Research

Molecular electronics


ab-initio & many-body approaches for molecular electronics

Within the LCAO formalism, the accuracy of density functional theory is limited (also) by the quality of the basis set, which is to some extent redundant and hence poses a problem of physical interpretation. A possible solution relies on the introduction of local orbitals (LOs) that inherit the information of the atomic chemical environment and provide a natural interpretation of chemical and physical properties. 
A projection onto a suitable subset of a few LOs allows for a significant reduction of computational resources for, e.g., transport and electronic structure calculations, without sacrificing the numerical accuracy. 

 
 Applications:

[1] Gandus et al., J. Chem. Phys.. 153, 194103 (2020)
[2] Gandus et al., arXiv:2301.00282 (2023)

Highlights:

Related readings:

It is interesting to consider how scattering processes are included in prominent theoretical transport methodologies. For a phenomenological static scattering rate (Γ) insightful numerical and analytical calculations reveal a clear hierarchy of transport approaches for carriers with finite lifetimes. Indeed, the Kubo linear-response formalism displays a hyperbolic scaling of the conductance with the length (N) of the molecular bridge, which converges to the Landauer-Büttiker exponential one upon reducing Γ. For infinitely long-lived quasi-particles, the coefficient of the leading 1/Γ order reduces to the Boltzmann expression. This is shown numerically for trans-polyacetylene molecular junctions within the Su–Schrieffer–Heeger model [3].
Such an analysis provides guidance for the choice of transport methodology in future ab-initio simulations for semi-conducting molecular systems.

[3] Valli and Tomczak,  J. Comput. Electron. 22, 1363–1376(2023) 

Spin phenomena — from adatoms to molecules

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 S(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 whole Co 3d shell. The consequent destabilization of the S=1 high-spin state gives rise to a strong enhancement of the Kondo scale [1], in line with experimental evidence.

Further insight can be obtained by tracing the time evolution of the spin fluctuations which sheds light on the physical processes behind the screening and exchange short- and long-timescales dynamics [2].

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

Related readings:

Molecular systems hosting localized magnetic moments represent a suitable platform to investigate spin phenomena. For instance, organic radicals such as triphenylmethyl are characterized by a fairly localized SOMO and are expected to realize a spin S=1/2 molecular Kondo effect. The microscopic understanding of the screening mechanism requires a realistic description of the chemical environment.

Other organic systems, such as conjugated hydrocarbons lacking a classical Kekulé structure, have open shells and display multi-radical character, where the spins are spatially delocalized within the π-system. Hence, one can expect complicated magnetic exchange interactions acting in synergy or in competition with the Kondo screening. 

Instead, transition metal-organic frameworks (e.g., porphyrins or phthalocyanines) also manifest phenomena such as spin crossovers (SCO) in which the spin of the molecule can switch between a low-spin (LS) and a high-spin (HS) state. The SCO arises from the interplay between the π-ligand field of the organic framework and the Coulomb interaction at the transition-metal center (e.g., Mn, Fe, Co, Ni, or Cu).  The balance can be tuned by external stimuli, allowing for the realization of molecular spin switches. 
The fingerprint of the SCO can be identified in the electronic transport properties of a FeP single-molecule junction as a function, e.g., of mechanical uniaxial strain [3]. An abrupt change of the transport characteristics follows from the orbital charge redistribution in the Fe-3d shell, as the softening of Fe-N bonds reduces the ligand field splitting.

[3] Bhandary et al., Nanoscale Adv.  3, 4990–4995 (2021)

Quantum interference

It is well established that, in the coherent electron transport regime, π-conjugated single-molecule junctions bridging metallic electrodes display quantum interference (QI) effects, which appear in the electronic transmission function. Typically, a Fano shape (with e.g., q>0) identifies the resonant scattering between a discrete state (resonance) and a continuum (background) while an antiresonance (q=0) is the hallmark of destructive QI. The latter is particularly interesting for its dramatic effects on the electronic transmission, which changes a few orders of magnitude over a narrow energy range. 

In graphene nanostructures, due to the sublattice imbalance realized at zigzag edges, the Coulomb interaction makes the π system unstable towards magnetism [1]. Remarkably, the simultaneous presence of a spin-ordered pattern and of destructive QI induces spin-resolved antiresonances, which selectively suppress electronic transport in each spin channel at different energies. This mechanism is at the heart of QI assisted spin-filtering effect [2]. 

Electrostatic control of the current spin polarization can be achieved by inducing a spatial charge modulation that can couple to external electric fields. This scenario could be realized in practice, e.g., by deposition of graphene on a suitable substrate, such as h-BN, which generates a different chemical environment for each sublattice [2,3].  

This represents a specific realization of a generic mechanism that applies also to other degrees of freedom besides spins, e.g., the valley index [3].

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

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It has been shown that QI features survive in the presence of electron-electron scattering [1,2,3], and are also resilient against electron-phonon scattering and disorder [4].

Remarkably, the transmission function exhibits a universal behavior that can be completely ascribed to the presence of a QI antiresonance [4]. Hence, the dramatic effects of QI are not limited to the conductance but extend away from the Fermi energy within the HOMO-LUMO gap. This suggests that the fingerprint of QI could be identified in the electronic response (e.g., the I-V characteristic) even when the suppression of the conductance is weak. 

[4] Valli et al., Carbon 214, 118358 (2023)

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The QI properties are strongly connected with the topological structure of the molecular bridge. In the case of the organometallic compound phenyl-lithium (PhLi) where a meta-benzene molecular junction bonds with a Li atom. The transport properties depend on the strength and the topology of the phenyl-Li bond, i.e., whether Li forms a π bond (e.g., with the Li atom in the hollow position) or a σ- bond with an sp3-hybridized C atom (effectively removing it from the π system).

[5] Valli, in preparation

Related readings:

The origin of QI can be understood in terms of the topological structure of the molecular orbitals, and it has been shown that, e.g., chemical functionalization can modify the interference pattern. In particular, the energy position of the QI resonances is sensitive to variations of the chemical environment. It does not necessarily require a chemical bond, and a weak interaction — such as in the case of physisorption — suffice. Hence, in the presence of an adsorbate, QI can be exploited as a paradigmatic mechanism for high-performance chemical- and bio-sensors.

Remarkably, due to the strong modulation of the electronic transmission, molecular cores exhibiting destructive QI effects typically yield a strong chemiresistive response to an adsorbate (i.e., display a high sensitivity) which allows the detection of individual molecules. As the sensor response displays a critical dependence on the properties of the adsorbate (e.g., compare H2O vs. NO2) it also results in an enhanced chemical selectivity [6].

[6] Şengül et al., Phys. Rev. B 105, 165428 (2022)

Simulations of realistic graphene nanosensors (~1-100 nm, thousands of atoms) are beyond the reach of ab-initio methods. To this end, we built an effective model with a few ab-initio tight-binding parameters for local orbitals (LOs) derived from the original LCAOs. We also identify the key effect induced by a molecule physisorbed on graphene and we demonstrate that it can be encoded in a single parameter, which depends on the charge transfer between the adsorbate and the surface. 
Transport calculations reveal that with such prescriptions, it is possible to quantitatively reproduce the energy shift of the QI antiresonance induced by the adsorbate [7]. thus allowing for large-scale simulation of chemical sensors. 

[7] Şengül et al., in preparation