## Highlights

## Discovery of the soft electronic modes of the trimeron order in magnetite

Magnetite (Fe_{3}O_{4}) was the first magnetic material discovered already in ancient Greece.
Verwey observed the dramatic drop of the electric conductivity by two orders of magnitude at temperature T = 125 K and proposed the charge ordering on iron ions as the mechanism of the phase transition.
It was demonstrated in recent years that the fundamental building blocks of the charge-ordered structure are three-site small polarons called trimerons (see the inset of the figure). However, electronic collective modes of this trimeron order have not been detected to date, and thus an understanding of the dynamics of the Verwey transition from an electronic point of view was still lacking. In the present studies, the signatures of the low-energy electronic excitations of the charge-orbital order were observed using the terahertz optical spectroscopy at the Massachusetts Institute of Technology. By driving these modes coherently with an ultrashort laser pulse towards the Verwey transition, the critical softening was observed. These findings shed new light on the cooperative mechanism at the origin of magnetite’s exotic ground state. We proposed that these excitations can be described by oscillations of the charge-orbital-lattice order using a model of coherent polaron tunneling. In the calculations performed in Cracow, we used the density functional theory to obtain the potential energy barrier for the tunneling process involving localized charge carriers on the central Fe sites of the trimerons. The characteristic energies of atomic vibrations coupled to tunneling electrons were calculated with the software PHONON (phonon density of states in magnetite is presented in the figure). The critical behavior of the experimentally observed collective modes was successfully reproduced within the time-dependent Ginsburg-Landau theory.

## Phonon confinement and spin-phonon coupling in tensile-strained ultrathin EuO films

Reducing the material sizes to the nanometer length scale leads to drastic modifications of the propagating lattice excitations (phonons) and their interactions with electrons and magnons. In EuO, a promising material for spintronic applications in which a giant spin-phonon interaction is present, this might imply a reduction of the degree of spin polarization in thin films. Therefore, a comprehensive investigation of the lattice dynamics and spin-phonon interaction in EuO films is necessary for practical applications. We report a systematic lattice dynamics study of ultrathin EuO(001) films using nuclear inelastic scattering on the Mössbauer-active isotope 151Eu and first-principles theory. The films were epitaxially grown on YAlO3(110), which induces a tensile strain of ca. 2%. By reducing the EuO layer thickness from 8 nm to a sub-monolayer coverage, the Eu-partial phonon density of states (PDOS) reveals a gradual enhancement of the number of low-energy phonon states and simultaneous broadening and suppression of the peaks. These deviations from bulk features lead to significant anomalies in the vibrational thermodynamic and elastic properties calculated from the PDOS. The experimental results, supported by first-principles theory, unveil a reduction of the strength of the spin-phonon interaction in the tensile-strained EuO by a factor of four compared to a strain-free lattice.

## Precise extrapolation of the correlation function in tensor networks

A complex quantum physical system may display emergent behavior that is very different from those of its individual parts. Precise descriptions of those phenomena, such as high-temperature superconductivity, are very challenging and usually require sophisticated numerical methods. Tensor networks, a powerful tool for simulating strongly correlated systems, have recently emerged as one such method. While they excel at predicting local observables, they are much worse at computing nonlocal properties that are a key ingredient for continuous phase transitions. Here, we show how to precisely extract that information from the commonly used uniform tensor network representation. This information is encoded in the correlation function and, more precisely, in the rate of its decay at very long distances. We analyze how the information is distorted by an approximation imposed by tensor network description. Understanding this allows us to provide a procedure to precisely extrapolate nonlocal properties of the quantum state. We also provide new insight into how the information about nonlocal characteristics of the exact quantum state is encoded in the uniform tensor network. This promises to extend the range of problems where uniform tensor networks can be accurately applied. Our method provides the means for detailed studies of phase diagrams of quantum models both in one and two dimensions.

## Lattice dynamics of epitaxial strain-free interfaces

We have performed a systematic lattice dynamics study of the technologically important Fe_{3}Si/GaAs heterostructure for Fe_{3}Si layer thicknesses of 3, 6, 8, and 36 monolayers. The Fe-partial phonon density of states obtained by nuclear inelastic scattering at the ID18 beamline in ESRF exhibits up to a twofold enhancement of the low-energy phonon states compared to the bulk material for layer thicknesses of 8 monolayers and below. First-principles calculations explain the observed effect by interface-specific phonon states originating from the significantly reduced atomic force constants and allow for achieving a comprehensive understanding of the lattice dynamics of epitaxial strain-free interfaces.

Phys. Rev. B 98, 121409(R) (2018)

## Finite Correlation Length Scaling with Infinite Projected Entangled-Pair States

We show how to accurately study two-dimensional quantum critical phenomena using infinite projected entangled-pair states (iPEPS). We identify the presence of a finite correlation length in the optimal iPEPS approximation to Lorentz-invariant critical states which we use to perform a finite correlation length scaling analysis to determine critical exponents. This is analogous to the one-dimensional finite entanglement scaling with infinite matrix product states. We provide arguments why this approach is also valid in 2D by identifying a class of states that, despite obeying the area law of entanglement, seems hard to describe with iPEPS. We apply these ideas to interacting spinless fermions on a honeycomb lattice and obtain critical exponents which are in agreement with quantum Monte Carlo results. Furthermore, we introduce a new scheme to locate the critical point without the need of computing higher-order moments of the order parameter. Finally, we also show how to obtain an improved estimate of the order parameter in gapless systems, with the 2D Heisenberg model as an example.

Phys. Rev. X **8**, 031031 (2018),
arXiv:1803.08445

## Reentrant Fulde-Ferrell-Larkin-Ovchinnikov superfluidity in the honeycomb lattice

We study superconducting properties of population-imbalanced ultracold Fermi mixtures in the honeycomb lattice that can be effectively described by the spin-imbalanced attractive Hubbard model in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain ground-state phase diagrams including the unconventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which is characterized by atypical behavior of the Cooper-pair total momentum. We show that the momentum changes its value as well as direction with a change of the system parameters. Moreover, we discuss the influence of Van Hove singularities on the possibility of the reentrant FFLO phase occurrence, without a BCS precursor.

Phys. Rev. A **97**, 053619 (2018),
arXiv:1710.06395

## Superconducting monolayer deposited on substrate: Effects of the spin-orbit coupling induced by proximity effects

The spin-orbit coupling can lead to exotic states of matter and unexpected behavior of the system properties. In this paper, we investigate the influence of spin-orbit coupling induced by proximity effects on a monolayer of superconductor (with s-wave or d-wave pairing) placed on an insulating bulk. We show that the critical temperatures T_{c} of the superconducting states can be tuned by the spin-orbit coupling both in the case of on-site and inter-site pairing. Moreover, we discuss a possibility of changing the location of the maximal T_{c} from the half-filling into the underdoped or overdoped regimes.

Phys. Rev. Materials **2**, 024801 (2018),
arXiv:1801.08055

## PhD positions

#### Ab initio studies of structural, magnetic and dynamic properties of nanomaterials containing transition metals.

We have open positions for PhD students in the field of computational material science. The PhD work will be guided by the professors of the Department and will be focused on computational investigation of crystals, nanostructures and surfaces.

## Research fields

Our reasearch activity focuses on solid state properties of a broad range of materials including bulk crystals, nanostructures, surfaces, and disordered systems. We study also strongly correlated systems and topological phases. Our present studies include:

- Anharmonic properties of crystals
- Iron-based superconductors
- Verwey transition in magnetite
- Lattice dynamics in metals and nanostructures of rare earths (Eu,Sm,Nd,Dy)
- Structural and dynamical properties of FePt nanoparticles
- Lattice dynamics in Fe-Si nanostructures