Research

Many-body effects — from bulk to the nanoscale

Overview

Bulk- and nano-materials with open-shell transition metal or molecular constituents typically host strong electronic correlations. As electrons are entangled, correlated materials are highly susceptible to external stimuli, and often display a drastic response to weak perturbations, thus making them incredibly fascinating both from a point of view of fundamental physical understanding, as well as application-wise. 

The complex electronic properties of correlated materials are encoded in the atomistic material detail, thus requiring the development of theoretical approaches that combine a realistic description of the chemical environment with the ability to account for many-body effects [1]. 

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

Another layer of complexity emerges in systems with intrinsic inhomogeneities. It can be a static property, as in the case of broken translational invariance in one or more spatial dimensions (e.g., for interfaces or hetero-structures) or systems with external confinement potentials (e.g., cold atoms in optical traps) or it can arise due to geometrical imperfections —vacancies, defects— or due to a complete lack of any underlying lattice structure, such as in the case of molecules. Inhomogeneities can also arise from the chemical properties, as in materials characterized by complex unit cells with locally inequivalent atoms (e.g., in mixed-valence compounds, with elements appearing simultaneously in different oxidation states). Interestingly, anisotropies can also arise dynamically, as symmetries are spontaneously broken (e.g., dimerization) or when the anisotropy manifests in the electronic properties or physical response, despite the chemical environment being symmetric (e.g., electronic nematicity).

Structural and electronic anisotropies manifest in a plethora of physical phenomena, ranging from site-selective Mott behavior [2,3,5], electronic superradiance [6], and short-range order [7-11]. It is important to stress that such effects can only be described by approaches with a real-space resolution of electronic correlations.

Electronic correlations at the nanoscale

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 [6]. 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) 

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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. 

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)

Quantum magnetism

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 also induce long-range (i.e., 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)

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)

Strongly correlated phases of unconventional superconductors

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 the electronic correlations is taken into account, i.e., within many-body approaches such as the dynamical mean-field theory (DMFT). Whereas, an opposite trend is observed, in which superconductivity is strongly suppressed, within less sophisticated approximations which only account for a static quasi-particle (QP) renormalization of the Fermi liquid [1]. 

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

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schematic orbital-dependent redistribution of spectral weight

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-based 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)


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