Green Function Techniques in the Treatment of Quantum Transport at the Molecular Scale

Interacting resonances and antiresonances in conjugated hydrocarbons: exceptional points and bound states in the continuum

Quantum interference dramatically modulates electron transport that provides exciting prospects for molecular electronics. We develop a holistic picture of quantum interference phenomena in molecular conductors based on conjugated hydrocarbons taking into account the interaction of resonances and antiresonances (AR). This interaction can result in the coalescence of resonances and ARs accompanied by a significant quantum transparency change. As such a change results from a small variation of the system parameters, it is essential for reducing power consumption in electronics. We establish that the coalescence of ARs is intimately connected with the exceptional point of an underlying non-Hermitian Hamiltonian. The coalescence of ARs cannot be explained considering only the LUMO and HOMO without orbitals beyond them. Cyclobutadiene is discussed as an example. We show that the interaction of resonances and ARs can also result in the formation of a bound state in the continuum (BIC). Our formalism accounting for separate descriptions of resonances and ARs is especially suitable for describing BICs, which can be considered as either a resonance or an AR with zero width. In particular, we show that benzene in the para-configuration possesses BICs, which can be revealed as narrow Fano resonances (FRs) in the transmission spectrum by perturbing the molecule symmetry. Any BIC can be turned into an FR by a proper change of the system parameters, but the reverse is not true. We demonstrate that BICs are related to such chemical concepts as non-bonding orbitals, radicals, and diradicals. Our analytical results within the Hückel formalism are closely reproduced by ab initio simulations. Therefore, experimentally revealing these phenomena looks quite probable.

Quantum Algorithm for Simulating Single-Molecule Electron Transport

An accurate description of electron transport at a molecular level requires a precise treatment of quantum effects. These effects play a crucial role in determining the electron transport properties of single molecules, which can be challenging to simulate classically. Here we introduce a quantum algorithm to efficiently calculate electronic current through single-molecule junctions in the weak-coupling regime. We show that a quantum computer programmed to simulate vibronic transitions between different charge states of a molecule can be used to compute electron-transfer rates and electronic current. In the harmonic approximation, the algorithm can be implemented using Gaussian boson sampling devices, which are a near-term platform for photonic quantum computing. We apply the algorithm to simulate the current and conductance of a magnesium porphine molecule. The algorithm provides a means for better understanding the mechanism of electron transport at a molecular level, which paves the way for building practical molecular electronic devices.

Assessing Possible Mechanisms of Micrometer-Scale Electron Transfer in Heme-Free Geobacter sulfurreducens Pili

The electrically conductive pili of Geobacter sulfurreducens are of both fundamental and practical interest. They facilitate extracellular and interspecies electron transfer (ET) and also provide an electrical interface between living and nonliving systems. We examine the possible mechanisms of G. sulfurreducens electron transfer in regimes ranging from incoherent to coherent transport. For plausible ET parameters, electron transfer in G. sulfurreducens bacterial nanowires mediated only by the protein is predicted to be dominated by incoherent hopping between phenylalanine (Phe) and tyrosine (Tyr) residues that are 3 to 4 Å apart, where Phe residues in the hopping pathways may create delocalized "islands." This mechanism could be accessible in the presence of strong oxidants that are capable of oxidizing Phe and Tyr residues. We also examine the physical requirements needed to sustain biological respiration via nanowires. We find that the hopping regimes with ET rates on the order of 10⁸ s^-1 between Phe islands and Tyr residues, and conductivities on the order of mS/cm, can support ET fluxes that are compatible with cellular respiration rates, although sustaining this delocalization in the heterogeneous protein environment may be challenging. Computed values of fully coherent electron fluxes through the pili are orders of magnitude too low to support microbial respiration. We suggest experimental probes of the transport mechanism based on mutant studies to examine the roles of aromatic amino acids and yet to be identified redox cofactors.

Circular current and induced force in a molecular ring junction

We consider bias-induced circular current in a molecular ring junction. It is natural to define circular current as a component of ring current that acts as a sole source of magnetic flux induced in the ring. Alternatively, the bias-induced circular current can also be determined from the magnetic response of the ring junction to an external flux in the zero-flux limit. This leads to determination of bias-induced circular current without actually calculating the bond currents. We also explore the possibility of circular current-induced force rupturing the covalent bonds in the ring leading to ultimate breakdown of the ring junction. Our calculations underscore the reliability problem posed by the current magnification effect in the molecular ring structures.

[Formula: see text]-symmetric interference transistor

We present a model of the molecular transistor, operation of which is based on the interplay between two physical mechanisms, peculiar to open quantum systems that act in concert: [Formula: see text] -symmetry breaking corresponding to coalescence of resonances at the exceptional point of the molecule, connected to the leads, and Fano-Feshbach antiresonance. This switching mechanism can be realised in particular in a special class of molecules with degenerate energy levels, e.g. diradicals, which possess mirror symmetry. At zero gate voltage infinitesimally small interaction of the molecule with the leads breaks the [Formula: see text] -symmetry of the system that, however, can be restored by application of the gate voltage preserving the mirror symmetry. [Formula: see text] -symmetry broken state at zero gate voltage with minimal transmission corresponds to the "off" state while the [Formula: see text] -symmetric state at non-zero gate voltage with maximum transmission - to the "on" state. At zero gate voltage energy of the antiresonance coincides with exceptional point. We construct a model of an all-electrical molecular switch based on such transistors acting as a conventional CMOS inverter and show that essentially lower power consumption and switching energy can be achieved, compared to the CMOS analogues.

Effects of acceptor doping on a metalorganic switch: DFT vs. model analysis

We propose a molecular switch based on copper dioxolene molecules with valence tautomeric properties. We study the system using density functional theory and a model Hamiltonian that can properly account for electronic correlations in these complex molecular systems. We compute the transport properties of the junction with a Cu-dioxolene unit sandwiched between gold electrodes and analyze its dependence on the valence tautomeric state of the molecule. We also study the effects of doping with ICl2 acceptor molecules on the magnetic and electronic features of the device. We find that in the absence of dopants, the Cu-dioxolene unit is weakly charged in a S = 1/2 spin state. However, the acceptors increase the charge state of the molecule and make possible a transition between the high-spin (S = 1) triplet and the low-spin (S = 0) singlet. The I-V dependence shows a manifestation of spin filtering and a voltage-induced multistable behavior that can have several applications in nanoscale electronic devices.

Conductance of graphene flakes contacted at their corners

Linear conductance of junctions formed by graphene flakes with the order of the nanometer-thick electrodes attached at the corners of the flakes is studied. The explored structures have sizes up to 20,000 atoms and the conductance is studied as a function of applied gate voltage varied around the Fermi level. The finding, obtained computationally, is that junctions formed by armchair-edge flakes with the electrodes connected at the acute-angle corners block the electron transport while only junctions with such electrodes at the obtuse-angle corners tend to provide the high electrical conductance typical for metallic GNRs. The finding in the case of zig-zag edges is similar with the exception of a relatively narrow gate voltage interval in which each studied junction is highly conductive as mediated by the edge states. The contrast between the conductive and insulating setups is typically several orders of magnitude in terms of ratio of their conductances. The main results of the paper also remain to a large extent valid in the presence of edge disorder.

On the separability of the extended molecule: Constructing the best localized molecular orbitals for an organic molecule bridging two model electrodes

Based on a quantum chemical valence formalism that allows the rigorous construction of best-localized molecular orbitals on specific parts of an extended system, we examined the separability of individual components of model systems relevant to the description of electron transport in molecular devices. We started by examining how to construct the maximally localized electronic density at the tip of a realistic model of a gold electrode. By varying the number of gold atoms included in the local region where to project the total electronic density, we quantitatively assess how many molecular orbitals are entirely localized in that region. We then considered a 1,4-benzene-di-thiol molecule connected to two model gold electrodes and examined how to localize the electronic density of the total system in the extended molecule, a fractional entity comprising the organic molecule plus an increasing number of the closest metal atoms. We were able to identify in a rigorous manner the existence of three physically different electronic populations, each one corresponding to a distinct set of molecular orbitals. First, there are those entirely localized in the extended molecule, then there is a second group of those completely distributed in the gold atoms external to that region, and, finally, there are those delocalized over the entire system. This latter group can be associated to the shared electronic population between the extended molecule and the rest of the system. We suggest that the treatment here presented could be useful in the theoretical analysis of the electronic transport in nanodevices whenever the use of localized molecular states are required by the physics of the specific problem, such as in cases of weak coupling and super-exchange limits.

The temperature dependence of quantum spin pumping generated using electron spin resonance with three-magnon splittings

On the basis of the Schwinger-Keldysh formalism, we have closely investigated the temperature dependence of quantum spin pumping generated using electron spin resonance. We have clarified that three-magnon splittings excite non-zero modes of magnons and characterize the temperature dependence of quantum spin pumping generated using electron spin resonance.

Time-dependent electron transport through a strongly correlated quantum dot: multiple-probe open-boundary conditions approach

We present a time-dependent study of electron transport through a strongly correlated quantum dot, which combines adiabatic lattice density functional theory in the Bethe ansatz local-density approximation (BALDA) to the Hubbard model, with the multiple-probe battery method for open-boundary simulations in the time domain. In agreement with the recently proposed dynamical picture of Coulomb blockade, a characteristic driven regime, defined by regular current oscillations, is demonstrated for a certain range of bias voltages. We further investigate the effects of systematically improving the approximation for the electron-electron interaction at the dot site (going from non-interacting, through Hartree-only to adiabatic BALDA) on the transmission spectrum and the I-V characteristics. In particular, a negative differential conductance is obtained at large bias voltages and large Coulomb interaction strengths. This is attributed to the combined effect of the electron-electron interaction at the dot and the finite bandwidth of the electrodes.

Field-controlled Luttinger liquid and possible crossover into spin liquid in strong-rail ladder systems

The thermodynamics and transport properties of strong-rail ladder systems are investigated by means of Green's function theory. It is shown that the magnetic behavior clearly manifests a typical antiferromagnetism with gapped or gapless low-lying excitations, which is in agreement with the experimental results. In addition, the temperature-field-induced phase diagram is explored, and we demonstrate a Luttinger liquid behavior in the window h(c) (marking the ending of the M=0 plateau)<h<h(s) (saturation magnetic field) within a narrow range of temperature. The spin liquid phase is uncovered for h<h(c) upon cooling down to zero temperature. It is also shown that the rung entanglement entropy is a good indicator for detecting the field-driven quantum criticality. Meanwhile, the magnetic susceptibility, the specific heat, and the thermal (spin) Drude weights are calculated to characterize the plentiful quantum phases, in which the thermal insulating and conducting behaviors can be controlled by magnetic fields.