Spinon Fermi Surface Research Articles

Magnetocaloric effect of topological excitations in Kitaev magnets

Traditional magnetic sub-Kelvin cooling relies on the nearly free local moments in hydrate paramagnetic salts, whose utility is hampered by the dilute magnetic ions and low thermal conductivity. Here we propose to use instead fractional excitations inherent to quantum spin liquids (QSLs) as an alternative, which are sensitive to external fields and can induce a very distinctive magnetocaloric effect. With state-of-the-art tensor-network approach, we compute low-temperature properties of Kitaev honeycomb model. For the ferromagnetic case, strong demagnetization cooling effect is observed due to the nearly free Z2 vortices via spin fractionalization, described by a paramagnetic equation of state with a renormalized Curie constant. For the antiferromagnetic Kitaev case, we uncover an intermediate-field gapless QSL phase with very large spin entropy, possibly due to the emergence of spinon Fermi surface and gauge field. Potential realization of topological excitation magnetocalorics in Kitaev materials is also discussed, which may offer a promising pathway to circumvent existing limitations in the paramagnetic hydrates.

Transition between Heavy-Fermion-Strange-Metal and Quantum Spin Liquid in a 4d-Electron Trimer Lattice.

We present experimental evidence that a heavy Fermi surface consisting of itinerant, charge-neutral spinons underpins both heavy-fermion-strange-metal (without f electrons) and quantum-spin-liquid states in the 4d-electron trimer lattice, Ba_{4}Nb_{1-x}Ru_{3+x}O_{12}(|x|<0.20). These two exotic states both exhibit an extraordinarily large entropy, a linear heat capacity extending into the milli-Kelvin regime, a linear thermal conductivity at low temperatures, and separation of charges and spins. Furthermore, the insulating spin liquid is a much better thermal conductor than the heavy-fermion-strange-metal that separately is observed to strongly violate the Wiedemann-Franz law. We propose that at the heart of this 4d system is a universal, heavy spinon Fermi surface that provides a unified framework for explaining the exotic phenomena observed throughout the entire series. The control of such exotic ground states provided by variable Nb concentration offers a new paradigm for studies of correlated quantum matter.

Machine learning reveals features of spinon Fermi surface

With rapid progress in simulation of strongly interacting quantum Hamiltonians, the challenge in characterizing unknown phases becomes a bottleneck for scientific progress. We demonstrate that a Quantum-Classical hybrid approach (QuCl) of mining sampled projective snapshots with interpretable classical machine learning can unveil signatures of seemingly featureless quantum states. The Kitaev-Heisenberg model on a honeycomb lattice under external magnetic field presents an ideal system to test QuCl, where simulations have found an intermediate gapless phase (IGP) sandwiched between known phases, launching a debate over its elusive nature. We use the correlator convolutional neural network, trained on labeled projective snapshots, in conjunction with regularization path analysis to identify signatures of phases. We show that QuCl reproduces known features of established phases. Significantly, we also identify a signature of the IGP in the spin channel perpendicular to the field direction, which we interpret as a signature of Friedel oscillations of gapless spinons forming a Fermi surface. Our predictions can guide future experimental searches for spin liquids.

Phonon thermal transport shaped by strong spin-phonon scattering in a Kitaev material Na2Co2TeO6

The report of a half-quantized thermal Hall effect and oscillatory structures in the magnetothermal conductivity in the Kitaev material α-RuCl3 have sparked a strong debate on whether it is generated by Majorana fermion edge currents, spinon Fermi surface, or whether other more conventional mechanisms are at its origin. Here, we report low temperature thermal conductivity (κ) of another candidate Kitaev material, Na2Co2TeO6. The application of a magnetic field (B) along different principal axes of the crystal reveals a strong directional-dependent B impact on κ, while no evidence for mobile quasiparticles except phonons can be concluded at any field. Instead, severely scattered phonon transport prevails across the B−T phase diagram, revealing cascades of phase transitions for all B directions. Our results thus cast doubt on recent proposals for significant itinerant magnetic excitations in Na2Co2TeO6, and emphasize the importance of discriminating true spin liquid transport properties from scattered phonons in candidate materials.

Detecting fractionalization in critical spin liquids using color centers

Quantum spin liquids are highly entangled ground states of insulating spin systems, in which magnetic ordering is prevented down to the lowest temperatures due to quantum fluctuations. One of the most extraordinary characteristics of quantum spin liquid phases is their ability to support fractionalized, low-energy quasiparticles known as spinons, which carry spin-1/2 but bear no charge. Relaxometry based on color centers in crystalline materials—of which nitrogen-vacancy (NV) centers in diamond are a well-explored example—provides an exciting new platform to probe the spin spectral functions of magnetic materials with both energy and momentum resolution and to search for signatures of these elusive, fractionalized excitations. In this work, we theoretically investigate the color-center relaxometry of two archetypal quantum spin liquids: the two-dimensional U(1) quantum spin liquid with a spinon Fermi surface and the spin-1/2 antiferromagnetic spin chain. The former is characterized by a metallic, spin-split ground state of mobile, interacting spinons, which closely resembles a spin-polarized Fermi liquid ground state but with neutral quasiparticles. We show that the observation of the Stoner continuum and the collective spin wave mode in the spin spectral function would provide a strong evidence for the existence of spinons and fractionalization. In one dimension, mobile spinons form a Luttinger liquid ground state. We show that the spin spectral function exhibits strong features representing the collective density and spin-wave modes, which are broadened in an algebraic fashion with an exponent characterized by the Luttinger parameter. The possibilities of measuring these collective modes and detecting the power-law decay of the spectral weight using NV relaxometry are discussed. We also examine how the transition rates are modified by marginally irrelevant operators in the Heisenberg limit. Published by the American Physical Society 2024

Possible quantum-spin-liquid state in van der Waals cluster magnet Nb3Cl8

The cluster magnet Nb3Cl8 consists of Nb3 trimmers that form an emergent S = 1/2 two-dimensional triangular layers, which are bonded by weak van der Waals interactions. Recent studies show that its room-temperature electronic state can be well described as a single-band Mott insulator. However, the magnetic ground state is non-magnetic due to a structural transition below about 100 K. Here we show that there exists a thickness threshold below which the structural transition will not happen. For a bulk crystal, a small fraction of the sample maintains the high-temperature structure at low temperatures and such remnant gives rise to linear-temperature dependence of the specific heat at very low temperatures. This is further confirmed by the measurements on ground powder sample or c-axis pressed single crystals, which prohibits the formation of the non-magnetic state. Moreover, the intrinsic magnetic susceptibility also tends to be constant with decreasing temperature. Our results suggest that Nb3Cl8 with the high-temperature structure may host a quantum-spin-liquid ground state with spinon Fermi surfaces, which can be achieved by making the thickness of a sample smaller than a certain threshold.

Spinon Heat Transport in the Three-Dimensional Quantum Magnet PbCuTe_{2}O_{6}.

Quantum spin liquids (QSLs) are novel phases of matter which remain quantum disordered even at the lowest temperature. They are characterized by emergent gauge fields and fractionalized quasiparticles. Here we show that the sub-kelvin thermal transport of the three-dimensional S=1/2 hyperhyperkagome quantum magnet PbCuTe_{2}O_{6} is governed by a sizeable charge-neutral fermionic contribution which is compatible with the itinerant fractionalized excitations of a spinon Fermi surface. We demonstrate that this hallmark feature of the QSL state is remarkably robust against sample crystallinity, large magnetic field, and field-induced magnetic order, ruling out the imitation of QSL features by extrinsic effects. Our findings thus reveal the characteristic low-energy features of PbCuTe_{2}O_{6} which qualify this compound as a true QSL material.

Alternative Structure Model of Correlated Charge Density Wave in Monolayer 1T-Nb(Ta)Se2.

The putative Mott charge density wave (CDW) phases of monolayer 1T-NbSe2 and 1T-TaSe2 have attracted a lot of recent interest due to the unexpected orbital texture of their Mott-Hubbard states and the superstructure related to an exotic possibility of a quantum spin liquid with a spinon Fermi surface. The origins of the orbital texture and the superstructure have been, however, elusive. We find by using density functional theory calculations that these CDW phases can have an alternative metastable structure, an anion (Se) centered cluster, in contrast to the prevailing model of a cation (Nb or Ta) centered David star cluster. This structure can be stabilized by the charge transfer from the bilayer graphene/SiC substrate used commonly in the experiments. The anion-centered structure has a similar electronic band structure of a charge transfer insulator to that of DS clusters but naturally explains the orbital texture of the upper Hubbard band from simply its atomic structure. Moreover, this band structure exhibits a Fermi surface nesting to possibly break the symmetry spontaneously into a -R30° superstructure observed experimentally. The resulting ground state of the superstructure is shown to be a trivial band insulator, in contrast to exotic proposals. This result emphasizes the huge structural flexibility of these heteroexpitaxial monolayers, for which careful studies on atomic structures and interactions with substrates are highly requested.

Electronic density of states of a U(1) quantum spin liquid with spinon Fermi surface. II. Zeeman magnetic field effects

This work studies the Zeeman magnetic field effect on a quantum spin liquid with a spinon Fermi surface. In the absence of gauge binding, the quantum spin liquid electronic density of states exhibits no Zeeman shift in the threshold energy. As the gauge binding increases, the band edge resonance peaks exhibit a reduced Zeeman shift and eventually have the Zeeman shift direction reversed for a sufficiently large gauge binding. The authors further suggest to use such anomalous Zeeman response to identify the gapless quantum spin liquid phase.

Electronic density of states of aU(1)quantum spin liquid with spinon Fermi surface. I. Orbital magnetic field effects

The authors study the orbital magnetic field induced Landau quantization of a quantum spin liquid with spinon Fermi surface. In the electronic density of states of the quantum spin liquid, the Landau quantization is found to induce a set of band-edge steps, band-edge resonance peaks, or in-gap bound states when the gauge-field fluctuations are negligible, weak, or strong, respectively. The results indicate that the Landau quantization of the spinon Fermi surface can be detected through scanning tunneling microscope measurements.

Proposal to detect emergent gauge field and its Meissner effect in spin liquids using NV centers

We show that NV centers could provide distinct signatures of emergent gauge fields in certain phase transitions in spin liquids. We consider the relaxation rate $1/T_1$ of a diamond NV center placed a distance $z_0$ above a crystal consisting of two dimensional layers which hosts a $U(1)$ quantum spin liquid with spinon Fermi surface. We show that during a spinon pairing transition from a $U(1)$ to a $\mathbb{Z}_2$ spin liquid, the relaxation rate exhibits a rapid fall just below the pairing transition. The drop is much faster than what can be accounted for by the opening of the energy gap. Instead, the rapid fall with a unique $z_0$ dependence of its height and width, is the signature of the Meissner effect of the gauge field. We identify the organic ET compound which has a phase transition at 6K as a candidate for the experimental observation of this phenomenon.

Spectral function of the J1−J2 Heisenberg model on the triangular lattice

Triangular lattice compounds have received extensive attention recently as quantum spin liquid candidates. Here, the authors look at the ${J}_{1}$-${J}_{2}$ Heisenberg model on the triangular lattice, and calculate the spectral function relevant for neutron scattering experiments. They find a high-energy spectrum consistent with reports of a spinon Fermi surface state in triangular lattice compounds, although the low-energy spectrum rules out such a phase, and points towards a U(1) Dirac spin liquid. They provide clear signatures to look for in future neutron scattering experiments to distinguish these two phases.

Spin-Liquid Insulators Can Be Landau's Fermi Liquids.

The long search for insulating materials that possess low-energy quasiparticles carrying electron's quantum numbers except charge-inspired by the neutral spin-1/2 excitations, the so-called spinons, exhibited by Anderson's resonating-valence-bond state-seems to have reached a turning point after the discovery of several Mott insulators displaying the same thermal and magnetic properties as metals, including quantum oscillations in a magnetic field. Here, we show that such anomalous behavior is not inconsistent with Landau's Fermi liquid theory of quasiparticles at a Luttinger surface. That is the manifold of zeros within the Brillouin zone of the single-particle Green's function at zero frequency, and which thus defines the spinon Fermi surface conjectured by Anderson.

Hund's coupling and spin-orbit interaction in the three-band Hubbard model: Anomalous mass renormalization in Sr2RuO4

We study electronic correlation effects in the three-band Hubbard model in presence of Hund's and spin-orbit couplings using slave-spin mean-field theory. We consider three different regimes of hopping parameter values for the model on a square lattice. For orbital diagonal and isotropic hopping, we show that spin-orbit coupling (SOC), in general, enhances electronic correlations via the reduction of orbital degeneracy. In presence of Hund's coupling $J$, SOC tends to oppose the effect of $J$ on electronic correlations. Considering symmetry allowed anisotropic hopping, we find that the quasiparticle weights become orbital selective in presence of interaction. The effect of $J$ is particularly interesting for the band filling of two particles per site. Here, the Janus-faced effect of $J$ on correlation is obtained only in the narrower band, whereas electronic correlation in the wider band get reduced by $J$ for all values of Hubbard repulsion $U$. For model parameters corresponding to ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, interestingly, we find that the mass renormalizations in the bands become anomalous in presence of strong $U$ and $J$. The effective mass enhancement in the wider band becomes greater compared to that in the narrower band. We show that it originates in the peculiar electronic band structure of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, in which the spinon Fermi surface topology changes in a particular way in the presence of interactions.

Doping a Mott insulator with excitons in a moiré bilayer: Fractional superfluid, neutral Fermi surface, and Mott transition

In this paper we explore possible phases arising from doping neutral excitons into a Mott insulator in the context of moir\'e bilayers. We consider two moir\'e layers coupled together only through inter-layer repulsion and there is a U(2)$\times$ U(2) symmetry. The densities of the two layers can be tuned to be $n_t=x,n_b=1-x$ with $n_t+n_b=1$. $x=0$ limit is a layer polarized Mott insulator and small $x$ regime can be reached by doping inter-layer excitons at density $x$. Charge gap can remain finite at small $x$, as is demonstrated experimentally in the WSe$_2$-hBN-WSe$_2$/WS$_2$ system. To capture the intertwinement of the spin and exciton degree of freedom, we propose a four-flavor spin model. In addition to the obvious possibility of single exciton condensation phase, we also identified more exotic physics with fractionalization: (I) We define spin gap $\Delta_t, \Delta_b$ for the two layers respectively. As long as the spin gap at either layer is finite, single exciton condensation is impossible and we can only have paired exciton condensation. If both spin gaps are finite, it can be a fractional exciton superfluid with paired exciton condensation coexisting with $Z_2$ spin liquid. Numerical evidences for such a phase will be provided. (II) If the layer polarized Mott insulator at $x=0$ is in a U(1) spin liquid with spinon Fermi surface, the natural phase at $x>0$ hosts neutral Fermi surface formed by fermionic excitons. There are metallic counter-flow transport and also Friedel oscillations in layer polarization in this exotic phase. Our numerical simulation in one dimension observes an analog of this neutral Fermi surface phase. (III) There could be a metal-insulator transition (MIT) by tuning $x$ in the universality class of a bandwidth tuned MIT. We provide one theory for such a continuous Mott transition and predicted a universal drag resistivity.

Theory of a continuous bandwidth-tuned Wigner-Mott transition

We develop a theory for a continuous bandwidth-tuned transition at fixed \textit{fractional} electron filling from a metal with a generic Fermi surface to a `Wigner-Mott' insulator that spontaneously breaks crystalline space-group symmetries. Across the quantum critical point, (i) the entire electronic Fermi surface disappears abruptly upon approaching from the metallic side, and (ii) the insulating charge gap and various order parameters associated with the spontaneously broken space-group symmetries vanish continuously upon approaching from the insulating side. Additionally, the insulating side hosts a Fermi surface of neutral spinons. We present a framework for describing such continuous metal-insulator transitions (MITs) and analyze the example of a bandwidth-tuned transition at a filling, $\nu=1/6$, for spinful electrons on the triangular lattice. By extending the theory to a certain large-$N$ limit, we provide a concrete example of such a continuous MIT and discuss numerous experimental signatures near the critical point. We place our results in the context of recent experiments in moir\'e transition metal dichalcogenide materials.

Collective effects in an incompressible electronic liquid.

Starting from Landau's kinetic equation, we show that an electronic liquid in d = 2, 3 spatial dimensions depicted by a Landau-type effective theory will become incompressible on condition that the Landau parameters satisfy either (i) [Formula: see text] or (ii) [Formula: see text]. Condition (i) is the Pomeranchuk instability in the current channel and suggests a quantum spin liquid (QSL) state with a spinon Fermi surface; while condition (ii) means that the strong repulsion in the charge channel leads to a conventional charge and thermal insulator. In the collisionless regime (ωτ ≫ 1) and the hydrodynamic regime (ωτ ≪ 1), the zero and first sound modes have been studied and classified by symmetries, including the longitudinal and transverse modes in d = 2, 3 and the higher angular momentum modes in d = 3. The sufficient (and/or necessary) conditions of these collective modes have been revealed. It has been demonstrated that some of these collective modes will behave in quite different manners under incompressibility condition (i) or (ii). Possible nematic QSL states and a hierarchy structure for gapless QSL states have been proposed in d = 3.

Probing the quantum noise of the spinon Fermi surface with NV centers

We study the transverse electrical conductivity and the corresponding magnetic noise of a two-dimensional U(1) spin liquid state with a spinon Fermi surface. We show that in the quasi-static regime these responses have the same wave-vector dependence as that of a metal but are reduced by a dimensionless pre-factor controlled by the ratio of orbital diamagnetic susceptibilities of the spinons and chargons, correcting previous work. We estimate that this quasi-static regime is comfortably accessed by the typical NV center splittings of a few GHz and estimate that the expected T1 times for an NV center placed above candidate materials, such as the organic dmit and ET salts, monolayer 1T-TaS2/Se2, would range from several tens to a few hundred milliseconds.

Noncoplanar magnetic orders and gapless chiral spin liquid on the kagome lattice with staggered scalar spin chirality

Chiral three-spin interactions can suppress long-range magnetic order and stabilize quantum spin liquid states in frustrated lattices. We study a spin-1/2 model on the kagome lattice involving a staggered three-spin interaction J_\chiJχ in addition to Heisenberg exchange couplings J_1J1 on nearest-neighbor bonds and J_dJd across the diagonals of the hexagons. We explore the phase diagram using a combination of a classical approach, parton mean-field theory, and variational Monte Carlo methods. We obtain a variety of noncoplanar magnetic orders, including a phase that interpolates between cuboc-1 and cuboc-2 states. In the regime of dominant J_{\chi}Jχ, we find a classically disordered region and argue that it may harbor a gapless chiral spin liquid with a spinon Fermi surface. Our results show that the competition between the staggered three-spin interaction and Heisenberg exchange interactions gives rise to unusual ground states of spin systems.

Spin dynamics, entanglement, and the nature of the spin liquid state in YbZnGaO4

Electron spin dynamics was studied down to 80 mK in the triangular-lattice quantum spin-liquid candidate ${\mathrm{YbZnGaO}}_{4}$ using muon spin relaxation, finding no evidence for freezing or ordering of the Yb spins. The muon spin relaxation rate can be represented by the sum of two contributions, one dependent on longitudinal magnetic field and the other independent of field. The field-dependent term follows the form expected for two-dimensional diffusion of mobile spin excitations. The spin-diffusion rate obtained for these excitations in the high temperature paramagnetic regime is comparable with the exchange coupling frequency $J/h$, reducing significantly in the low temperature quantum regime. This slowdown is assigned to the effect of quantum entanglement. The exchange coupling $J$ is estimated to be 2.0(2) K from the crossover between the two regimes. The field-independent term is only weakly dependent on temperature, and at 15 K its absolute value is consistent with dipolar coupling of the muon to the three Yb moments closest to the muon site, where the spin dynamics of these moments is determined by exchange fluctuations. The temperature-dependent properties in the quantum regime are compared against the three possible U(1) spin-liquid models that have been obtained for the strongly spin-orbit coupled triangular lattice by Y.-D. Li, Y.-M. Lu, and G. Chen [Phys. Rev. B 96, 054445 (2017)]. The comparison with theory takes published specific heat and thermal conductivity data into account, along with the spin-diffusion rate obtained from the muons. It is found that the nodal spin-liquid model U1A11 containing both linear and quadratic nodes provides better agreement with experiment than either the U1A00 spinon Fermi surface (FS) model or the U1A01 model that contains only linear nodes.