Bulk- and nano-materials with open-shell configurations host strong electronic correlations. Correlated electronic states often exhibit a drastic response to weak perturbations, making them incredibly fascinating from the point of view of fundamental physical understanding, as well as for technological applications. 

Theoretical modeling and numerical simulations play pivotal roles in distilling the mechanism controlling the behavior of correlated electrons. At the same time, relevant information is encoded in the chemical environment. Therefore, merging realistic simulations of materials with state-of-the-art many-body techniques becomes important to obtain numerical methods with predictive power that allow a direct comparison with the experiments.

Another layer of complexity emerges in systems with inhomogeneities. Among the possible origin we can identify:

• Reduced symmetry. The (effective) dimensionality can be determined by broken translational invariance on one or more spatial dimensions (e.g., for interfaces or hetero-structures) or arise from the lack of an underlying lattice (e.g., molecules). It can be either intrinsic (i.e., due to the atomic structure) or induced by external conditions (e.g., strain or external potentials). 

• Chemical environment. Anisotropies can also arise from material imperfections (e.g., vacancies, defects) or their chemical nature (e.g., mixed-valence compounds, where a given element exists in different oxidation states). 

For a recent review of advances in realistic simulations of materials — with an emphasis on nanostructures — hosting strong electronic correlations, see e.g., Ref. [1]. Structural and chemical anisotropies manifest in a plethora of physical phenomena, including site- or orbital-selective Mott behavior [2,3,5,10], an electronic analog of superradiance [6], short-range charge [4,5] and spin [7-11] order, and the Kondo effect [12], which will be discussed below. A common thread is that they can be described by approaches that allow for a real-space resolution of electronic correlations.

 [1] Schüler et al., Eur. Phys. J. Special Topics 226, 2615–2640 (2017) 

Quantum spatial confinement of electrons on the scale of the de Broglie wavelength can drastically influence the response of a material. A prototype scenario is provided by a collection of atoms at the edge of a tip (e.g., either of a break junction or a scanning tunneling microscope) where spatial confinement leads to conductance quantization. However, at atoms close to the edge, electronic correlations are enhanced by the reduced spatial connectivity, and the electrons can undergo a site-selective Mott crossover and develop a large effective mass [2,3].

The change in the electronic properties is reflected in the electron transport across the tip. The expected exponential decay of the conductance with the height of the tunneling barrier (which depends on the distance of the tip from the surface and the difference in the electrochemical potentials) is further suppressed, reflecting the insulating character of the injected electrons. This effect could be relevant in the interpretation of tunneling spectra with d-shell electron sources (e.g., Ni or W, rather than Au).

[2] Valli et al., Phys. Rev. Lett. 104, 246402 (2010)
[3] Valli et al., Phys. Rev. B 86, 115418 (2012)

Among the transition-metal oxides (TMO) of considerable interest for both fundamental and applied science is the family of manganites. While most compounds are paramagnetic insulators above room temperature, they display a complex phase diagram characterized by the interplay of orbital, spin, and lattice degrees of freedom. The most prominent feature is the colossal magnetoresistance (CMR) i.e., a dramatic change in the electrical resistance in response to a change in the external magnetic field. 

Experimental evidence suggests that the charge-ordered antiferromagnetic state of bulk La0.5Ca0.5MnO3 can be destabilized in favor of a ferromagnetic metallic state with external stimuli, such as electromagnetic fields or strain. This property is of extreme relevance for CMR applications. 

The structural changes that follow upon size reduction can also trigger such a behavior, and they appear to be distinctively different from those induced by the application of hydrostatic pressure [4]. In the bulk, half-doped compound (i.e., substituted with a Ca atom for each La in the unit formula) the orbital and magnetic transitions are concomitant. However, electronic correlations are shown to enhance the stability of the charge-orbitally ordered state in the bulk, even in the absence of long-range magnetic order [4]. 

Finally, in stoichiometric finite-size manganite nanoclusters, the Coulomb interaction is responsible for the onset of a site- and orbital-selective Mott state, which can be induced by electrostatic doping through a gate voltage [5]. 

[4] Das et al., Phys. Rev. Lett. 107, 197202 (2011)
[5] Valli et al., Phys. Rev. B 92, 115143 (2015) 

Related readings:

• Press release: "Big success with tiny crystals" [link]

A suggestive route towards the realization of efficient solid-state devices relies on exploiting quantum coherence on timescales compatible with every-day technology. The possibility to generate, control, and collect charges without losing the information stored in the quantum phase would pave the way to the design of novel building blocks for quantum computation or optoelectronic devices with unprecedented performances.

The concept of coherence-assisted transport has been suggested to address the hitherto unexplained efficiency of light-harvesting processes in molecular biocomplexes. A paradigmatic manifestation of quantum coherence is the phenomenon of superradiance. In systems with a decay channel, the optimal transport condition is realized at a finite dephasing. At the sweet spot — when the inverse lifetime of the electronic excitations due to the coupling to the sink becomes of the order of the average level spacing, a super-radiant state appears (spatially localized at the edge of the conducting channel, where the overlap with the sink is sizable) and the average transfer time is minimal. Thus, superradiance gives rise to fast quantum coherent transport with an optimal current [6].

Remarkably,  superradiance is robust against dephasing, disorder, and electron-electron interactions in the range of parameters compatible with implementations of light-harvesting devices in a few monolayer transition-metal-oxide heterostructures [6]. 

[6] Kropf et al., Phys. Rev. B 100, 035126 (2019)

With high electron mobility and ultralong spin lifetime (exceeding a few ns) graphene represents an ideal platform for next-generation spintronics. For this reason, the prediction of edge magnetism in nanostructures with zigzag edges raised great interest in the community. 

In hexagonal graphene nanoflakes, a local Coulomb repulsion entails short-range antiferromagnetic correlations, which result in a Néel spin-ordered pattern, where the edge spins alignment is parallel along an edge, but antiparallel between consecutive edges [7,8,9]. Interestingly, electrostatic doping (e.g., via a gate voltage) can induce long-range (e.g., edge-to-edge) correlation with ferromagnetic character, mediated by hole charge carriers delocalized along the edges. Above a critical density of holes, the competition between magnetic correlations on different length scales eventually turns the spin state ferromagnetic [7].

[7] Valli et al., Phys. Rev. B 94, 245146 (2016)
[8] Valli et al., Nano Lett. 18, 2158–2164 (2018)
[9] Valli et al., Phys. Rev. B 100, 075118 (2019)

Cross-reference:

• An interesting interplay between edge magnetism and quantum interference in the electron transport properties is discussed among the [Molecule Electronics] topics.

While experimental evidence of edge magnetism in solid-state graphene samples so far remains somewhat elusive, systems of ultracold atoms in optical lattices represent an ideal platform for the realization of quantum effects within a controlled environment. An interesting research line exploits ultracold atoms as many-body quantum simulators, as the Coulomb repulsion can be tailored, e.g., with Feshbach resonances. 

A suitable protocol allows the realization of artificial edges, where the competition between the Coulomb repulsion and spatial confinement stabilizes an incompressible fermionic fluid. Under the proper conditions, the spatial density profile can displays atomically-sharp edges, separating empty and occupied lattice sites, which support spin-ordered patterns [10].

In the presence of spin-orbit coupling (SOC) an edge state reconstruction can be realized at the boundaries between topological insulator (TI) and AF insulator in models with non-trivial topology [11] (e.g., Bernevig-Hughes-Zhang and Kane-Mele) supplemented with a local Coulomb repulsion. Spatial confinement can hence be rightfully regarded as another knob to tune the topological properties in many-body systems.

[10] Baumann et al., Phys. Rev. A 101, 033611 (2020)
[11] Amaricci et al., Phys. Rev. B 98, 045133 (2018)

The Kondo effect is a fascinating phenomenon, arising when a localized spin is quantum mechanically screened by the conduction electrons of a metallic host. A prototypical Kondo system, which is considered to be relatively well understood, is realized by a single Co impurity on a metallic substrate (e.g., Cu, Au, or Ag). While the experimental evidence of the Kondo effect is overwhelming, the details of the screening mechanism are subtle, and different scenarios are possible.

A systematic analysis of Co/Cu(100) reveals that the parametrization of the Coulomb tensor drastically affects the Kondo screening. If the Hund exchange is the dominant interaction, it locks the two (nearly half-filled) Kondo-active orbitals in an S=1 high-spin state, while the rest of the Co 3d shell is inert (i.e., it consists of full or empty orbitals). In this configuration, the Kondo temperature is strongly suppressed, as predicted within the Nevimodskyy-Coleman scenario. More sophisticated SU(2) rotationally-invariant parametrizations of the Coulomb tensor include additional processes (e.g., spin-flip and pair hopping) that compete with the Hund exchange, quenching spin fluctuations and enhancing charge fluctuations within the Co 3d shell. The consequent destabilization of the S=1 high-spin state results in a strong enhancement of the Kondo scale [12], which could explain the experimental evidence.

Further insight can be obtained by tracing the (imaginary) time evolution of spin fluctuations, which sheds some light on the physical processes behind the screening and exchange short- and long-timescales dynamics [13].

[12] Valli et al., Phys. Rev. Research 2, 033432 (2020)
[13] Valli et al., in preparation

Related readings:

• Nevidomskyy & Coleman, Phys. Rev. Lett. 103, 147205 (2009)

• Watzenböck et al., Phys. Rev. Lett. 125, 086402 (2020)

Interestingly, anisotropies can also arise dynamically, as a symmetry is spontaneously broken.  It can be a lattice symmetry (e.g., dimerization) or a symmetry related to other degrees of freedom (e.g., spin, orbital). 

Surprisingly, some of the best superconductors (i.e., characterized by the highest critical temperature) display bad metallic behavior in the normal state. The electronic correlations in the Hund's metal are revealed to be beneficial to the formation of Cooper pairs between renormalized quasi-electrons. As a consequence, the superconducting phase is found to be more resilient against the repulsive Coulomb interaction [1]. 
This effect manifests when the dynamical nature of electronic correlations, i.e., energy-dependent renormalization,  is taken into account within many-body approaches such as the dynamical mean-field theory (see [link] for a more detailed discussion). Instead, within less sophisticated approximation, relying only on a static renormalization of the quasi-particle features, the opposite trend is found and superconductivity is strongly suppressed [1]. 

[1] Fanfarillo et al., Phys. Rev. Lett. 125, 177001 (2020)

Related readings:

• Press release: "The transformation of a pair: how electrons supertransport current in bad metals" [link]

The experimental observation of nematicity in several families of iron superconductors raised significant attention. In the nematic phase, the C4 lattice rotational symmetry in the Fe plane is lowered to C2, as the x and y crystallographic directions are not equivalent, and the electronic properties are strongly anisotropic. As several degrees of freedom are strongly entwined, it remains unclear whether at the origin of nematicity is a structural phase transition (i.e., from tetragonal to orthorhombic) or a spontaneous breaking of orbital or spin symmetry, making this a physical realization of the chicken and egg problem.

The orbital selective behavior of Hund's metals is also key to understanding the nematic spectral features observed in photoemission spectra (ARPES) from different families of iron superconductors. In systems where the electronic correlations in the metallic state are dominated by Hund's coupling, a nematic perturbation does not result in a (trivial) energy shift in the electronic spectra. Instead, it entails a rich spectral weight redistribution between the coherent quasi-particle peak (QPP) and the incoherent (lower) Hubbard band (LHB) — which is observed together with an orbital-selective coherence, thus providing a natural explanation of the ARPES experimental evidence [2]. 

[2] Fanfarillo et al., Phys. Rev. B 107, L081114 (2023)

Related readings:

• Fernandes et al., Nature Phys. 10, 97 (2014)

• Pfau et al., Phys. Rev. B 103, 165136 (2021); Pfau et al.,  Phys. Rev. B 104, L241101 (2021)