arXiv subjects

Lucile Savary

Publications and source records attributed to Lucile Savary.

At least 19 recordsLinked to original sources

arXiv2025

Quantum geometry from the Moyal product: quantum kinetic equation and non-linear response

We systematically derive the dissipationless quantum kinetic equation for a multi-band free fermionic system with U(1) symmetry. Using the Moyal product formalism, we fully band-diagonalize the dynamics. Expanding to the second order in gradients, which is beyond the semiclassical limit, we give a complete analysis of the band-resolved thermodynamics and transport properties, especially those arising from the quantum geometric tensor. We apply our framework to a Bloch band theory under electric fields near equilibrium and find the linear and nonlinear transport coefficients. We also obtain the dynamical density-density response functions in the metallic case, including quantum metric corrections. Our results and approach can be applied very generally to multi-band problems even in situations with spatially varying Hamiltonians and distributions.

cond-mat.mes-hall↗

arXiv2025

Identifying Instabilities with Quantum Geometry in Flat Band Systems

The absence of a well-defined Fermi surface in flat-band systems challenges the conventional understanding of instabilities toward Landau order based on nesting. We investigate the existence of an intrinsic nesting structure encoded in the band geometry (i.e. the wavefunctions of the flat band(s)), which leads to a maximal susceptibility at the mean-field level and thus determines the instability towards ordered phases. More generally, we show that for a given band structure and observable, we can define two vector fields: one which corresponds to the Bloch vector of the projection operator onto the manifold of flat bands, and another which is "dressed" by the observable. The overlap between the two vector fields, possibly shifted by a momentum vector $\boldsymbol{Q}$, fully determines the mean field susceptibility of the corresponding order parameter. When the overlap is maximized, so is the susceptibility, and this geometrically corresponds to "perfect nesting" of the band structure. In that case, we show that the correlation length of this order parameter, even for $\boldsymbol{Q}\neq \boldsymbol{0}$, is entirely characterized by a generalized quantum metric in an intuitive manner, and is therefore lower-bounded in topologically non-trivial bands. As an example, we demonstrate hidden nesting for staggered antiferromagnetic spin order in an exactly flat-band model, which is notably different from the general intuition that flat bands are closely associated with ferromagnetism. We check the actual emergence of this long-range order using the determinantal quantum Monte Carlo algorithm. Additionally, we demonstrate that a Fulde-Ferrell-Larkin-Ovchinnikov-like state (pairing with non-zero center of mass momentum) can arise in flat bands upon breaking time-reversal symmetry, even if Zeeman splitting is absent.

cond-mat.str-el↗

arXiv2025

Analytic Formulas for the Anomalous Hall Effect in Itinerant Magnets

We clarify the origin of what is sometimes called the "topological anomalous Hall effect," provide analytical formulas to compute all the contributions to the Hall conductivity in the presence of Kondo-coupled spins and spin orbit coupling. The derivation is technical but we emphasize that the results can be very easily applied.

cond-mat.str-el↗

arXiv2024

Quantum kinetic equation and thermal conductivity tensor for bosons

We systematically derive the quantum kinetic equation in full phase space for any quadratic hamiltonian of bosonic fields, including in the absence of translational invariance. This enables the treatment of boundaries, inhomogeneous systems and states with non-trivial textures, such as skyrmions in the context of magnetic bosons. We relate the evolution of the distribution of bosons in phase space to single-electron, band-diagonal, physical quantities such as Berry curvature and energy magnetization, by providing a procedure to "diagonalize" the Hamiltonian in phase space, using the formalism of the Moyal product. We obtain exact equations, which can be expanded order by order, for example in the "smallness" of the spatial gradients, providing a "semiclassical" approximation. In turn, at first order, we recover the usual full Boltzmann equation and give a self-contained and exact derivation of the intrinsic thermal Hall effect of bosons. The formulation clarifies the contribution from "energy magnetization" in natural manner, and does not require the inclusion of Luttinger's pseudo-gravitational field to obtain thermal transport quantities.

cond-mat.str-el↗

arXiv2022

Thermal Conductivity and Theory of Inelastic Scattering of Phonons by Collective Fluctuations

We study the intrinsic scattering of phonons by a general quantum degree of freedom, i.e. a fluctuating "field" $Q$, which may have completely general correlations, restricted only by unitarity and translational invariance. From the induced scattering rates, we obtain the consequences on the thermal conductivity tensor of the phonons. We find that the lowest-order diagonal scattering rate, which determines the longitudinal conductivity, is controlled by two-point correlation functions of the $Q$ field, while the off-diagonal scattering rates involve a minimum of three to four point correlation functions. We obtain general and explicit forms for these correlations which isolate the contributions to the Hall conductivity, and provide a general discussion of the implications of symmetry and equilibrium. We evaluate these two- and four-point correlation functions and hence the thermal transport for the illustrative example of an ordered two dimensional antiferromagnet. In this case the $Q$ field is a composite of magnon operators arising from spin-lattice coupling. A numerical evaluation of the required integrals demonstrates that the results satisfy all the necessary symmetry restrictions but otherwise lead to non-vanishing scattering and Hall effects, and in particular that this mechanism leads to comparable thermal Hall conductivity for thermal currents within and normal to the plane of the antiferromagnetism.

cond-mat.str-el↗

arXiv2022

Phonon Thermal Hall Conductivity from Scattering with Collective Fluctuations

Because electrons and ions form a coupled system, it is a priori clear that the dynamics of the lattice should reflect symmetry breaking within the electronic degrees of freedom. This has been recently clearly evidenced for the case of time-reversal and mirror symmetry breakings by observations of a large phononic thermal Hall effect in many strongly correlated electronic materials. The mechanism by which time-reversal breaking and chirality is communicated to the lattice is, however, far from evident. In this paper we discuss how this occurs via many-body scattering of phonons by collective modes: a consequence of non-Gaussian correlations of the latter modes. We derive fundamental new results for such skew (i.e. chiral) scattering and the consequent thermal Hall conductivity. From this we also obtain general formulae for these quantities for ordered antiferromagnets. From the latter we obtain the scaling behavior of the phonon thermal Hall effect in clean antiferromagnets. The calculations show several different regimes and give quantitative estimates of similar order to that seen in recent experiments.

cond-mat.str-el↗

arXiv2022

Phase diagrams and excitations of anisotropic $S=1$ quantum magnets on the triangular lattice

The $S=1$ bilinear-biquadratic Heisenberg exchange model on the triangular lattice with a single-ion anisotropy has previously been shown to host a number of exotic magnetic and nematic orders [Moreno-Cardoner $\textit{et al.}$, Phys. Rev. B $\textbf{90}$, 144409 (2014)], including an extensive region of "supersolid" order. In this work, we amend the model by an XXZ anisotropy in the exchange interactions. Tuning to the limit of an exactly solvable $S=1$ generalized Ising-/Blume-Capel-type model provides a controlled limit to access phases at finite transverse exchange. Notably, we find an additional macroscopically degenerate region in the phase diagram and study its fate under perturbation theory. We further map out phase diagrams as a function of the XXZ anisotropy parameter, ratio of bilinear and biquadratic interactions and single-ion anisotropy, and compute corrections to the total ordered moment in various phases using systematically constructed linear flavor-wave theory. We also present linear flavor-wave spectra of various states, finding that the lowest-energy band in three-sublattice generalized (i.e. with $S^z=\pm1,0$) Ising/Blume-Capel states, stabilized by strong exchange anisotropies, is remarkably flat, opening up the way to flat-band engineering of magnetic excitation via stabilizing non-trivial Ising-ordered ground states.

cond-mat.str-el↗

arXiv2022

Anisotropic exchange and non-collinear antiferromagnets on a noncentrosymmetric fcc structure as in the half-Heuslers

One of the signatures of the face-centered cubic (fcc) antiferromagnet as a typical example of a geometrically frustrated system is the large ground state degeneracy of the classical nearest neighbor and next-nearest neighbor Heisenberg (isotropic) model on this lattice. In particular, collinear states are degenerate with non-collinear and non-coplanar ones: this degeneracy is accidental and is expected to be lifted by anisotropic exchange interactions. In this work, we derive the most general nearest and next-nearest neighbor exchange model allowed by the space-group symmetry of the noncentrosymmetric half-Heusler compounds, which includes three anisotropic terms: the so-called Kitaev, Gamma and Dzyaloshinskii-Moriya interactions -- most notably, the latter is allowed by the breaking of inversion symmetry in these materials and has not been previously been studied in the context of the fcc lattice. We compute the resulting phase diagram and show how the different terms lift the ground state degeneracy of the isotropic model, and lay emphasis on finding regimes where multi-q (non-collinear/non-coplanar) states are selected by anisotropy. We then discuss the role of quantum fluctuations and the coupling to a magnetic field in the ground state selection, and show that these effects can stabilize non-coplanar (triple-q) states. These results suggest that some half-Heusler antiferromagnets might host rare non-collinear/non-coplanar orders, which may in turn explain the unusual transport properties detected in these semimetals.

cond-mat.str-el↗

arXiv2021

Phonon Hall Viscosity in Magnetic Insulators

The Phonon Hall Viscosity is the leading term evincing time-reversal symmetry breaking in the low energy description of lattice phonons. It may generate phonon Berry curvature, and can be observed experimentally through the acoustic Faraday effect and thermal Hall transport. We present a systematic procedure to obtain the phonon Hall viscosity induced by phonon-magnon interactions in magnetic insulators under an external magnetic field. We obtain a general symmetry criterion that leads to non-zero Faraday rotation and Hall conductivity, and clarify the interplay between lattice symmetry, spin-orbit-coupling, external magnetic field and magnetic ordering. The symmetry analysis is verified through a microscopic calculation. By constructing the general symmetry-allowed effective action that describes the spin dynamics and spin-lattice coupling, and then integrating out the spin fluctuations, the leading order time-reversal breaking term in the phonon effective action, i.e. the phonon Hall viscosity, can be obtained. The analysis of the square lattice antiferromagnet for a cuprate Mott insulator, Sr$_2$CuO$_2$Cl$_2$, is presented explicitly, and the procedure described here can be readily generalized to other magnetic insulators.

cond-mat.str-el↗

arXiv2020

Nematic insulator at charge neutrality in twisted bilayer graphene

We investigate twisted bilayer graphene near charge neutrality using a generalized Bistritzer-MacDonald continuum model, accounting for corrugation effects. The Fermi velocity vanishes for particular twist angles properly reproducing the physics of the celebrated magic angles. Using group representation theory, we identify all contact interaction potentials compatible with the symmetries of the model. This enables us to identify two classes of quartic interactions leading to either the opening of a gap or to nematic ordering. We then implement a renormalization group analysis to study the competition between these interactions for a twist angle approaching the first magic value. This combined group theory-renormalization study reveals that the proximity to the first magic angle favors the occurrence of a layer-polarized, gapped state with a spatial modulation of interlayer correlations, which we call nematic insulator.

cond-mat.str-el↗

arXiv2020

Dimer description of the SU(4) antiferromagnet on the triangular lattice

In systems with many local degrees of freedom, high-symmetry points in the phase diagram can provide an important starting point for the investigation of their properties throughout the phase diagram. In systems with both spin and orbital (or valley) degrees of freedom such a starting point gives rise to SU(4)-symmetric models. Here we consider SU(4)-symmetric "spin" models, corresponding to Mott phases at half-filling, i.e. the six-dimensional representation of SU(4). This may be relevant to twisted multilayer graphene. In particular, we study the SU(4) antiferromagnetic "Heisenberg" model on the triangular lattice, both in the classical limit and in the quantum regime. Carrying out a numerical study using the density matrix renormalization group (DMRG), we argue that the ground state is non-magnetic. We then derive a dimer expansion of the SU(4) spin model. An exact diagonalization (ED) study of the effective dimer model suggests that the ground state breaks translation invariance, forming a valence bond solid (VBS) with a 12-site unit cell. Finally, we consider the effect of SU(4)-symmetry breaking interactions due to Hund's coupling, and argue for a possible phase transition between a VBS and a magnetically ordered state.

cond-mat.str-el↗

arXiv2018

Quantization of the thermal Hall conductivity at small Hall angles

We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev's non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity $κ_{xx}$ due to phonons is much larger than the expected quantized thermal Hall conductance $κ_{xy}^{\rm q}=\frac{πT}{12} \frac{k_B^2}{\hbar}$ of the ideal isolated edge mode, so that the thermal Hall angle, i.e., the angle between the thermal current and the temperature gradient, is small. By modeling the interaction between a Majorana edge and bulk phonons, we show that the exchange of energy between the two subsystems leads to a transverse component of the bulk current and thereby an {\em effective} Hall conductivity. Remarkably, the latter is equal to the quantized value when the edge and bulk can thermalize, which occurs for a Hall bar of length $L \gg \ell$, where $\ell$ is a thermalization length. We obtain $\ell \sim T^{-5}$ for a model of the Majorana-phonon coupling. We also find that the quality of the quantization depends on the means of measuring the temperature and, surprisingly, a more robust quantization is obtained when the lattice, not the spin, temperature is measured. We present general hydrodynamic equations for the system, detailed results for the temperature and current profiles, and an estimate for the coupling strength and its temperature dependence based on a microscopic model Hamiltonian. Our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, $κ_{xy}/κ_{xx} \sim 10^{-3}$, in $α$-RuCl$_3$.

cond-mat.str-el↗

arXiv2018

Pairing states of spin-3/2 fermions: Symmetry-enforced topological gap functions

We study the topological properties of superconductors with paired $j=\frac{3}{2}$ quasiparticles. Higher spin Fermi surfaces can arise, for instance, in strongly spin-orbit coupled band-inverted semimetals. Examples include the Bi-based half-Heusler materials, which have recently been established as low-temperature and low-carrier density superconductors. Motivated by this experimental observation, we obtain a comprehensive symmetry-based classification of topological pairing states in systems with higher angular momentum Cooper pairing. Our study consists of two main parts. First, we develop the phenomenological theory of multicomponent (i.e., higher angular momentum) pairing by classifying the stationary points of the free energy within a Ginzburg-Landau framework. Based on the symmetry classification of stationary pairing states, we then derive the symmetry-imposed constraints on their gap structures. We find that, depending on the symmetry quantum numbers of the Cooper pairs, different types of topological pairing states can occur: fully gapped topological superconductors in class DIII, Dirac superconductors and superconductors hosting Majorana fermions. Notably, we find a series of nematic fully gapped topological superconductors, as well as double-Dirac superconductors with quadratic dispersion. Our approach, applied here to the case of $j=\frac{3}{2}$ Cooper pairing, is rooted in the symmetry properties of pairing states, and can therefore also be applied to other systems with higher angular momentum and high-spin pairing. We conclude by relating our results to experimentally accessible signatures in thermodynamic and dynamic probes.

cond-mat.supr-con↗

arXiv2017

Superconductivity in three-dimensional spin-orbit coupled semimetals

Motivated by the experimental detection of superconductivity in the low-carrier density half-Heusler compound YPtBi, we study the pairing instabilities of three-dimensional strongly spin-orbit coupled semimetals with a quadratic band touching point. In these semimetals the electronic structure at the Fermi energy is described by spin j=3/2 quasiparticles, which are fundamentally different from those in ordinary metals with spin j=1/2. We develop a general approach to analyzing pairing instabilities in j=3/2 materials by decomposing the pair scattering interaction into irreducible channels, projecting them to the Fermi surface and deriving the corresponding Eliashberg theory. Applying our method to a generic density-density interaction in YPtBi we establish the following results: (i) The pairing strength in each channel uniquely encodes the j=3/2 nature of the Fermi surface band structure--a manifestation of the fundamental difference with ordinary metals. In particular, this implies that Anderson's theorem, which addresses the effect of spin-orbit coupling and disorder on pairing states of spin-1/2 electrons, cannot be applied in this case. (ii) The leading pairing instabilities are different for electron and hole doping. This implies that superconductivity depends on carrier type. (iii) In the case of hole doping--relevant to YPtBi, we find two odd-parity channels in close competition with s-wave pairing. One of these two channels is a multicomponent pairing channel, allowing for the possibility of time-reversal symmetry breaking. (iv) In the case of Coulomb interactions mediated by the long-ranged electric polarization of optical phonon modes, a significant coupling strength is generated in spite of the extremely low density of carriers. Furthermore, non-linear response and Fermi liquid corrections can favor non-s-wave pairing and potentially account for the experimentally-observed Tc.

cond-mat.supr-con↗

arXiv2016

Quantum spin ice on the breathing pyrochlore lattice

The Coulombic quantum spin liquid in quantum spin ice is an exotic quantum phase of matter that emerges on the pyrochlore lattice and is currently actively searched for. Motivated by recent experiments on the Yb-based breathing pyrochlore material Ba$_3$Yb$_2$Zn$_5$O$_{11}$, we theoretically study the phase diagram and magnetic properties of the relevant spin model. The latter takes the form of a quantum spin ice Hamiltonian on a breathing pyrochlore lattice, and we analyze the stability of the quantum spin liquid phase in the absence of the inversion symmetry which the lattice breaks explicitly at lattice sites. Using a gauge mean-field approach, we show that the quantum spin liquid occupies a finite region in parameter space. Moreover, there exists a direct quantum phase transition between the quantum spin liquid phase and featureless paramagnets, even though none of theses phases break any symmetry. At nonzero temperature, we show that breathing pyrochlores provide a much broader finite temperature spin liquid regime than their regular counterparts. We discuss the implications of the results for current experiments and make predictions for future experiments on breathing pyrochlores.

cond-mat.str-el↗

arXiv2016

Disorder-Induced Entanglement in Spin Ice Pyrochlores

We propose that in a certain class of magnetic materials, known as non-Kramers 'spin ice,' disorder induces quantum entanglement. Instead of driving glassy behavior, disorder provokes quantum superpositions of spins throughout the system, and engenders an associated emergent gauge structure and set of fractional excitations. More precisely, disorder transforms a classical phase governed by a large entropy, classical spin ice, into a quantum spin liquid governed by entanglement. As the degree of disorder is increased, the system transitions between (i) a "regular" Coulombic spin liquid, (ii) a phase known as "Mott glass," which contains rare gapless regions in real space, but whose behavior on long length scales is only modified quantitatively, and (iii) a true glassy phase for random distributions with large width or large mean amplitude.

cond-mat.str-el↗

arXiv2016

Quantum Spin Liquids

Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons that are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments to study quantum spin liquids, and to the diverse probes used therein.

cond-mat.str-el↗

arXiv2015

Quantum Loop States in Spin-Orbital Models on the Honeycomb Lattice

We construct a physically realistic and analytically tractable model for spin-1 systems with orbital degeneracy on the honeycomb lattice, relevant to honeycomb materials with large Hund's and weak spin-orbit couplings, and two electrons in t2g orbitals. This model realizes many new phases whose building blocks are orbital loops decorated by Haldane chains. These include a Haldane loop crystal, a symmetry-protected topological phase, and, notably, a regime where the decorated loops resonate. When taken to the three-dimensional hyperhoneycomb lattice, the latter regime becomes a (symmetry-enriched) U(1) quantum spin-orbital liquid, "disordered" both in the spin and orbital channels. We hope this construction will pave the way for realizing many of the Haldane-chain-based phases which have been theoretically proposed in the literature.

cond-mat.str-el↗