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Ultrafast dynamics of fractional particles in $\alpha$-RuCl$_3$

Haochen Zhang, Subin Kim, Young‐June Kim, Hae‐Young Kee, Luyi Yang

Published Aug 13, 2019• 0 citations
OpenAlex

Abstract

In a Kitaev spin liquid, electron spins can break into fractional particles known as Majorana fermions and Z$_2$ fluxes. Recent experiments have indicated the existence of such fractional particles in a two-dimensional Kitaev material candidate, $\alpha$-RuCl$_3$. These exotic particles can be used in topological quantum computations when braided within their lifetimes. However, the lifetimes of these particles, critical for applications in topological quantum computing, have not been reported. Here we study ultrafast dynamics of photoinduced excitations in single crystals of $\alpha$-RuCl$_3$ using pump-probe transient grating spectroscopy. We observe intriguing photoexcited nonequilibrium states in the Kitaev paramagnetic regime between $T_N$~7 K and $T_H$~100 K, where $T_N$ is the N\'eel temperature and $T_H$ is set by the Kitaev interaction. Two distinct lifetimes are detected: a longer lifetime of ~50 ps, independent of temperature; a shorter lifetime of 1-20 ps, with a strong temperature dependence, $T^{-1.40}$. We analyze the transient grating signals using coupled differential equations and propose that the long and short lifetimes are associated with fractional particles in the Kitaev paramagnetic regime, Z$_2$ fluxes and Majorana fermions, respectively.

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Ultrafast dynamics of fractional particles in α\alphaα-RuCl3_33​
In a Kitaev spin liquid, electron spins can break into fractional particles known as Majorana fermions and Z2_22​ fluxes. Recent experiments have indicated the existence of such fractional particles in a two-dimensional Kitaev material candidate, α\alphaα-RuCl3_33​. These exotic particles can be used in topological quantum computations when braided within their lifetimes. However, the lifetimes of these particles, critical for applications in topological quantum computing, have not been reported. Here we study ultrafast dynamics of photoinduced excitations in single crystals of α\alphaα-RuCl3_33​ using pump-probe transient grating spectroscopy. We observe intriguing photoexcited nonequilibrium states in the Kitaev paramagnetic regime between TNT_NTN​~7 K and THT_HTH​~100 K, where TNT_NTN​ is the N'eel temperature and THT_HTH​ is set by the Kitaev interaction. Two distinct lifetimes are detected: a longer lifetime of ~50 ps, independent of temperature; a shorter lifetime of 1-20 ps, with a strong temperature dependence, T−1.40T^{-1.40}T−1.40. We analyze the transient grating signals using coupled differential equations and propose that the long and short lifetimes are associated with fractional particles in the Kitaev paramagnetic regime, Z2_22​ fluxes and Majorana fermions, respectively.
Detecting spin dynamics in quantum spin liquids presents significant challenges. Here, the authors explore photoinduced excitations in the Kitaev spin liquid candidate $\ensuremath{\alpha}$-RuCl3{}_{3}3​ using heterodyne transient grating spectroscopy. This method allows for a comprehensive characterization of different photoinduced components. They identify signatures of spin excitations within the Kitaev paramagnetic phase. The two distinct lifetimes observed in this temperature regime, on the order of tens of picoseconds, likely correspond to the dynamics of unconventional spin excitations predicted by the Kitaev model.
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 characterized by topological entanglement and fractional excitations, whose possible application to topological quantum computation is recently discussed intensively. As a prime candidate for such exotic states, we here focus on the Kitaev magnets, a subgroup of the spin-orbit Mott insulators. After a brief overview of the Kitaev model and the fractionalization of spins in the exact ground state, we review recent explosive development in this rapidly growing field, with a focus on numerical solutions of the Kitaev model at finite temperatures and the comparison with experiments. The key concept is thermal fractionalization --- two types of fractional excitations manifest themselves at largely different temperatures. This leads to distinct thermodynamics and spin dynamics in a variety of experimentally measurable quantities. We discuss such peculiar behaviors as the signatures of fractional quasiparticles, in careful comparison with the available experimental data for the candidate materials of the Kitaev magnets. Our review gives an overview of the current status of the identification of Majorana fermions in the Kitaev magnets, which would serve as a basis for further experimental and theoretical studies toward the manipulation of the exotic particles for topological quantum computation.
High-field fate of the Kitaev quantum spin liquid in ααα-RuCl3_33​
Kitaev quantum spin liquids (KQSLs) host fractionalized excitations described by itinerant Majorana quasiparticles and gapped Z2Z_2Z2​ fluxes (visons), providing a platform for emergent topological matter. Whether such a state survives under strong magnetic fields, however, remains an open question. The layered honeycomb magnet ααα-RuCl3_33​ is a leading candidate material: an in-plane field of ∼\sim∼ 7 T suppresses antiferromagnetic order and induces a quantum-disordered phase exhibiting signatures consistent with Majorana excitations, including an anomalous thermal Hall effect and field-angle-dependent specific heat. At higher fields, the magnetization approaches saturation, suggesting a transition to a spin-polarized state, yet the microscopic evolution between these limits remains unresolved. Here we report high-field specific heat measurements up to 24 T that reveal a distinct crossover at $μ_0H^*\approx$15 T, beyond which the perturbative Kitaev description breaks down. Above H∗H^*H∗, the characteristic six-fold angular modulation of the specific heat collapses and the excitation gap deviates from the predicted H3H^3H3 scaling. Meanwhile, the gap decreases with increasing field and the in-plane magnetization anisotropy persists up to ∼\sim∼ 24 T, both in sharp contrast to a trivial spin-polarized state, indicating that KQSL signatures are preserved even at ∼\sim∼ 90 % of magnetization saturation. These results reveal that the KQSL in ααα-RuCl3_33​ extends well beyond the perturbative window, persisting as a nonperturbative regime in which the Majorana and vison energy scales merge, before eventually giving way to spin polarization. This thermodynamic roadmap provides a basis for understanding how fractionalized phases evolve under strong magnetic fields.
Unambiguous identification of fractionalized excitations in quantum spin liquids has been a long-standing issue in correlated topological phases. Conventional spectroscopic probes, such as the dynamical spin structure factor, can only detect composites of fractionalized excitations, leading to a broad continuum in energy. Lacking a clear signature in conventional probes has been the biggest obstacle in the field. In this work, we theoretically investigate what kinds of distinctive signatures of fractionalized excitations can be probed in two-dimensional nonlinear spectroscopy by considering the exactly solvable Kitaev spin liquids. We demonstrate the existence of a number of salient features of the Majorana fermions and fluxes in two-dimensional nonlinear spectroscopy, which provide crucial information about such excitations.
In Kitaev spin liquids, SSS = \textonehalf{} quantum spins on a honeycomb lattice with bond-dependent interactions fractionalize into Majorana fermions. Fingerprints of these fractionalized excitations can be detected via thermodynamic measurements. Here, the authors perform detailed heat capacity experiments on the spin-liquid candidate $\ensuremath{\alpha}$-RuCl3{}_{3}3​ as function of temperature and magnetic field. To estimate the intrinsic phonon contribution, they measure the nonmagnetic reference compound RhCl3{}_{3}3​ and perform $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ phonon calculations. Measurements and analysis provide experimental evidence of fractionalized excitations in good agreement with theoretical predictions.
Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response χyzx(2)(ω1,ω2)χ^{(2)}_{yzx}(ω_1, ω_2)χyzx(2)​(ω1​,ω2​) when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by Z2\mathbb{Z}_2Z2​ flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wavefunctions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our work can guide future 2DCS experiments on Kitaev magnets.