Based on an unrestricted Gutzwiller approximation of the extended…
A method is proposed to test for the nature of the pseudogap phase in cuprates using the recently developed technique of Fourier transform scanning tunneling spectroscopy. We show that the observed quasiparticle interference patterns depend critically on the quasiparticle coherence factors, making it possible to distinguish between the pseudogap dominated by superconducting fluctuations and by various particle-hole condensates.
Recent advances in scanning tunneling spectroscopy performed on heavy-fermion metals provide a window onto local electronic properties of composite heavy-electron quasiparticles. Here we theoretically investigate the energy and temperature evolution of single-particle spectra and their quasiparticle interference caused by point-like impurities in the framework of a periodic Anderson model. By numerically solving dynamical-mean-field-theory equations, we are able to access all temperatures and to capture the crossover from weakly interacting c and f electrons to fully coherent heavy quasipartic…
We describe the non-equilibrium dynamics of the Sachdev-Ye-Kitaev models of fermions with all-to-all interactions. These provide tractable models of the dynamics of quantum systems without quasiparticle excitations. The Kadanoff-Baym equations show that the final state is thermal, and their numerical analysis appears consistent with a thermalization rate proportional to the absolute temperature of the final state. We also obtain an exact analytic solution of the non-equilibrium dynamics in the large $q$ limit of a model with $q$ fermion interactions: in this limit, the thermalization of the fe…
We show that a single-fermion quantum dot acquires odd-frequency Gor'kov anomalous averages in proximity to strongly correlated Majorana zero modes, described by the Sachdev-Ye-Kitaev (SYK) model. Despite the presence of finite anomalous pairing, the superconducting gap vanishes for the intermediate coupling strength between the quantum dot and Majoranas. The increase of the coupling leads to smooth suppression of the original quasiparticles. This effect might be used as a characterization tool for recently proposed tabletop realizations of the SYK model.
We present scanning tunneling microscopy studies of the LaOFeAs parent compound of iron pnictide superconductors. Topographic imaging reveals two types of atomically flat surfaces, corresponding to the exposed LaO layer and FeAs layer respectively. On one type of surface, we observe strong standing wave patterns induced by quasiparticle interference of two-dimensional surface states. The distribution of scattering wavevectors exhibits pronounced two-fold symmetry, consistent with the nematic electronic structure found in the Ca(Fe1-xCox)2As2 parent state.
One of the key issues in unraveling the mystery of high Tc superconductivity in the cuprates is to understand the normal state outside the superconducting dome. Here we perform scanning tunneling microscopy and spectroscopy measurements on a heavily overdoped, non-superconducting (Bi,Pb)2Sr2CuO6+x cuprate. Spectroscopic imaging reveals dispersive quasiparticle interferences and the Fourier transforms uncover the evolution of momentum space topology. More interestingly, we observe nanoscale patches of static charge order with sqrt(2)*sqrt(2) periodicity. Both the dispersive quasiparticle interf…
Recent scanning tunnelling spectroscopy measurements [Y. Koksaka et al., Nature 454, 1072 (2008)] have shown that dispersing quasiparticle interference peaks in Fourier transformed conductance maps disappear as the bias voltage exceeds a certain threshold corresponding to the coincidence of the contour of constant quasiparticle energy with the antiferromagnetic zone boundary. Here we argue that this is caused by quasistatic short-range coexisting order present in the d-wave superconducting phase, and that the most likely origin of this order is disorder-induced incommensurate antiferromagnetis…
Phase-sensitive measurements of the superconducting gap in Fe-based superconductors have proven more difficult than originally anticipated. While quasiparticle interference (QPI) measurements based on scanning tunneling spectroscopy are often proposed as defnitive tests of gap structure, the analysis typically relies on details of the model employed. Here we point out that the temperature dependence of momentum-integrated QPI data can be used to identify gap sign changes in a qualitative way, and present an illustration for $s_{\pm}$ and $s_{++}$ states in a system with typical Fe-pnictide Fer…
The recent discovery of superconductivity in the iron-based layered pnictides with T_c ranging between 26 and 56K generated enormous interest in the physics of these materials. Here, we review some of the peculiarities of the antiferromagnetic order in the iron pnictides, including the selection of the stripe magnetic order and the formation of the Ising-nematic state in the unfolded BZ within an itinerant description. In addition we analyze the properties of the quasiparticle interference spectrum in the parent antiferromagnetic phase.
Electrons on the surface of a strong topological insulator, such as Bi2Te3 or Bi1-xSnx, form a topologically protected helical liquid whose excitation spectrum contains an odd number of massless Dirac fermions. A theoretical survey and classification is given of the universal features, observable by the ordinary and spin-polarized scanning tunneling spectroscopy, in the interference patterns resulting from the quasiparticle scattering by magnetic and non-magnetic impurities in such a helical liquid. Our results confirm the absence of backscattering from non-magnetic impurities observed in rece…
The stability of the topological order phase induced by the $Z_3$ Kitaev model, which is a candidate for fault-tolerant quantum computation, against the local order phase induced by the 3-State Potts model is studied. We show that the low energy sector of the Kitaev-Potts model is mapped to the Potts model in the presence of transverse magnetic field. Our study relies on two high-order series expansion based on continuous unitary transformations in the limits of small- and large-Potts couplings as well as mean-field approximation. Our analysis reveals that the topological phase of the $Z_3$ Ki…
Magnetoelastic interaction couples spin and lattice degrees of freedom and plays a key role in thermal transport properties of magnetic insulators. In the Kitaev quantum spin liquid, the low energy excitations are charge neutral Majorana fermions, which transform the magnetoelasctic interaction into Majorana-phonon scattering. Motivated by anomalous thermal properties of the Kitaev quantum spin liquid candidate RuCl$_3$, in this letter, we combine meV resolution inelastic x-ray scattering and theoretical calculation to examine the Majorana-phonon scattering. We analytically derive the velocity…
We investigate the quasiparticle interference in the heavy Fermion superconductor CeCoIn_5 as direct method to confirm the d-wave gap symmetry. The ambiguity between d_{xy} and d_{x^2-y^2} symmetry remaining from earlier specific heat and thermal transport investigations has been resolved in favor of the latter by the observation of a spin resonance that can occur only in d_{x^2-y^2} symmetry. However these methods are all indirect and depend considerably on theoretical interpretation. Here we propose that quasiparticle interference (QPI) spectroscopy by scanning tunneling microscopy (STM) can…
We report the first observation of coherent surface states on cubic perovskite oxide SrVO3(001) thin films through spectroscopic imaging scanning tunneling microscopy. A direct link between the observed atomic-scale interference patterns and the formation of a dxy-derived surface state is supported by first-principles calculations. Furthermore, we show that the apical oxygens on the topmost VO2 plane play a critical role in controlling the spectral weight of the observed coherent surface state.
The quasiparticle scattering interference phenomenon characterized by the peaks in the local density of states is studied within the kinetic energy driven superconducting mechanism in the presence of a single impurity. By calculation of the Fourier transformed ratio of the local density of states at opposite energy, it is shown that the quasiparticle scattering interference phenomenon can be described qualitatively by a single impurity in the kinetic energy driven homogeneous d-wave superconducting state. The amplitude of the peak increases with increasing energy at the low energy, and reaches…
We systematically calculate quasiparticle interference (QPI) signatures for the whole phase diagram of iron-based superconductors. Impurities inherent in the sample together with ordered phases lead to distinct features in the QPI images that are believed to be measured in spectroscopic imaging-scanning tunneling microscopy (SI-STM). In the spin-density wave phase the rotational symmetry of the electronic structure is broken, signatures of which are also seen in the coexistence regime with both superconducting and magnetic order. In the superconducting regime we show how the different scatteri…
Using a realistic ten-orbital tight-binding model Hamiltonian fitted to the angle-resolved photoemission (ARPES) data on LiFeAs, we analyze the temperature, frequency, and momentum dependencies of quasiparticle interference (QPI) to identify gap sign changes in a qualitative way, following our original proposal [Phys. Rev. B 92, 184513 (2015)]. We show that all features present for the simple two-band model for the sign-changing $s_{+-}$-wave superconducting gap employed previously are still present in the realistic tight-binding approximation and gap values observed experimentally. We discuss…
