arXiv subjects

Natalia B. Perkins

Publications and source records attributed to Natalia B. Perkins.

At least 37 records · Page 2Linked to original sources

arXiv2024

Topological transitions in the Yao-Lee spin-orbital model and effects of site disorder

The Yao-Lee model is an example of exactly solvable spin-orbital models that are generalizations of the original Kitaev honeycomb model with extra local orbital degrees of freedom. Similar to the Kitaev model, both spin and orbital degrees of freedom are effectively represented using sets of three-flavored Majorana fermions. The Yao-Lee model exhibits a quantum spin liquid ground state with gapped and immobile $Z_2$ fluxes and three-fold degenerate itinerant Majorana fermions. Our work demonstrated that by introducing different time-reversal symmetry (TRS) breaking fields one can split the degeneracy of Majorana fermions and close the gap for some of the bands, thus changing its topology. We calculated a comprehensive topological phase diagram for the Yao-Lee model by considering various combinations of TRS-breaking fields. This investigation revealed the emergence of distinct topological regions, each separated by nodal lines, signifying an evolution in the model's topological properties. We also investigated the impact of vacancies in the system. Our findings revealed that while vacancies modify the low-energy spectrum of the model, their presence has a limited impact on the topological properties of the model, at least for small enough concentrations.

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arXiv2024

Beyond Kitaev physics in strong spin-orbit coupled magnets

We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To that end, we give a comprehensive overview of the most relevant exchange interactions in $d^5$ and $d^7$ iridates and similar compounds, an exposition of their microscopic origin, and a systematic attempt to map out the most interesting correlated regimes of the multi-dimensional parameter space, guided by powerful symmetry and duality transformations as well as by insights from wide-ranging analytical and numerical studies. We also survey recent exciting results on quasi-1D models and discuss their relevance to higher-dimensional models. Finally, we highlight some of the key questions in the field as well as future directions.

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arXiv2023

Dynamics of vacancy-induced modes in the non-Abelian Kitaev spin liquid

We study the dynamical response of vacancy-induced quasiparticle excitations in the site-diluted Kitaev spin liquid with a magnetic field. Due to the flux-binding effect and the emergence of dangling Majorana fermions around each spin vacancy, the low-energy physics is governed by a set of vacancy-induced quasi-zero-energy modes. These localized modes result in unique characteristics of the dynamical spin correlation functions, which intriguingly mimic the single-quasiparticle density of states and further exhibit a quasi-zero-frequency peak. By recognizing the potential observability of these local correlation functions via scanning tunneling microscopy (STM), we show how the STM response is sensitive to the local flux configuration, the magnetic field strength, and the vacancy concentration. Constructing a simple model of the localized modes, we also elucidate how the local correlation functions can be interpreted in terms of the hybridization between these modes.

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arXiv2023

Collective magnetic Higgs excitation in a pyrochlore ruthenate

The emergence of scalar Higgs-type amplitude modes in systems where symmetry is spontaneously broken has been a highly successful, paradigmatic description of phase transitions, with implications ranging from high-energy particle physics to low-energy condensed matter systems. Here, we uncover two successive high temperature phase transitions in the pyrochlore magnet Nd$_2$Ru$_2$O$_7$ at $T_{\mathrm{N}} = 147$ K and $T^* = 97$ K, that lead to giant phonon instabilities and culminate in the emergence of a highly coherent excitation. This coherent excitation, distinct from other phonons and from conventional magnetic modes, stabilizes at a low energy of 3 meV. We assign it to a collective Higgs-type amplitude mode, that involves bond energy modulations of the Ru$_4$ tetrahedra. Its striking two-fold symmetry, incompatible with the underlying crystal structure, highlights the possibility of multiple entangled broken symmetries.

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arXiv2023

Vacancy spectroscopy of non-Abelian Kitaev spin liquids

Spin vacancies in the non-Abelian Kitaev spin liquid are known to harbor Majorana zero modes, potentially enabling topological quantum computing at elevated temperatures. Here, we study the spectroscopic signatures of such Majorana zero modes in a scanning tunneling setup where a non-Abelian Kitaev spin liquid with a finite density of spin vacancies forms a tunneling barrier between a tip and a substrate. Our key result is a well-defined peak close to zero bias voltage in the derivative of the tunneling conductance whose voltage and intensity both increase with the density of vacancies. This ''quasi-zero-voltage peak'' is identified as the closest analog of the zero-voltage peak observed in topological superconductors that additionally reflects the fractionalized nature of spin-liquid-based Majorana zero modes. We further highlight a single-fermion Van Hove singularity at a higher voltage that reveals the energy scale of the emergent Majorana fermions in the Kitaev spin liquid. Our proposed signatures are within reach of current experiments on the candidate material $α$-RuCl$_3$.

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arXiv2023

Phonon Dynamics in the Generalized Kitaev Spin Liquid

Candidate materials for the Kitaev spin liquid generically have residual interactions beyond the Kitaev coupling. It therefore becomes necessary to understand how signatures of the quantum spin liquid, e.g., fractionalization of the spin excitations, are affected by the presence of these interactions. Recently it was shown that phonon dynamics is an indirect but effective probe to study fractionalized excitations in the Kitaev spin liquid. Ultrasound experiments can measure sound attenuation, which should show characteristic temperature and angular dependence of the sound attenuation coefficient if the scattering of phonons happens predominantly on Majorana fermions. So far the computation of the sound attenuation was only done in the pure spin-phonon coupled Kitaev model, without taking into account residual interactions. In order to understand experimental signatures, here we present a mean-field study of the sound attenuation in the generalized $J$-$K$-$Γ$ model, which is relevant to candidate materials. Our findings show that as long as the system is in the spin liquid phase, characteristic features of the sound attenuation remain observable even in the presence of residual interactions.

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arXiv2023

Fractionalized Excitations Probed by Ultrasound

In this work, we study magnetoelastic interactions by means of ultrasound experiments in $α$-RuCl$_3$ -- a prototypical material for the Kitaev spin model on the honeycomb lattice, with a possible spin-liquid state featuring Majorana fermions and $\mathbb{Z}_{2}$-flux excitations. We present results of the temperature and in-plane magnetic-field dependence of the sound velocity and sound attenuation for several longitudinal and transverse phonon modes propagating along high-symmetry crystallographic directions. A comprehensive data analysis above the ordered state provides strong evidence of phonon scattering by Majorana fermions. This scattering depends sensitively on the value of the phonon velocities relative to the characteristic velocity of the low-energy fermionic excitations describing the spin dynamics of the underlying Kitaev magnet. Moreover, our data displays a distinct reduction of anisotropy of the sound attenuation, consistent with randomization, generated by thermally excited $\mathbb{Z}_2$ visons. We demonstrate the potential of phonon dynamics as a promising probe for uncovering fractionalized excitations in $α$-RuCl$_3$ and provide new insights into the $H$-$T$ phase diagram of this material.

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arXiv2022

Magnetic Excitations and Interactions in the Kitaev Hyperhoneycomb Iridate $β$-Li$_2$IrO$_3$

We present a thorough experimental study of the three-dimensional hyperhoneycomb Kitaev magnet $β$-Li$_2$IrO$_3$, using a combination of inelastic neutron scattering (INS), time-domain THz spectroscopy, and heat capacity measurements. The main results include a massive low-temperature reorganization of the INS spectral weight that evolves into a broad peak centered around 12 meV, and a distinctive peak in the THz data at 2.8(1) meV. A detailed comparison to powder-averaged spin-wave theory calculations reveals that the positions of these two features are controlled by the anisotropic $Γ$ coupling and the Heisenberg exchange $J$, respectively. The refined microscopic spin model places $β$-Li$_2$IrO$_3$ in close proximity to the Kitaev spin liquid phase.

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arXiv2022

Sound attenuation in the hyperhoneycomb Kitaev spin liquid

In recent years, it has been shown that the phonon dynamics may serve as an indirect probe of fractionalization of spin degrees of freedom. Here we propose that the sound attenuation measurements allows for the characterization and identification of the Kitaev quantum spin liquid on the hyperhoneycomb lattice, which is particularly interesting since the strong Kitaev interaction was observed in the the hyperhoneycomb magnet $β$-Li$_2$IrO$_3$. To this end we consider the low-temperature scattering between acoustic phonons and gapless Majorana fermions with nodal-line band structure. We find that the sound attenuation has a characteristic angular dependence, which is explicitly shown for the high-symmetry planes at temperatures below the flux gap energy.

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arXiv2022

Spin- and Flux-gap Renormalization in the Random Kitaev Spin Ladder

We study the Kitaev spin ladder with random couplings by using the real-space renormalization group technique. This model is the minimum model in Kitaev systems that has conserved plaquette fluxes, and its quasi-one-dimensional geometry makes it possible to study the strong-disorder fixed points for both spin- and flux- excitation gaps. In the Ising limit, the behavior of the spin gap is consistent with the familiar random transverse-field Ising chain, but the flux gap is dominated by the y-coupling. In the XX limit, while the x- and y-couplings are renormalized simultaneously, the z-couplings are not renormalized drastically and lead to non-universal disorder criticality at low-energy scales.

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arXiv2022

Signatures of non-Loudon-Fleury Raman scattering in the Kitaev magnet $β$-Li$_2$IrO$_3$

We investigate the magnetic excitations of the hyperhoneycomb Kitaev magnet $β$-$\text{Li}_2\text{IrO}_3$ by means of inelastic Raman scattering. The spectra exhibits a coexistence of a broad scattering continuum and two sharp low-energy peaks at 2.5 meV and 3 meV, with a distinctive polarization dependence. While the continuum is suggestive of fractional quasi-particles emerging from a proximate quantum spin liquid phase, the sharp peaks provide the first experimental signature of the `non-Loudon-Fleury' one-magnon scattering processes proposed recently [Phys. Rev. B 104, 144412 (2021)]. The corresponding microscopic mechanism is similar to the one leading to the symmetric off-diagonal exchange interaction $Γ$ (as it involves a combination of both direct and ligand-mediated exchange paths), but is otherwise completely unexpected within the traditional Loudon-Fleury theory of Raman scattering. The present experimental verification therefore calls for a drastic reevaluation of Raman scattering in similar systems with strong spin orbit coupling and multiple exchange paths.

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arXiv2021

Non-Loudon-Fleury Raman scattering in spin-orbit coupled Mott insulators

We revisit the theory of magnetic Raman scattering in Mott insulators with strong spin-orbit coupling, with a major focus on Kitaev materials. We show that Kitaev materials with bond-anisotropic interactions are generally expected to show both one- and two-magnon responses. It is further shown that, in order to obtain the correct leading contributions to the Raman vertex operator $\mc{R}$, one must take into account the precise, photon-assisted microscopic hopping processes of the electrons and that, in systems with multiple hopping paths, $\mc{R}$ contains terms beyond those appearing in the traditional Loudon-Fleury theory. Most saliently, a numerical implementation of the revised formalism to the case of the three-dimensional hyperhoneycomb Kitaev material $β$-Li$_2$IrO$_3$ reveals that the non-Loudon-Fleury scattering terms actually dominate the Raman intensity. In addition, they induce a qualitative modification of the polarization dependence, including, e.g., the emergence of a sharp one-magnon peak at low energies which is not expected in the traditional Loudon-Fleury theory. This peak is shown to arise from microscopic photon-assisted tunneling processes that are of similar type with the ones leading to the symmetric off-diagonal interaction $Γ$ (known to be present in many Kitaev materials), but take the form of a bond-directional magnetic dipole term in the Raman vertex. These results are expected to apply across all Kitaev materials and mark a drastic change of paradigm for the understanding of Raman scattering in materials with strong spin-orbit coupling and multiple exchange paths.

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arXiv2021

Temperature evolution of the phonon dynamics in the Kitaev spin liquid

Here we present a study of the phonon dynamics in the honeycomb Kitaev spin model at finite temperatures. We show that the fractionalized spin excitations of the Kitaev spin liquid, the itinerant Majorana fermions and static $Z_2$ fluxes, have distinct effects on the phonon dynamics, which makes the phonon dynamics a promising tool for exploring the Kitaev spin liquid candidate materials. In particular, we will focus on the signature of the fractionalized excitations in the thermodynamic behaviour of the sound attenuation and the phonon Hall viscosity: The former describes the phonon decay into the fractionalized excitations, and the later is the leading order time reversal symmetry breaking effect on the acoustic phonon. We find that the angular dependence of the attenuation coefficient and its magnitude are modified by the thermal excitation of the $Z_2$ fluxes. The strength of this effect strongly depends on the relative magnitude of the sound velocity and the Fermi velocity characterizing the low-energy Majorana fermions. We also show that the Hall viscosity is strongly suppressed by the increase of the density of the $Z_2$ fluxes at finite temperatures. All these observations reflect the effects of the emergent disorder on the Majorana fermions introduced by the $Z_2$ fluxes. Our analysis is based on the complementary analytical calculations in the low-temperature zero-flux sector, and numerical calculations in the inhomogeneous flux sectors at intermediate and high temperatures with stratified Monte Carlo (strMC) method.

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arXiv2021

Disorder upon disorder: localization effects in the Kitaev spin liquid

In recent years, several magnetic Mott insulators with strong spin-orbit couplings were suggested to be proximate to the Kitaev quantum spin liquid (QSL) whose one of the most exciting features is the fractionalization of spin excitations into itinerant Majorana fermions and static $Z_2$ fluxes. Motivated by the emergence of this plethora of 4d and 5d transition metal Kitaev materials and by the fact that some level of disorder is inevitable in real materials, here we study how the Kitaev QSL responds to various forms of disorder, such as vacancies, impurities, and bond randomness. First, we argue that the presence of the quenched disorder in the Kitaev QSL can lead to the Anderson localization of Majorana fermions and the appearance of Lifshitz tails. We point out that the Anderson localization of low-energy states is particularly strong in the extended Kitaev model with the time reversal symmetry breaking term. Second, we show that the disorder effects on the low-energy Majorana fermion modes can be detected in thermal transport. Third, we show that at finite temperatures the $Z_2$ fluxes become thermally excited and give rise to an additional disorder for the Majorana fermions. This source of the disorder dominates at high temperatures. Fourth, we demonstrate that both the structure of the energy spectrum and the thermal transport properties of the disordered Kitaev QSL depend strongly on the character of disorder. While we find that both the site disorder and the bond randomness suppress the longitudinal thermal conductivity, the low-energy localization is stronger in the case of the site disorder.

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arXiv2021

Magnon-spinon dichotomy in the Kitaev hyperhoneycomb $β$-Li$_2$IrO$_3$

The family of edge-sharing tri-coordinated iridates and ruthenates has emerged in recent years as a major platform for Kitaev spin liquid physics, where spins fractionalize into emergent magnetic fluxes and Majorana fermions with Dirac-like dispersions. While such exotic states are usually pre-empted by long-range magnetic order at low temperatures, signatures of Majorana fermions with long coherent times have been predicted to manifest at intermediate and higher energy scales, similar to the observation of spinons in quasi-1D spin chains. Here we present a Resonant Inelastic X-ray Scattering study of the magnetic excitations of the hyperhoneycomb iridate $β$-Li$_2$IrO$_3$ under a magnetic field with a record-high-resolution spectrometer. At low-temperatures, dispersing spin waves can be resolved around the predicted intertwined incommensurate spiral and field-induced zigzag orders, whose excitation energy reaches a maximum of 16meV. A 2T magnetic field softens the dispersion around ${\bf Q}=0$. The behavior of the spin waves under magnetic field is consistent with our semiclassical calculations for the ground state and the dynamical spin structure factor, which further predicts that the ensued intertwined uniform states remain robust up to very high fields (100 T). Most saliently, the low-energy magnon-like mode is superimposed by a broad continuum of excitations, centered around 35meV and extending up to 100meV. This high-energy continuum survives up to at least 300K -- well above the ordering temperature of 38K -- and gives evidence for pairs of long-lived Majorana fermions of the proximate Kitaev spin liquid.

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arXiv2021

Further insights into the thermodynamics of the Kitaev honeycomb model

Here we revisit the thermodynamics of the Kitaev quantum spin liquid realized on the honeycomb lattice. We address two main questions: First, we investigate whether there are observable thermodynamic signatures of the topological Majorana boundary modes of the Kitaev honeycomb model. We argue that for the time-reversal invariant case the residual low-temperature entropy is the primary thermodynamic signature of these Majorana edge modes, and verify using large-scale Monte Carlo simulations that this residual entropy is present in the full Kitaev model. When time-reversal symmetry is broken, the Majorana edge modes are potentially observable in more direct thermodynamic measurements such as the specific heat, though only at temperatures well below the bulk gap. % Second, we study the energetics, and the corresponding thermodynamic signatures, of the flux excitations in the Kitaev model. Specifically, we study the flux interactions on both cylinder and torus geometries numerically, and quantify their impact on the thermodynamics of the Kitaev spin liquid by using a polynomial fit for the average flux energy as a function of flux density and extrapolating it to the thermodynamic limit. By comparing this model to Monte Carlo simulations, we find that flux interactions have a significant quantitative impact on the shape and the position of the low-temperature peak in the specific heat.

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arXiv2020

Phonon dynamics in the Kitaev spin liquid

The search for fractionalization in quantum spin liquids largely relies on their decoupling with the environment. However, the spin-lattice interaction is inevitable in a real setting. While the Majorana fermion evades a strong decay due to the gradient form of spin-lattice coupling, the study of the phonon dynamics may serve as an indirect probe of fractionalization of spin degrees of freedom. Here we propose that the signatures of fractionalization can be seen in the sound attenuation and the Hall viscosity. Despite the fact that both quantities can be related to the imaginary part of the phonon self-energy, their origins are quite different, and the time-reversal symmetry breaking is required for the Hall viscosity. First, we compute the sound attenuation due to a phonon scattering off of a pair of Majorana fermions and show that it is linear in temperature ($\sim T$). We argue that it has a particular angular dependence providing the information about the spin-lattice coupling and the low-energy Majorana fermion spectrum. The observable effects in the absence of time-reversal symmetry are then analyzed. We obtain the phonon Hall viscosity term from the microscopic Hamiltonian with time-reversal symmetry breaking term. Importantly, the Hall viscosity term mixes the longitudinal and transverse phonon modes and renormalize the spectrum in a unique way, which may be probed in spectroscopy measurement.

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arXiv2020

Vacancy-induced low-energy density of states in the Kitaev spin liquid

The Kitaev honeycomb model has attracted significant attention due to its exactly solvable spin-liquid ground state with fractionalized Majorana excitations and its possible materialization in magnetic Mott insulators with strong spin-orbit couplings. Recently, the 5d-electron compound H$_{3}$LiIr$_{2}$O$_{6}$ has shown to be a strong candidate for Kitaev physics considering the absence of any signs of a long-range ordered magnetic state. In this work, we demonstrate that a finite density of random vacancies in the Kitaev model gives rise to a striking pileup of low-energy Majorana eigenmodes and reproduces the apparent power-law upturn in the specific heat measurements of H$_{3}$LiIr$_{2}$O$_{6}$. Physically, the vacancies can originate from various sources such as missing magnetic moments or the presence of non-magnetic impurities (true vacancies), or from local weak couplings of magnetic moments due to strong but rare bond randomness (quasivacancies). We show numerically that the vacancy effect is readily detectable even at low vacancy concentrations and that it is not very sensitive neither to nature of vacancies nor to different flux backgrounds. We also study the response of the site-diluted Kitaev spin liquid to the three-spin interaction term, which breaks time-reversal symmetry and imitates an external magnetic field. We propose a field-induced flux-sector transition where the ground state becomes flux free for larger fields, resulting in a clear suppression of the low temperature specific heat. Finally, we discuss the effect of dangling Majorana fermions in the case of true vacancies and show that their coupling to an applied magnetic field via the Zeeman interaction can also account for the scaling behavior in the high-field limit observed in H$_{3}$LiIr$_{2}$O$_{6}$.

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