## Workshop Report

*What about U in nanoscale systems?*

**ZCAM/BIFI, Zaragoza, Spain, May 21-24 2019**

**Organizers:** David Jacob (UPV/EHU, San Sebastian), Massimo Capone (SISSA, Trieste), Silke Biermann (Ecole Polytechnique, Paris)

**Local Organizers:** Beatriz Antoli, Adrian Velazquez-Campoy (ZCAM, BIFI, Zaragoza)

The Workshop “What about U in nanoscale systems?” took place at the CECAM node in Zaragoza from May 21 to May 24 2019. It followed the format of previous What about U editions, bringing together colleagues from different communities (including experimentalists) and providing ample discussion time. The new aspect this year was the focus on nanoscale systems, while also general aspects of correlations found their place.

### Day 1

The first scientific talk was given by **George Sawatzky**, Vancouver. Under the title “I am interested in U (don’t take it personally!)”, he presented a large panorama of various aspects related to screening of Coulomb interactions in solids. The origin of screening in bulk and nanosystems was scrutinized, and directly observable consequences of strong local Coulomb interactions such as multiplets in spectroscopies for f-electron materials were reviewed.

**Massimo Capone** followed up with a pedagogical introduction to Dynamical Mean Field Theory, covering basic concepts, advantages and limitations, as well as an overview of the wide spectrum of branching applications, among others to nanoscale systems.

**Andrea Droghetti** (UPV/EHU San Sebastian) presented his work on electronic transport through correlated molecular junctions from first principles following two different routes: (i) staying in a density-functional framework and (ii) by combination of DFT calculations with impurity solvers for treating a small strongly correlated subspace in the molecule. Interestingly, he showed that the addition of a derivative discontinuity to the LDA xc potential in realistic calculations ab initio calculations of a molecular junction allows to describe the Kondo plateau in zero-bias conductance as a function of gate voltage.

**Ivan Rungger’s** (NPL, Teddington) presentation of dynamical mean field theory calculations for piezoresistive materials for thin films for novel transistor applications demonstrated impressively how closely the field can nowadays connect to questions of practical relevance in materials science. The materials under scrutiny, SmSe and SmS, whose multiplet structures evidence the true need for a many-body description beyond DFT or DFT+methods, was discussed in comparison to the celebrated SmB6.

In the afternoon session, **Katharina Franke** (FU Berlin) introduced her audience to the magic world of Scanning Tunneling Spectroscopy (STS) of magnetic atoms and molecules on superconducting substrates. So-called Shiba states which emerge in these systems as a direct consequence of the interaction between the magnetic moment and the superconducting states, can be measured by STS and allow to characterize magnetic states and the interaction strength with atomic-scale resolution.

During the last talk of the first day, **Samir Lounis** (FZ Jülich) demonstrated an original combination of time-dependent density functional and many-body perturbation theory and its application to magnetic atoms on surfaces. Among other issues, he pointed out the need of an improved functional that he constructs based on sum rules and exact limits. His first principles description of zero-point fluctuations of magnetic moments in these systems provoked a heated discussion, since the persistence of magnetic moments at zero temperature was suspected to be an artifact of the method that does not describe Kondo screening. Nevertheless, it was speculated that this zero-temperature calculation might find a regime of application just slightly above the Kondo temperature, if zero point fluctuations survive up to that energy scale.

The day ended with a **poster session** with wine and tapas, and lively discussions.

### Day 2

The second day was opened by **Robert van Leeuwen** (U Jyväskylä) who introduced his work on higher order expansions of the many-body perturbation theory series beyond the GW approximation, and the pitfalls that open already at second order in W: unless special criteria for selecting diagrams (that sum up to completed squares in a way defined by Robert) are selected, such straightforward looking extensions lead to negative spectral weights. The audience was also intrigued by his finding of a careful selection of higher order diagrams finally leading to a result that comes close to a much simpler second-Born like choice of terms, if undressed Green’s functions are used. Finally, Robert introduced his audience to non-equilibrium many-body theory, preparing also the terrain for the following talk by Martin Eckstein.

**Martin Eckstein** (FAU Erlangen-Nürnberg) showed dynamical mean field theory results within a Keldysh non-equilibrium formalism, relating to ultrafast spectroscopy experiments. An intriguing result concerned the comparison between Hartree-Fock+DMFT and GW+DMFT, which in the case investigated showed impressive agreement at equilibrium while the cheaper Hartree-Fock based scheme was clearly falling short in the out-of-equilibrium case.

**Gianluca Stefanucci** (Rome Tor Vergata) presented a novel density functional-based description of transport, called i-DFT: in the i-DFT formalism the Hohenberg-Kohn description is augmented by an additional variable, the current, which is conjugate to the bias voltage. Gianluca made his audience appreciate the existence of an exchange bias and the possibilities of constructing explicit functionals, at least in the case of an Anderson impurity-type problem,

In the following talk, **Stefan Kurth** (UPV/EHU San Sebastian) showed that the i-DFT formalism could be used to extract the true many-body spectral function of a system from a DFT calculation in a special setup, where one of the electrodes becomes effectively decoupled (ideal STM limit). These two talks also triggered a most interesting philosophical discussion on the transferability of results based on a functional that is designed on the basis of a relatively specific physical system (single-orbital Anderson impurity problem). The opportunities opened by a relatively little costly DFT-based description were highlighted.

In the afternoon session, **Wolfgang Kuch** (FU Berlin) surprised his audience by his report on the emergence of a cooperative spin-switching effect whose appearance in a system of molecules on a Au surface depends however on the coverage. While many aspects of the thermodynamics of such systems seem to be well understood, the mechanism of cooperative switching bears still several mysterious aspects, and is likely to further stimulate theoretical (and experimental) work.

**Andrew Mitchell** (UC Dublin) talked on “What about U in molecules”, presenting an introduction and advanced discussion on Kondo blockade effects in multi-channel systems. His audience was most astonished about his finding of the exchange coupling derived by straightforward Schrieffer-Wolff arguments to match a directly calculated value only at truly high values of U, extremely far in the strong-coupling limit. Andrew presented improved exchange couplings that are substantially smaller than the naive value Andrew Mitchell , while still demonstrating that the form of the effective Hamiltonian is the expected one.

The last item on the agenda of the day was a round table discussion chaired by **George Sawatzky**, where different aspects of downfolding to low-energy effective Hamiltonians were discussed. **Andrea Droghetti** took the occasion to present work on the choice of an optimized basis spanning a low-energy space, while **Silke Biermann** advertized the recently developed “constrained GW” technique. The discussion highlighted the different approaches inspired from solid state physics or quantum chemistry, confronting various ways of thinking about the problem. While solid state physicists usually prefer to keep the quasi-momentum k as a quantum number, defining low-energy spaces spanned by sets of single-particle states, the focus of quantum chemists on finite (and most often small) systems allows for local descriptions. Another point of discussion was on the suitable interactions to be used within effective descriptions were solid state physicists tend to try to incorporate some degree of screening already at the level of the effective interaction, while quantum chemists do not mind to work with bare interactions. These preferences are likely not merely cultural preferences but motivated by the huge effects of screening (reducing Coulomb interactions typically by an order of magnitude) in extended solid state systems.

The conference dinner was a perfect occasion to digest the insights of the day.

### Day 3

Thursday was opened by **George Booth** (King’s College London) who presented his recent attempts of a DMET/DMFT-inspired scheme working on the basis of density matrices while still giving access to spectral properties. His scheme is based on self-consistency relations for a (chosen) number of moments of the density matrix. His first results demonstrate that at least for the case of a half-filled particle-hole symmetric Hubbard models, these moments indeed capture a fair amount of the physics, realizing e.g. a Mott transition in the infinite dimensional Hubbard model on the Bethe lattice in a similar way as DMFT.

**Angelo Valli** (TU Vienna) presented his recent work on correlation effects in nanoscale systems, concentrating on two very different systems: small graphene flakes and the drosophila system of strong correlations and in particular of the Kondo effect in nanoscale electronics, Co adatoms on the Cu surface. In the former, using the Nano-DMFT approach for a finite Hubbard model connected to electrodes of the graphene flake, he demonstrated an intriguing spin/valley filter behavior which depended on which C sites of the flake were connected to the electrodes. In the case of Co on Cu, using DFT+CTQMC impurity solver calculations, he showed that a Kondo effect is not easy to achieve in the theoretical description of this system, and depends strongly on the choice of parametrization of Coulomb integrals, which is highly surprising given that the Co@Cu system is considered the Kondo system par excellence. A controversial discussion on the reasons behind these findings followed.

The last talk of the day was given by **Steffen Backes** (Polytechnique, Paris) who presented a study into the experimentally very important question of the nature of satellites (Hubbard or plasmonic) in strongly correlated materials using the GW+DMFT approach. On the examples of SrV03 and SrMoO3 he showed that by artificially reducing the static part of the interaction, Hubbard bands are strongly reduced, thus leaving only the plasmon satellites. It thus turns out that the lower satellite in SrV03 is dominantly a Hubbard band, while the upper one is a mixture of both Hubbard and plasmon contributions. This is in contrast to SrMoO3, where both lower and upper satellites are a strong mixture of Hubbard and plasmonic effects.

In the afternoon session, the only talk was given by **Michael Sentef** (MPI Hamburg) who presented work on dynamical materials engineering, and specifically on the effect of a time-dependent U on material properties within an DFT+U scheme. The up-shot was that in NiO a phase transition from charge-transfer insulator to Mott insulator can be induced by an ultrafast reduction of U in a pump-probe experiment.

The day finished with a very nice guided Tour of the beautiful city of Zaragoza.

### Day 4

The last day of the conference was dedicated to the recent experimental realization of the 2D Hubbard model in magic-angle twisted bilayer graphene (MA-tBLG). These systems offer the possibility to experimentally measure the theoretically much sought-after phase diagram of the 2D Hubbard model. **José Pizarro** (U Bremen) first gave a nice introduction to twisted bilayer graphene and the theoretical prediction of the emergence of a flat band at magic angles, corresponding to an effective 2D Hubbard model. In the second part of his talk he elaborated on the theoretically and computationally challenging task of computing the effective interaction U for the emergent Hubbard model. **Dimitri Efetov** (IFCO, Barcelona) showed beautiful experimental results from his group at IFCO in Barcelona, realizing very clean samples of MA-tBLG. Thanks to the improved quality of the samples, they were able to observe large variety of previously unobserved states, including new superconducting domes, orbital magnets and Chern insulating states.

**David Jacob** closed the workshop with a few concluding remarks.

### Conclusions

The workshop followed very closely the CECAM spirit by giving ample discussion time (talks were 30 min, followed by 15 min discussion; in addition to the round table discussion). A decisive advantage which made the workshop truly interesting was the diverse background of the speakers and participants: it was the occasion to confront density functional-based theories to many-body approaches, the quest for parameter-free descriptions to phenomenological models, quantum chemistry to solid state approaches, to argue about general strategies, identify differences in goals (spectroscopy vs. total energies) and jargon, to translate between the different languages of different communities and last but not least, to confront theoretical concepts and results to experimental findings.

It was the first What about U? workshop in Zaragoza, which turned out to be an appreciated choice. Warm thanks go to the local CECAM organizer Beatriz Antoli, who took care of all practical aspects with a welcoming smile.

The conference website with the program and the list of participants can be found at:

https://www.cecam.org/workshop1677