Unraveling the Mott-Peierls intrigue in vanadium dioxide
Grandi F., Amaricci A., 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 localization or the Peierls distortion. Here, we suggest that this problem is in fact ill posed: The electronic correlations and the lattice vibrations conspire to stabilize the monoclinic insulator, and so they must be both considered to not miss relevant pieces of the VO2 physics. Specifically, we design a minimal model for VO2 that includes all the important physical ingredients: The electronic correlations, the multiorbital character, and the two components of the antiferrodistortive mode that condense 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.
Reply to: Ultrafast evolution and transient phases of a prototype out-of-equilibrium Mott-Hubbard material
Boschetto D., Weis M., Zhang J., Caillaux J., Nilforoushan N., Lantz G., Mansart B., Papalazarou E., Moisan N., Grieger D., Perfetti L., Jacques V.L.R., Bolloc’h D.L., Laulhé C., Ravy S., Rueff J.P., Glover T.E., Hertlein M.P., Hussain Z., Song S., Chollet M., Valley Jahn-Teller Effect in Twisted Bilayer Graphene
Angeli M., Tosatti E., The surprising insulating and superconducting states of narrow-band graphene twisted bilayers have been mostly discussed so far in terms of strong electron correlation, with little or no attention to phonons and electron-phonon effects. We found that, among the 33 492 phonons of a fully relaxed θ=1.08° twisted bilayer, there are few special, hard, and nearly dispersionless modes that resemble global vibrations of the moiré supercell, as if it were a single, ultralarge molecule. One of them, doubly degenerate at Γ with symmetry A1+B1, couples very strongly with the valley degrees of freedom, also doubly degenerate, realizing a so-called EâŠ-e Jahn-Teller (JT) coupling. The JT coupling lifts very efficiently all degeneracies which arise from the valley symmetry, and may lead, for an average atomic displacement as small as 0.5 m Å, to an insulating state at charge neutrality. This insulator possesses a nontrivial topology testified by the odd winding of the Wilson loop. In addition, freezing the same phonon at a zone boundary point brings about insulating states at most integer occupancies of the four ultraflat electronic bands. Following that line, we further study the properties of the superconducting state that might be stabilized by these modes. Since the JT coupling modulates the hopping between AB and BA stacked regions, pairing occurs in the spin-singlet Cooper channel at the inter-(AB-BA) scale, which may condense a superconducting order parameter in the extended s-wave and/or d±id-wave symmetry.
Lindblad dissipative dynamics in the presence of phase coexistence
Nava A., We investigate the dissipative dynamics yielded by the Lindblad equation within the coexistence region around a first-order phase transition. In particular, we consider an exactly solvable, fully connected quantum Ising model with n-spin exchange (n>2) - the prototype of quantum first-order phase transitions - and several variants of the Lindblad equations. We show that physically sound results, including exotic nonequilibrium phenomena such as the Mpemba effect, can be obtained only when the Lindblad equation involves jump operators defined for each of the coexisting phases, whether stable or metastable.
Early-stage dynamics of metallic droplets embedded in the nanotextured Mott insulating phase of V2 O3
Ronchi A., Homm P., Menghini M., Franceschini P., Maccherozzi F., Banfi F., Ferrini G., Cilento F., Parmigiani F., Dhesi S.S., Unveiling the physics that governs the intertwining between the nanoscale self-organization and the dynamics of insulator-to-metal transitions (IMTs) is key for controlling on demand the ultrafast switching in strongly correlated materials and nanodevices. A paradigmatic case is the IMT in V2O3, for which the mechanism that leads to the nucleation and growth of metallic nanodroplets out of the supposedly homogeneous Mott insulating phase is still a mystery. Here, we combine x-ray photoemission electron microscopy and ultrafast nonequilibrium optical spectroscopy to investigate the early-stage dynamics of isolated metallic nanodroplets across the IMT in V2O3 thin films. Our experiments show that the low-temperature monoclinic antiferromagnetic insulating phase is characterized by the spontaneous formation of striped polydomains, with different lattice distortions. The insulating domain boundaries accommodate the birth of metallic nanodroplets, whose nonequilibrium expansion can be triggered by the photoinduced change of the 3d-orbital occupation. We address the relation between the spontaneous nanotexture of the Mott insulating phase in V2O3 and the timescale of the metallic seeds growth. We speculate that the photoinduced metallic growth can proceed along a nonthermal pathway in which the monoclinic lattice symmetry of the insulating phase is partially retained.
Exciton Mott transition revisited
Guerci D., Capone M., The dissociation of excitons into a liquid of holes and electrons in photoexcited semiconductors, despite being one of the first recognized examples of a Mott transition, still defies a complete understanding, especially regarding the nature of the transition, which is found to be continuous in some cases and discontinuous in others. Here we consider an idealized model of photoexcited semiconductors that can be mapped onto a spin-polarized half-filled Hubbard model, whose phase diagram reproduces most of the phenomenology of those systems and uncovers the key role of the exciton binding energy in determining the nature of the exciton Mott transition. We find indeed that the transition changes from discontinuous to continuous as the binding energy increases. Moreover, we uncover a rather anomalous electron-hole liquid phase next to the transition, which still sustains excitonic excitations despite being a degenerate Fermi liquid of heavy mass quasiparticles.
Charge Disproportionation, Mixed Valence, and Janus Effect in Multiorbital Systems: A Tale of Two Insulators
Isidori A., Berović M., Fanfarillo L., De'Medici L., Multiorbital Hubbard models host strongly correlated "Hund's metals" even for interactions much stronger than the bandwidth. We characterize this interaction-resilient metal as a mixed-valence state. In particular, it can be pictured as a bridge between two strongly correlated insulators: a high-spin Mott insulator and a charge-disproportionated insulator which is stabilized by a very large Hund's coupling. This picture is confirmed comparing models with negative and positive Hund's coupling for different fillings. Our results provide a characterization of the Hund's metal state and connect its presence with charge disproportionation, which has indeed been observed in chromates and proposed to play a role in iron-based superconductors.
Emergent D6 symmetry in fully relaxed magic-angle twisted bilayer graphene
Angeli M., Mandelli D., Valli A., Amaricci A., Capone M., Tosatti E., We present a tight-binding calculation of a twisted bilayer graphene at magic angle θ∼1.08, allowing for full, in- and out-of-plane, relaxation of the atomic positions. The resulting band structure displays, as usual, four narrow minibands around the neutrality point, well separated from all other bands after the lattice relaxation. A thorough analysis of the miniband Bloch functions reveals an emergent D6 symmetry, despite the lack of any manifest point-group symmetry in the relaxed lattice. The Bloch functions at the Γ point are degenerate in pairs, reflecting the so-called valley degeneracy. Moreover, each of them is invariant under C3z, i.e., transforming like a one-dimensional, in-plane symmetric irreducible representation of an "emergent" D6 group. Out of plane, the lower doublet is even under C2x, while the upper doublet is odd, which implies that at least eight Wannier orbitals, two s-like and two pz-like ones for each of the supercell sublattices AB and BA, are necessary but probably not sufficient to describe the four minibands. This unexpected one-electron complexity is likely to play an important role in the still unexplained metal-insulator-superconductor phenomenology of this system.
Correlation-driven Lifshitz transition and orbital order in a two-band Hubbard model
Grandi F., Amaricci A., Capone M., 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 localization while the wider one being still itinerant. At quarter-filling, the physical behavior 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 favor 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.
Selective Transient Cooling by Impulse Perturbations in a Simple Toy Model
We show in a simple exactly solvable toy model that a properly designed impulse perturbation can transiently cool down low-energy degrees of freedom at the expense of high-energy ones that heat up. The model consists of two infinite-range quantum Ising models: one, the high-energy sector, with a transverse field much bigger than the other, the low-energy sector. The finite-duration perturbation is a spin exchange that couples the two Ising models with an oscillating coupling strength. We find a cooling of the low-energy sector that is optimized by the oscillation frequency in resonance with the spin exchange excitation. After the perturbation is turned off, the Ising model with a low transverse field can even develop a spontaneous symmetry breaking despite being initially above the critical temperature.
Cooling quasiparticles in A 3 C 60 fullerides by excitonic mid-infrared absorption
Nava A., Giannetti C., Georges A., Tosatti E., Long after its discovery, superconductivity in alkali fullerides A 3 C 60 still challenges conventional wisdom. The freshest inroad in such ever-surprising physics is the behaviour under intense infrared excitation. Signatures attributable to a transient superconducting state extending up to temperatures ten times higher than the equilibrium T c ∼ 20 K have been discovered in K 3 C 60 after ultra-short pulsed infrared irradiation-an effect which still appears as remarkable as mysterious. Motivated by the observation that the phenomenon is observed in a broad pumping frequency range that coincides with the mid-infrared electronic absorption peak still of unclear origin, rather than to transverse optical phonons as has been proposed, we advance here a radically new mechanism. First, we argue that this broad absorption peak represents a â € super-exciton' involving the promotion of one electron from the t 1u half-filled state to a higher-energy empty t 1g state, dramatically lowered in energy by the large dipole-dipole interaction acting in conjunction with the Jahn-Teller effect within the enormously degenerate manifold of (t 1u) 2 (t 1g) 1 states. Both long-lived and entropy-rich because they are triplets, the infrared-induced excitons act as a sort of cooling mechanism that permits transient superconductive signals to persist up to much higher temperatures.
Ultrafast orbital manipulation and Mott physics in multi-band correlated materials
Ronchi A., Franceschini P., Fanfarillo L., Homm P., Menghini M., Peli S., Ferrini G., Banfi F., Cilento F., Damascelli A., Parmigiani F., Locquet J.P., Multiorbital correlated materials are often on the verge of multiple electronic phases (metallic, insulating, superconducting, charge and orbitally ordered), which can be explored and controlled by small changes of the external parameters. The use of ultrashort light pulses as a mean to transiently modify the band population is leading to fundamentally new results. In this paper we will review recent advances in the field and we will discuss the possibility of manipulating the orbital polarization in correlated multi-band solid state systems. This technique can provide new understanding of the ground state properties of many interesting classes of quantum materials and offers a new tool to induce transient emergent properties with no counterpart at equilibrium. We will address: the discovery of high-energy Mottness in superconducting copper oxides and its impact on our understanding of the cuprate phase diagram; the instability of the Mott insulating phase in photoexcited vanadium oxides; the manipulation of orbital-selective correlations in iron-based superconductors; the pumping of local electronic excitons and the consequent transient effective quasiparticle cooling in alkali-doped fullerides. Finally, we will discuss a novel route to manipulate the orbital polarization in a a k-resolved fashion.
Interplay of charge and spin dynamics after an interaction quench in the Hubbard model
Wysokiński M., We investigate the unitary dynamics following a sudden increase ΔU>0 of repulsion in the paramagnetic sector of the half-filled Hubbard model on a Bethe lattice, by means of a variational approach that combines a Gutzwiller wave function with a partial Schrieffer-Wolff transformation, both defined through time-dependent variational parameters. Besides recovering at ΔUc the known dynamical transition linked to the equilibrium Mott transition, we find a pronounced dynamical anomaly at larger ΔU∗>ΔUc manifested in a singular behavior of the long-time average of double occupancy. Although the real-time dynamics of the variational parameters at ΔU∗ strongly resembles the one at ΔUc, a careful frequency spectrum analysis suggests a dynamical crossover, instead of a dynamical transition, separating regions of a different behavior of the spin exchange.
Unbinding slave spins in the Anderson impurity model
Guerci D., We show that a generic single-orbital Anderson impurity model, lacking, for instance, any kind of particle-hole symmetry, can be exactly mapped without any constraint onto a resonant level model coupled to two Ising variables, which reduce to one if the hybridization is particle-hole symmetric. The mean-field solution of this model is found to be stable to unphysical spontaneous magnetization of the impurity, unlike the saddle-point solution in the standard slave-boson representation. Remarkably, the mean-field estimate of the Wilson ratio approaches the exact value RW=2 in the Kondo regime.
Nanomechanical dissipation at a tip-induced Kondo onset
Baruselli P.P., The onset or demise of Kondo effect in a magnetic impurity on a metal surface can be triggered, as sometimes observed, by the simple mechanical nudging of a tip. Such a mechanically driven quantum phase transition must reflect in a corresponding mechanical dissipation peak; yet, this kind of signature has not been focused upon so far. Aiming at the simplest theoretical modeling, we treat the impurity as an Anderson impurity model, the tip action as a hybridization switching, and solve the problem by numerical renormalization group. Studying this model as function of temperature and magnetic field we are able to isolate the Kondo contribution to dissipation. While that is, reasonably, of the order of the Kondo energy, its temperature evolution shows a surprisingly large tail even above the Kondo temperature. The detectability of Kondo mechanical dissipation in atomic force microscopy is also discussed.
Mottness at finite doping and charge instabilities in cuprates
Peli S., Dal Conte S., Comin R., Nembrini N., Ronchi A., Abrami P., Banfi F., Ferrini G., Brida D., Lupi S., The influence of Mott physics on the doping-temperature phase diagram of copper oxides represents a major issue that is the subject of intense theoretical and experimental efforts. Here, we investigate the ultrafast electron dynamics in prototypical single-layer Bi-based cuprates at the energy scale of the O-2p → Cu-3d charge-transfer (CT) process. We demonstrate a clear evolution of the CT excitations from incoherent and localized, as in a Mott insulator, to coherent and delocalized, as in a conventional metal. This reorganization of the high-energy degrees of freedom occurs at the critical doping pcr 0.16 irrespective of the temperature, and it can be well described by dynamical mean-field theory calculations. We argue that the onset of lowerature charge instabilities is the low-energy manifestation of the underlying Mottness that characterizes the p
Mott physics beyond the Brinkman-Rice scenario
Wysokiński M., The main flaw of the well-known Brinkman-Rice description, obtained through the Gutzwiller approximation, of the paramagnetic Mott transition in the Hubbard model is in neglecting high-energy virtual processes that generate, for instance, the antiferromagnetic exchange J∼t2/U. Here, we propose a way to capture those processes by combining the Brinkman-Rice approach with a variational Schrieffer-Wolff transformation, and apply this method to study the single-band metal-to-insulator transition in a Bethe lattice with infinite coordination number, where the Gutzwiller approximation becomes exact. We indeed find for the Mott transition a description very close to the real one provided by the dynamical mean-field theory, an encouraging result in view of possible applications to more involved models.
Quantum fluctuations beyond the Gutzwiller approximation
We present a simple scheme to evaluate linear response functions including quantum fluctuation corrections on top of the Gutzwiller approximation. The method is derived for a generic multiband lattice Hamiltonian without any assumption about the dynamics of the variational correlation parameters that define the Gutzwiller wave function, and which thus behave as genuine dynamical degrees of freedom that add on those of the variational uncorrelated Slater determinant. We apply the method to the standard half-filled single-band Hubbard model. We are able to recover known results, but, as a by-product, we also obtain a few other results. In particular, we show that quantum fluctuations can reproduce, almost quantitatively, the behavior of the uniform magnetic susceptibility uncovered by dynamical mean-field theory, which, though enhanced by correlations, is found to be smooth across the paramagnetic Mott transition. By contrast, the simple Gutzwiller approximation predicts that susceptibility to diverge at the transition.
Non-Fermi-liquid behavior in quantum impurity models with superconducting channels
Žitko R., We study how the non-Fermi-liquid nature of the overscreened multichannel Kondo impurity model affects the response to a BCS pairing term that, in the absence of the impurity, opens a gap Δ. We find that the low-energy spectrum in the limit Δ→0 actually does not correspond to the spectrum strictly at Δ=0. In particular, in the two-channel Kondo model, the Δ→0 ground state is an orbitally degenerate spin singlet, while it is an orbital singlet with a residual spin degeneracy at Δ=0. In addition, there are fractionalized spin-1/2 subgap excitations whose energy in units of Δ tends toward a finite and universal value when Δ→0, as if the universality of the anomalous power-law exponents that characterize the overscreened Kondo effect turned into universal energy ratios when the scale invariance is broken by Δ≠0. This intriguing phenomenon can be explained by the renormalization flow toward the overscreened fixed point and the gap cutting off the orthogonality catastrophe singularities. We also find other non-Fermi-liquid features at finite Δ: the local density of states lacks coherence peaks, the states in the continuum above the gap are unconventional, and the boundary entropy is a nonmonotonic function of temperature. The persistent subgap excitations are characteristic of the non-Fermi-liquid fixed point of the model, and thus depend on the impurity spin and the number of screening channels.
Ultrafast evolution and transient phases of a prototype out-of-equilibrium Mott-Hubbard material
Lantz G., Mansart B., Grieger D., Boschetto D., Nilforoushan N., Papalazarou E., Moisan N., Perfetti L., Jacques V.L.R., Le Bolloc'h D., Laulhé C., Ravy S., Rueff J.P., Glover T.E., Hertlein M.P., Hussain Z., Song S., Chollet M., The study of photoexcited strongly correlated materials is attracting growing interest since their rich phase diagram often translates into an equally rich out-of-equilibrium behaviour. With femtosecond optical pulses, electronic and lattice degrees of freedom can be transiently decoupled, giving the opportunity of stabilizing new states inaccessible by quasi-adiabatic pathways. Here we show that the prototype Mott-Hubbard material V 2 O 3 presents a transient non-thermal phase developing immediately after ultrafast photoexcitation and lasting few picoseconds. For both the insulating and the metallic phase, the formation of the transient configuration is triggered by the excitation of electrons into the bonding a 1g orbital, and is then stabilized by a lattice distortion characterized by a hardening of the A 1g coherent phonon, in stark contrast with the softening observed upon heating. Our results show the importance of selective electron-lattice interplay for the ultrafast control of material parameters, and are relevant for the optical manipulation of strongly correlated systems.