Opendata, web and dolomites

Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - FIRSTORM (Modeling first-order Mott transitions)

Teaser

The so-called Mott transition, i.e., the metal-insulator transition driven by a strong Coulomb repulsion, is a fascinating phenomenon, especially since it is frequently surrounded by a wealth of different phases with intriguing physical properties, the most spectacular being...

Summary

The so-called Mott transition, i.e., the metal-insulator transition driven by a strong Coulomb repulsion, is a fascinating phenomenon, especially since it is frequently surrounded by a wealth of different phases with intriguing physical properties, the most spectacular being high-temperature superconductivity in doped cuprates. Furthermore, Mott insulators are also of potential interest for technological applications. Indeed, a Mott insulator is essentially an “unsuccessful metal” that possesses a large density of carriers whose motion at equilibrium is however impeded by Coulomb repulsion, but which could, in principle, become all of a sudden available for transport in non-equilibrium conditions.

It’s a given that Mott transitions in real materials have all first order character, frequently quite a strong one, with the resistivity changing by several orders of magnitude. This property is not just an accidental consequence of the lattice distortions, or other phenomena, like, e.g., magnetism, that usually accompany the electronic transition, but seems to be a distinctive feature of the Mott\'s charge localisation phenomenon by its own. Indeed, it is by now widely accepted that a correlated metal in the proximity of a Mott transition displays physical properties that, depending on the energy scale, can be either those of a conventional metal with coherent quasiparticles, in a narrow region peaked at the chemical potential μ, or those of an insulator, far away from μ, with well-defined atomic-like excitations. Such Janus-faced character of a correlated metal is not only the precursor of a purely electronic first-order character of the Mott transition, but entails broad metal-insulator coexistence.

The inherent metal-insulator coexistence is a distinctive property of correlated metals and Mott insulators, and offers unique opportunities unattainable in more conventional band insulators, where such phenomenon might eventually be achieved only at extreme conditions. Its potentials started to reveal themselves only recently in a series of remarkable experiments.
For instance, the dielectric breakdown of narrow gap Mott insulators resembles more a genuine resistive transition, rather than a Landau-Zener tunnelling breakdown as in conventional semiconductors, see, e.g., Stoliar et al., Advanced Materials 25, 3222 (2013). This unusual behaviour is most likely consequence of the electric field stabilising a metal phase that existed also in the absence of the field but only as a metastable state.
Even more, there are by now abundant evidences that non-thermal, i.e. inaccessible at equilibrium, states of matter with notable properties can be reached by shooting with properly designed laser pulses correlated materials, both metallic and insulating. In some cases, these seem to be hidden states, metastable in equilibrium, and thus accessible only in strong out-of-equilibrium conditions, see, e.g., Stojchevska et al., Science 344, 177 (2014).
In other cases, the laser pulse stabilises instead phases that are observed in equilibrium, although at different external conditions. We just mention the striking and, somehow, seminal experiment by Fausti et al., Science 331, 189 (2011), where a non-superconducting sample of La1.675Eu0.2Sr0.125CuO4 irradiated by a laser pulse was shown to display typical signatures of the superconducting state observed at different La concentrations. This work actually pioneered a whole series of other experiments, the most recent being the observation of a superconducting optical response well above the equilibrium critical temperature in K3C60 molecular conductor shot by a mid-infrared laser pulse, see Mitrano et al., Nature 530, 461 (2016). This represents a truly unexpected phenomenon since, in common experience, shooting a material by a laser should heat it, and thus effectively raise the temperature, whereas the experiment detects a behaviour that is observed only at much lower temperatures.

Such

Work performed

The project has proceeded in many directions bringing about several results. I will herein present what I repute the main ones.

1. The work presented in [1] was stimulated by a very puzzling experiment [2] where a transient superconducting optical response was observed well above Tc in K3C60 after irradiation by a mid-infrared femtosecond laser pulse. We have proposed that the phenomenon actually realizes a novel laser cooling mechanism that is made possible by the dual nature, partly metallic and partly insulating, of the correlated molecular conductor K3C60. Specifically, we performed a thorough molecular calculation for an isolated C60 trivalent cation, and found an odd-parity spin-triplet molecular excitation that lies 30 meV above the ground state, close to the mid-infrared absorption peak hit by the laser frequency. We speculated that such molecular excitation becomes a genuine spin triplet exciton in metal K3C60, which is not far from a first order Mott transition and can thus display molecular-like excitations despite it is a metal. Being a spin triplet, this exciton can be created by light only by absorbing, if the laser frequency is below resonance, or emitting, if the frequency is above, spin-triplet particle-hole excitations. In the former case, the light-induced creation of the excitons goes along with a depopulation of thermally excited particle-hole excitations, which therefore effectively cool down.
As a matter of fact, our transient cooling mechanism is quite general, as we discuss in [3] and pictorially explain in Fig. 1, and it might be realized in other correlated metals, too. It is sufficient that the metal hosts localized excitations, which can serve as entropy sink when the laser is on, and which very gradually release back that entropy when the laser is off.


2. V2O3 is the prototypical Mott-Hubbard compound. Its phase diagram includes a metal phase and two Mott insulating ones, one antiferromagnetic at low temperature, and another paramagnetic at high temperature, separated by first order transition lines. Our experimental colleagues in Paris found [4] that the gap of the paramagnetic insulator near the Mott transition collapses down after an ultra-short near-infrared laser pulse shoots V2O3, and, concurrently, the frequency of an A1g phonon mode, which modulates the V-V distance along the c-axis, is blue shifted, see panels (a), (b) and (c) in Fig. 2. These results are genuinely non-thermal, since, e.g., that phonon frequency decreases by rising temperature.
We argued [4] that these experimental findings could be explained by the laser pulse stabilizing a metastable metal phase. The vanadium t2g d-orbitals in V2O3 are split into a lower eg doublet and upper a1g singlet. The latter is directed along the c-axis, and therefore it is strongly involved in the covalent bond of the V-V pairs along that axis. It is believed that the insulating state of V2O3 sets in when the conduction band of predominant a1g character empties. The laser frequency in the experiment is actually in resonance with the energy cost in transferring one electron from the eg valence band to the a1g conduction one. We thus performed a constrained ab-initio band structure calculation at fixed occupancy of the a1g orbital, and found that the energy has two minima: a lower one, corresponding to the stable insulator with almost empty a1g, and a higher one, with substantial a1g occupancy, which describes instead a metastable metal. A possible explanation of the experiment is therefore that the laser pulse drives V2O3 in the metastable metal phase by increasing the a1g population. To further support this scenario, we performed an ab-initio calculation of the band structure and phonon frequencies assuming a unit cell with constant volume but variable c/a ratio. We found that reducing the c/a ratio leads to an increase of the A1g phonon frequency, and, concurrently, to a growth of the a1g occupancy, see panel (d) in Fig. 2, not unsurpris

Final results

The works that I have discusses in the previous section constitute already a progress, both conceptual and technical, beyond the state of the art, which we intend to pursue until the end of the project. For instance, we aim to investigate whether the physics uncovered in K3C60 might show up in other organic superconductors, which also often show exciton signals in the absorption spectrum. We will also continue our activities on V2O3 or other correlated materials.

Here instead I would like to discuss works that, in my opinion, constitute a progress beyond the state of the art in the tools to tackle correlated electron systems.

1. The Gutzwiller variational wavefunction consists of a Slater determinant to which one applies a product of linear operators P(i), one for each site i, which act on the local Hilbert space, and contain variational parameters to be determined by minimizing the total energy. The expectation values on this wavefunction can be computed analytically only in lattices with infinite coordination number, although it is common to keep using the same expressions also in finite-coordination lattices. This is what is commonly referred to as the Gutzwiller approximation, which represents a very simple yet effective tool to deal with models of correlated electrons. In the past years, the Gutzwiller approximation has been notably improved, allowing now tackling multiband models at equilibrium and out-of-equilibrium. In [7] we develop a general and consistent scheme to compute dynamical susceptibilities by linearizing the equations of motions of the time-dependent Gutzwiller approximation, which we developed in 2010, at first order in the external field. This method works for a generic multiband model, it is simple and computationally inexpensive, and provide rather accurate results when compared with more rigorous, yet numerically much more demanding, tools.

2. A trick that is frequently used to study models of correlated electrons is to enlarge the Hilbert space by adding auxiliary degrees of freedom that are coupled to the electron charge by a holonomic constraint. For this reason, such auxiliary degrees of freedom are commonly referred to as slave particles. Such trick allows disentangling the charge of the electron from its spin already at the mean-field level, thus accessing phenomena like the Mott transition or the Kondo effect, where indeed the electron charge freezes, while the spin is still free. The known flaw of this slave particles approach is that in mean-field the holonomic constraint is imposed only on average, which leads to some incorrect results. For instance, the magnetic susceptibility of an Anderson impurity calculated by this method becomes singular above a critical value of the interaction, signaling a spontaneous magnetization of the impurity, which is physically wrong because of the Mermin-Wagner theorem. In [8] we develop a novel formulation based on auxiliary slave-spins, which does not require imposing any constraint. Applying this new method to study in mean-field the Anderson impurity model, we do not encounter any magnetic instability, and recover the well-known universal Wilson ratio.

3. I mentioned that the Gutzwiller approximation provides strictly variational results in lattices with infinite coordination number. However, although this variational approach allows describing a Mott transition, the comparison with exact results obtained by dynamical mean field theory is very poor in the Mott insulating phase. In [9] we improve the Gutzwiller wavefunction by combining it with a partial Schrieffer-Wolff transformation, which depends on additional variational parameters. We show that this method improves rather substantially the description of the Mott insulator. In [10] we extend the method in the time-domain, allowing the Schrieffer-Wolff transformation to become time-dependent. We apply this new tool to study a quantum quench in the half-filled Hubbard model.


4. Recently, t

Website & more info

More info: https://firstorm.sissa.it.