arXiv subjects

Francesco Grandi

Publications and source records attributed to Francesco Grandi.

14 recordsLinked to original sources

arXiv2026

Electronic correlations and fluctuating lattice distortions in vanadium dioxide

Metal-insulator transitions in correlated materials are often accompanied by a change of crystal structure. They are commonly described within a coherent lattice approximation, which combines a correlated treatment of the electrons with a lattice represented by one or a few classical distortion coordinates fixed by minimizing an energy. The structural degrees of freedom then carry no entropy of their own, even though the partition of the transition entropy between electrons and lattice is often what decides the transition temperature. Here we develop a stochastic semiclassical extension of dynamical mean-field theory in which correlated electrons and fluctuating lattice distortions are evolved together, extending previous formulations from linear to nonlinear electron-phonon interactions and from a single to several coupled lattice modes. The resulting non-conservative Langevin equations have deterministic forces, damping, and correlated noise generated self-consistently by the interacting electronic subsystem. Applying the approach to a minimal two-orbital model containing the two symmetry-distinct distortions of the monoclinic phase of vanadium dioxide, we find that the two distortions melt at well separated temperatures, giving an insulating, an intermediate metallic, and a high-symmetry phase. The two transitions have different origins: the melting of the dimerization is driven by the coupling to the correlated electrons and is captured already within the coherent lattice approximation, whereas the restoration of the undistorted structure requires the entropy of the fluctuating lattice. Since the electronic subsystem is treated within nonequilibrium dynamical mean-field theory, the framework can be extended in future work to photoexcited systems with nonthermal electronic distributions.

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arXiv2024

Theories for charge-driven nematicity in kagome metals

Starting from a low-energy continuum model for the band dispersion of the $2 \times 2$ charge-ordered phase of the kagome metals $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs), we show that nematicity can develop in this state driven either by three inequivalent $1 \times 4$ charge fluctuations preemptive of a $1 \times 4$ charge order (CO), or by an actual zero momentum $d$-wave charge Pomeranchuk instability (PI). We perform a Kohn-Luttinger analysis in the particle-hole sector, which allows us to establish a criterion for the development of an attractive nematic channel near the onset of the $1 \times 4$ CO and near the $d$-wave charge PI, respectively. We derive an effective charge-fermion model for the $d$-wave PI with a nematic susceptibility given via a random phase approximation (RPA) summation. By contrast, for the finite momentum CO, the RPA scheme breaks down and needs to be improved upon by including Aslamazov-Larkin contributions to the nematic pairing vertex. We then move to the derivation of the Ginzburg-Landau potentials for the $1 \times 4$ CO and for the $d$-wave PI, and we obtain the corresponding analytical expression for the nematic susceptibility at the nematic transition temperature T $ \sim \text{T}_\text{nem}$ in both cases. Our work establishes a relation between the nematicity observed in some of the iron-based superconductors, where the nematic phase might be driven by spin fluctuations, and the vanadium-based kagome metals, where charge fluctuations likely induce nematicity. The two microscopic mechanisms we propose for the stabilization of the nematic state in $A$V$_3$Sb$_5$ are distinguishable by diffusive scattering experiments, meaning that it is possible to gauge which of the two theories, if any, is the most likely to describe this phase. Both mechanisms might also be relevant for the recently discovered titanium-based family $A$Ti$_3$Sb$_5$.

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arXiv2024

Nonthermal order by disorder

The quench dynamics of systems exhibiting cooperative or almost competitive orders in equilibrium are explored using Ginzburg-Landau theory plus fluctuations. We show that when the renormalization of the free energy by fluctuations is taken into account, anisotropic stiffnesses and relaxation rates of the order parameters can lead to a stabilization of ordered states at transient free energy minima which are distinct from any (global or local) minima of the equilibrium free energy. This theory demonstrates that nonequilibrium fluctuations play a pivotal role in forming nonthermal orders. As nonthermal order and nonthermal fluctuations mutually stabilize each other over some time, this mechanism could be seen as a nonequilibrium variant of the order-by-disorder phenomenon. We discuss the potential relevance of these findings for systems with intertwined orders, such as superconductivity and density wave orders, relevant for high-temperature superconductors and the kagome metals, as well as for systems that show orbital ordering.

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arXiv2024

Nonequilibrium control of kagome metals

Exotic quantum order in kagome metals, i.e., quantum materials with a Fermi liquid parent state of electrons on a kagome lattice, has appeared as a vibrant emerging field of condensed matter physics. Already in a small kagome material subclass such as vanadium-based compounds $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs), the first wave of experimental exploration has brought about manifold evidence for hitherto largely elusive phenomena such as high-temperature charge ordering with orbital currents, nematic order, cascades of charge ordering transitions with hierarchies of ordering vectors, and unconventional superconductivity. We argue that kagome metals promise to be a prototypical ground for the non-equilibrium analysis of quantum order through time-dependent parameter control and manipulation. In particular, we propose to investigate the nematic character of kagome quantum order through light and strain pulses, as well as the nature of time-reversal symmetry breaking and chirality through properly polarized laser pulses.

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arXiv2024

The kagome Hubbard model from a functional renormalization group perspective

The recent discovery of a variety of intricate electronic order in kagome metals has sprouted significant theoretical and experimental interest. From an electronic perspective on the potential microscopic origin of these phases, the most basic model is given by a Hubbard model on the kagome lattice. We employ functional renormalization group (FRG) to analyze the kagome Hubbard model. Through our methodological refinement of FRG both within its N-patch and truncated unity formulation, we resolve previous discrepancies of different FRG approaches (Wang et al., 2013 vs. Kiesel et al., 2013), and analyze both the pure ($p$-type) and mixed ($m$-type) van Hove fillings of the kagome lattice. We further study the RG flow into symmetry broken phases to identify the energetically preferred linear combination of the respective order parameter without any need for additional mean field analysis. Our findings suggest some consistency with recent experiments, and underline the richness of electronic phases already found in the kagome Hubbard model. We also provide a no-go theorem for a complex charge bond ordered phase in the single orbital kagome Hubbard model, suggesting that this model cannot capture aspects of orbital current phases.

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arXiv2023

Stochastic semiclassical theory for non-equilibrium electron-phonon coupled systems

We discuss a semiclassical approach to solve the quantum impurity model within non-equilibrium dynamical mean-field theory for electron-lattice models. The effect of electronic fluctuations on the phonon is kept beyond Ehrenfest dynamics, leading to a stochastic phonon evolution with damping and noise terms that are self-consistently determined by the electronic correlation functions in the fluctuating phonon field. Together with a solution of the electronic model based on a non-perturbative quantum Boltzmann equation, the approach can be used to address the coupled dynamics of the electrons and the lattice during photo-induced phase transitions. Results for the Anderson-Holstein model are benchmarked against numerically exact quantum Monte Carlo data. We find good agreement for the phonon distribution function at temperatures comparable to the charge ordering temperature. The general formulation can be extended to models with electron-electron interactions or multi-orbital systems.

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arXiv2023

Inhomogeneous disordering at a photo-induced charge density wave transition

Using ultrashort laser pulses, it has become possible to probe the dynamics of long-range order in solids on microscopic timescales. In the conventional description of symmetry-broken phases within time-dependent Ginzburg-Landau theory, the order parameter evolves coherently, with small fluctuations along an average trajectory. Recent experiments, however, indicate that some systems can support a different scenario, named ultrafast inhomogeneous disordering, where the average order parameter is no longer representative of the state on the atomic scale. Here we theoretically show that ultrafast disordering can occur in a minimal, yet paradigmatic, model for a Peierls instability if atomic scale inhomogeneities of both the electronic structure and the charge density wave order parameter are taken into account. The latter is achieved using a non-equilibrium generalization of statistical dynamical mean-field theory, coupled to stochastic differential equations for the order parameter.

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arXiv2023

Theory of nematic charge orders in kagome metals

Kagome metals $A$V$_3$Sb$_5$ ($A=$K, Rb, Cs) exhibit an exotic charge order (CO), involving three order parameters, with broken translation and time-reversal symmetries compatible with the presence of orbital currents. The properties of this phase are still intensely debated, and it is unclear if the origin of the CO is mainly due to electron-electron or electron-phonon interactions. Most of the experimental studies confirm the nematicity of this state, a feature that might be enhanced by electronic correlations. However, it is still unclear whether the nematic CO becomes stable at a temperature equal to ($T_{\text{nem}} = T_\text{C}$) or lower than ($T_{\text{nem}} < T_\text{C}$) the one of the CO itself. Here, we systematically characterize several CO configurations, some proposed for the new member of the family ScV$_6$Sn$_6$, by combining phenomenological Ginzburg-Landau theories, valid irrespective of the specific ordering mechanism, with mean-field analysis. We find a few configurations for the CO that are in agreement with most of the experimental findings to date and that are described by different Ginzburg-Landau potentials. We propose to use resonant ultrasound spectroscopy to experimentally characterize the order parameters of the CO, such as the number of their components and their relative amplitude, and provide an analysis of the corresponding elastic tensors. This might help understand which mean-field configuration found in our study is the most representative for describing the CO state of kagome metals, and it can provide information regarding the nematicity onset temperature $T_\text{nem}$ with respect to $T_\text{C}$.

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arXiv2022

Ultrafast control of spin-orbital separation probed with time-resolved RIXS

Quasi-one-dimensional systems exhibit many-body effects elusive in higher dimensions. A prime example is spin-orbital separation, which has been measured by resonant inelastic X-ray scattering (RIXS) in Sr$_2$CuO$_3$. Here, we theoretically analyze the time-resolved RIXS spectrum of Sr$_2$CuO$_3$ under the action of a time-dependent electric field. We show that the external field can reversibly modify the parameters in the effective $t-J$ model used to describe spinon and orbiton dynamics in the material. For strong driving amplitudes, we find that the spectrum changes qualitatively as a result of reversing the relative spinon to orbiton velocity. The analysis shows that in general, the spin-orbital dynamics in Mott insulators in combination with time-resolved RIXS should provide a suitable platform to explore the reversible control of many-body physics in the solid with strong laser fields.

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arXiv2021

Ultrafast metal-to-insulator switching in a strongly correlated system

Light-manipulation of correlated electronic phases in solids offers the tantalizing prospect of realizing electronic devices operating at the ultrafast time-scale. In this context, the experimental realization of non-equilibrium transitions from a metal to a band or Mott insulator has shown to be particularly elusive. Using dynamical mean-field theory, we study a simple model representing the main physical properties of the oxygen-enriched compound LaTiO$_{3+x}$. By properly optimizing the photo-doping of electrons from a low-energy band into the valence states of the system, we show it is possible to induce a valence transition from a correlated metallic state to a Mott insulator at ultrashort time scales and to contain the heating during this process, with the final non-thermal valence insulator having almost the same effective temperature of the starting metal.

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arXiv2021

Fluctuation control of non-thermal orbital order

Orbitally ordered states exhibit unique features which make them a promising platform for exploring the ultrafast dynamics of long-range order in solids: Their free energy typically has multiple discrete minima, and electric laser fields or selectively excited phonons can exert effective forces that may be used to steer the order parameter through these free energy landscapes. Moreover, their free energy strongly depends on fluctuations, and in some cases restoring forces close to a minimum are exclusively of entropic origin (order-by-disorder mechanisms). This can open pathways to control the dynamics of the order parameter via non-thermal fluctuations. In this work, we study the laser-induced non-equilibrium dynamics in a $120^\circ$ compass model, using time-dependent Ginzburg-Landau theory. We analyze protocols to switch the order parameter between equivalent configurations, with a focus on the interplay between the external force due to the driving field, and the non-thermal entropic forces. In particular, we find that remanent non-thermal fluctuations after some excitation can stabilize the high-symmetry phase even when the homogeneous potential has retrieved its low-temperature form, which facilitates laser-induced switching.

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arXiv2021

Ultrafast Mott transition driven by nonlinear electron-phonon interaction

Nonlinear phononics holds the promise for controlling properties of quantum materials on the ultrashort timescale. Using nonequilibrium dynamical mean-field theory, we solve a model for the description of organic solids, where correlated electrons couple nonlinearly to a quantum phonon mode. Unlike previous works, we exactly diagonalize the local phonon mode within the noncrossing approximation to include the full phononic fluctuations. By exciting the local phonon in a broad range of frequencies near resonance with an ultrashort pulse, we show it is possible to induce a Mott insulator-to-metal phase transition. Conventional semiclassical and mean-field calculations, where the electron-phonon interaction decouples, underestimate the onset of the quasiparticle peak. This fact, together with the nonthermal character of the photoinduced metal, suggests a leading role of the phononic fluctuations and of the dynamic nature of the state in the vibrationally induced quasiparticle coherence.

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arXiv2020

Unraveling the Mott-Peierls intrigue in Vanadium dioxide

Vanadium dioxide is one of the most studied strongly correlated materials. Nonetheless, the intertwining between electronic correlation and lattice effects has precluded a comprehensive description of the rutile metal to monoclinic insulator transition, in turn triggering a longstanding "the chicken or the egg" debate about which comes first, the Mott localisation or the Peierls distortion. Here, we suggest that this problem is in fact ill-posed: the electronic correlations and the lattice vibrations conspire to stabilise the monoclinic insulator, and so they must be both considered not to miss relevant pieces of the VO$_2$ physics. Specifically, we design a minimal model for VO$_2$ that includes all the important physical ingredients: the electronic correlations, the multi-orbital character, and the two components antiferrodistortive mode that condenses in the monoclinic insulator. We solve this model by dynamical mean-field theory within the adiabatic Born-Oppenheimer approximation. Consistently with the first-order character of the metal-insulator transition, the Born-Oppenheimer potential has a rich landscape, with minima corresponding to the undistorted phase and to the four equivalent distorted ones, and which translates into an equally rich thermodynamics that we uncover by the Monte Carlo method. Remarkably, we find that a distorted metal phase intrudes between the low-temperature distorted insulator and high-temperature undistorted metal, which sheds new light on the debated experimental evidence of a monoclinic metallic phase.

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arXiv2018

Correlation-driven Lifshitz transition and orbital order in a two-band Hubbard model

We study by dynamical mean field theory the ground state of a quarter-filled Hubbard model of two bands with different bandwidths. At half-filling, this model is known to display an orbital selective Mott transition, with the narrower band undergoing Mott localisation while the wider one being still itinerant. At quarter-filling, the physical behaviour is different and to some extent reversed. The interaction generates an effective crystal field splitting, absent in the Hamiltonian, that tends to empty the narrower band in favour of the wider one, which also become more correlated than the former at odds with the orbital selective paradigm. Upon increasing the interaction, the depletion of the narrower band can continue till it empties completely and the system undergoes a topological Lifshitz transition into a half-filled single-band metal that eventually turns insulating. Alternatively, when the two bandwidths are not too different, a first order Mott transition intervenes before the Lifshitz's one. The properties of the Mott insulator are significantly affected by the interplay between spin and orbital degrees of freedom.

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