Nonadiabatic Tunneling Research Articles

Effect of the band structure of the electrodes on the non-adiabatic electron tunneling through a one-level redox molecule

Effect of the band structure of the electrodes having the relatively narrow density of states on the non-adiabatic electron tunneling (the weak tunneling limit) through a one-level redox molecule is considered. The differential conductance, amplification and rectification of the tunnel current are studied and calculated. It is shown that, for some narrow-band electrodes, the dependences of these tunnel current characteristics on the bias voltage differs essentially from those both for the vacuum tunneling contacts and the electrochemical tunneling contacts based on the wide-band electrodes. It is also shown that the band structure effects are of importance and can lead to a number of peculiarities in amplification and rectification of the tunnel current including the possibility to obtain the larger amplification and rectification as compared with those for the in situ tunneling contacts having the wide-band electrodes.

Adiabaticity of the proton-coupled electron-transfer step in the reduction of superoxide effected by nickel-containing superoxide dismutase metallopeptide-based mimics.

Nickel-containing superoxide dismutases (NiSODs) are bacterial metalloenzymes that catalyze the disproportionation of O2(-). These enzymes take advantage of a redox-active nickel cofactor, which cycles between the Ni(II) and Ni(III) oxidation states, to catalytically disprotorptionate O2(-). The Ni(II) center is ligated in a square planar N2S2 coordination environment, which, upon oxidation to Ni(III), becomes five-coordinate following the ligation of an axial imidazole ligand. Previous studies have suggested that metallopeptide-based mimics of NiSOD reduce O2(-) through a proton-coupled electron transfer (PCET) reaction with the electron derived from a reduced Ni(II) center and the proton from a protonated, coordinated Ni(II)-S(H(+))-Cys moiety. The current work focuses on the O2(-) reduction half-reaction of the catalytic cycle. In this study we calculate the vibronic coupling between the reactant and product diabatic surfaces using a semiclassical formalism to determine if the PCET reaction is proceeding through an adiabatic or nonadiabatic proton tunneling process. These results were then used to calculate H/D kinetic isotope effects for the PCET process. We find that as the axial imidazole ligand becomes more strongly associated with the Ni(II) center during the PCET reaction, the reaction becomes more nonadiabatic. This is reflected in the calculated H/D KIEs, which moderately increase as the reaction becomes more nonadiabatic. Furthermore, the results suggest that as the axial ligand becomes less Lewis basic the observed reaction rate constants for O2(-) reduction should become faster because the reaction becomes more adiabatic. These conclusions are in-line with experimental observations. The results thus indicate that variations in the axial donor's ability to coordinate to the nickel center of NiSOD metallopeptide-based mimics will strongly influence the fundamental nature of the O2(-) reduction process.

Tunneling dynamics in multiphoton ionization and attoclock calibration.

The intermediate domain of strong-field ionization between the tunneling and multiphoton regimes is investigated using the strong-field approximation and the imaginary-time method. An intuitive model for the dynamics is developed which describes the ionization process within a nonadiabatic tunneling picture with a coordinate dependent electron energy during the under-the-barrier motion. The nonadiabatic effects in the elliptically polarized laser field induce a transversal momentum shift of the tunneled electron wave packet at the tunnel exit and a delayed appearance in the continuum as well as a shift of the tunneling exit towards the ionic core. The latter significantly modifies the Coulomb focusing during the electron excursion in the laser field after exiting the ionization tunnel. We show that nonadiabatic effects are especially large when the Coulomb field of the ionic core is taken into account during the under-the-barrier motion. The simple man model modified with these nonadiabatic corrections provides an intuitive background for exact theories and has direct implications for the calibration of the attoclock technique.

Nonadiabatic tunneling ionization of atoms in elliptically polarized laser fields

We theoretically investigate the nonadiabatic effects in strong field tunneling ionization of atoms in elliptically polarized laser fields by solving the 3D time-dependent Schrödinger equation (TDSE). Comparing our TDSE results with those of two semi-classical methods, i.e., the quantum-trajectory Monte Carlo simulation (QTMC) and the Coulomb-corrected strong field approximation (CCSFA), we confirm the existence of the nonadiabatic effects with its fingerprint in the nonzero initial lateral velocity at the tunneling exit in the laser polarization plane. Our study shows that these nonadiabatic initial lateral momentum effects become significant in high ellipticity or circularly polarized laser field. These results indicate that the calibration of the experimental laser intensity in this situation should be performed nonadiabatically, which may strongly affect the results of the real tunneling time delay measurements.

Effect of the asymmetry of the coupling of the redox molecule to the electrodes in the one-level electrochemical bridged tunneling contact on the Coulomb blockade and the operation of molecular transistor

Effect of the asymmetry of the redox molecule (RM) coupling to the working electrodes on the Coulomb blockade and the operation of molecular transistor is considered under ambient conditions for the case of the non-adiabatic tunneling through the electrochemical contact having a one-level RM. The expressions for the tunnel current, the positions of the peaks of the tunnel current/overpotential dependencies, and their full widths at the half maximum are obtained for arbitrary values of the parameter d describing the coupling asymmetry of the tunneling contact and the effect of d on the different characteristics of the tunneling contact is studied. The tunnel current/overpotential and the differential conductance/bias voltage dependencies are calculated and interpreted. In particular, it is shown that the effect of the Coulomb blockade on the tunnel current and the differential conductance has a number of new features in the case of the large coupling asymmetry. It is also shown that, for rather large values of the solvent reorganization energy, the coupling asymmetry enhanced strongly amplification and rectification of the tunnel current in the most of the regions of the parameter space specifying the tunneling contact. The regions of the parameter space where both strong amplification and strong rectification take place are also revealed. The obtained results allow us to prove the possibility of the realization of the effective electrochemical transistor based on the one-level RM.

A three-step kinetic model for electrochemical charge transfer in the hopping regime.

Single-step nonadiabatic electron tunneling models are widely used to analyze electrochemical rates through self-assembled monolayer films (SAMs). For some systems, such as nucleic acids, long-range charge transfer can occur in a "hopping" regime that involves multiple charge transfer events and intermediate states. This report describes a three-step kinetic scheme to model charge transfer in this regime. Some of the features of the three-step model are probed experimentally by changing the chemical composition of the SAM. This work uses the three-step model and a temperature dependence of the charge transfer rate to extract the charge injection barrier for a SAM composed of a 10-mer peptide nucleic acid that operates in the hopping regime.

Comparison of theory and experiment for nonadiabatic tunneling in circularly polarized fields

We compare results of the recent experiment by Herath et al [T. Herath, L. Yan, S. K. Lee, and W. Li, Phys. Rev. Lett. 109, 043004 (2012)] on strong-field nonadiabatic tunneling in circularly polarized laser fields with the original predictions of our theory [I. Barth and O. Smirnova, Phys. Rev A 84, 063415 (2011)] that stimulated these experiments. We show that the theory and experiment are in very good agreement. We also explain why the initial comparison performed by Herath et al [T. Herath, L. Yan, S. K. Lee, and W. Li, Phys. Rev. Lett. 109, 043004 (2012)] has suggested quantitative discrepancies with our theory. We confirm that these seeming discrepancies are removed with an accurate application of our theoretical model. We suggest an experiment for unique determination of the ionization preference of valence orbitals p+ or p-.

Nonadiabatic tunneling in circularly polarized laser fields. II. Derivation of formulas

We provide detailed analysis of strong field ionization of degenerate valence $p$ orbitals by circularly polarized fields. Our analytical approach is conceptually equivalent to the Perelomov, Popov, and Terent'ev (PPT) theory and is virtually exact for short-range potentials. After benchmarking our results against the PPT theory for $s$ orbitals, we obtain the results for $p$ orbitals. We also show that, as long as the dipole approximation is valid, both the PPT method and our results are gauge invariant, in contrast with widely used strong field approximation (SFA). Our main result, which has already been briefly outlined in [I. Barth and O. Smirnova, Phys. Rev. A 84, 063415 (2011)], is that strong field ionization preferentially removes electrons counter-rotating to the circularly polarized laser field. The result is illustrated using the example of Kr atom. Strong, up to one order of magnitude, sensitivity of strong field ionization to the sense of electron rotation in the initial state is one of the key signatures of nonadiabatic regime of strong field ionization.

Vibrational quenching of excitonic splittings in H-bonded molecular dimers: Adiabatic description and effective mode approximation

The quenching of the excitonic splitting in hydrogen-bonded molecular dimers has been explained recently in terms of exciton coupling theory, involving Förster's degenerate perturbation theoretical approach [P. Ottiger, S. Leutwyler, and H. Köppel, J. Chem. Phys. 136, 174308 (2012)]. Here we provide an alternative explanation based on the properties of the adiabatic potential energy surfaces. In the proper limit, the lower of these surfaces exhibits a double-minimum shape, with an asymmetric distortion that destroys the geometric equivalence of the excitonically coupled monomers. An effective mode is introduced that exactly reproduces the energy gain and amount of distortion that occurs in a multi-dimensional normal coordinate space. This allows to describe the quenched exciton splitting as the energy difference of the two (S(1) and S(2)) vibronic band origins in a one-dimensional (rather than multi-dimensional) vibronic calculation. The agreement with the earlier result (based on Förster theory) is excellent for all five relevant cases studied. A simple rationale for the quenched exciton splitting as nonadiabatic tunneling splitting on the lower double-minimum potential energy surface is given.

Erratum: Nonadiabatic tunneling in circularly polarized laser fields: Physical picture and calculations [Phys. Rev. A84, 063415 (2011)

Erratum: Nonadiabatic tunneling in circularly polarized laser fields: Physical picture and calculations [Phys. Rev. A<b>84</b>, 063415 (2011)

Erratum: Nonadiabatic tunneling in circularly polarized laser fields: Physical picture and calculations [Phys. Rev. A84, 063415 (2011)

Erratum: Nonadiabatic tunneling in circularly polarized laser fields: Physical picture and calculations [Phys. Rev. A<b>84</b>, 063415 (2011)

Coherent Manipulation of Polarization in Mixed-Valence Compounds by Electric Pulse via Landau–Zener Transitions

In this contribution, we predict and theoretically investigate the effects of the electric field pulse in mixed valence (MV) dimers. These systems exhibit bistability with a large internal dipole moment mediated by the itinerant electron trapped by the vibronic coupling. In this sense, they are similar to single molecular magnets (SMMs) that are bistable systems possessing large long-living magnetization and exhibiting Landau–Zener (LZ) transitions. We propose a scheme for a controllable LZ tunnelling in MV systems that provides also a possibility to control the dipole moment of a dimeric MV unit. It is supposed that the static electric field initially polarizes the system, and then the unit is subjected to a short electric pulse controlling the LZ transitions. The model includes the vibronic pseudo Jahn–Teller (JT) coupling in a MV dimeric system belonging to Class II in Robin and Day classification. We elucidate the main factors controlling coherent nonadiabatic LZ tunneling between the low-lying vibronic levels induced by a short pulse of the electric field. The transition probabilities and consequently polarization induced via the LZ transitions are shown to be dependent on both the time of the pulse and total spin of the cluster. We have suggested to employ the electric field pulse as a tool for the direct observation of the tunneling splitting through the coherent LZ transitions. The magnetic MV systems in which the double exchange is operative are shown to provide a possibility to control electric polarization through the spin-dependent LZ tunneling by applying an additional static magnetic field. The ability of MV systems to change electric polarization in a controllable manner seems to be significant for potential applications.

Classical analog of quasilinear Landau-Zener tunneling

In this paper we develop an analytical framework to study the effect of nonlinearity on irreversible energy transfer in a system of two weakly coupled oscillators with time-dependent parameters, with special attention to an analogy between classical energy transfer and nonadiabatic quantum tunneling. For preciseness, we suppose that a linear oscillator with constant parameters is excited by an initial impulse but a coupled quasilinear oscillator with slowly varying parameters is initially at rest. It is shown that the equations of the slow passage through resonance in this system are identical to quasilinear equations of nonadiabatic Landau-Zener tunneling. Due to revealed equivalence, a recently found analogy between irreversible energy transfer in a classical linear system and conventional linear Landau-Zener tunneling can be extended to quasilinear systems. An explicit analytical solution of the quasilinear problem is found with the help of an iteration procedure, wherein the linear solution is chosen as an initial approximation. Correctness of the constructed approximations is confirmed by numerical simulations. The results presented in this paper, in addition to providing an analytical framework for understanding the transient dynamics of coupled oscillators, suggest an approximate procedure for solving the quasilinear Landau-Zener equations with arbitrary initial conditions over a finite time interval.

Nonadiabatic tunneling in circularly polarized laser fields: Physical picture and calculations

We consider selectivity of strong-field ionization in circularly polarized laser fields to the sense of electron rotation in the laser polarization plane in the initial state. We show that, in contrast to the textbook examples of one-photon ionization and bound-state excitations with increase in the electron angular momentum, and also in contrast to the well-studied ionization of Rydberg atoms in microwave fields, which all prefer corotating electrons, optical tunneling selectively depletes states where the electron initially rotates against the laser field. We also show that key assumptions regarding adiabaticity of optical tunneling may quickly become inaccurate in typical experimental conditions.

A theory of single-electron non-adiabatic tunneling through a small metal nanoparticle with due account of the strong interaction of valence electrons with phonons of the condensed matter environment

A theory of electrochemical behavior of small metal nanoparticles (NPs) which is governed both by the charging effect and the effect of the solvent reorganization on the dynamic of the electron transfer (ET) is considered under ambient conditions. The exact expression for the rate constant of ET from an electrode to NP which is valid for all values of the reorganization free energy E(r), bias voltage, and overpotential is obtained in the non-adiabatic limit. The tunnel current/overpotential relations are studied and calculated for different values of the bias voltage and E(r). The effect of E(r) on the full width at half maximum of the charging peaks is investigated at different values of the bias voltage. The differential conductance/bias voltage and the tunnel current/bias voltage dependencies are also studied and calculated. It is shown that, at room temperature, the pronounced Coulomb blockade oscillations in the differential conductance/bias voltage curves and the noticeable Coulomb staircase in the tunnel current/bias voltage relations are observed only at rather small values of E(r) in the case of the strongly asymmetric tunneling contacts.

A theory of molecular transistor based on the two-center electrochemical bridged tunneling contact

It is shown that the two-center bridged tunneling contact in the serial configuration based on the donor–acceptor single redox molecule immersed in the electrolyte solution at the ambient conditions (i.e., room temperature and condensed matter environment) demonstrates pronounced transistor-like features for certain sets of the physical parameters of the system. Electrons at the redox centers of the bridge molecule are coupled strongly to the classical phonon modes of the condensed matter environment and Debye screening of the electric field is taken into account. The case of the non-adiabatic tunneling of electrons between the centers and between the centers and electrodes is considered and the limit of the infinite Coulomb repulsion between electrons occupying the same center is used. The regions of the physical parameters where both strong rectification and strong amplification (over three orders of magnitude) take place for all positive (or negative) values of the bias voltage are revealed and the transistor-like current/bias voltage characteristics are calculated.

Single-electron non-adiabatic tunneling through a metal nanoparticle with due account of the solvent dynamic effect: The generalization of the “orthodox” theory

A theory of electron tunneling through a small metal nanoparticle (NP) which is governed both by the charging effect and the effect of the solvent reorganization on the tunnel current is presented. The exact expression for the rate constant of electron transfer from an electrode to NP which is valid for all values of the reorganization Gibbs energy E r, bias voltage and overpotential is obtained in the non-adiabatic limit. The tunnel current/overpotential relations are studied for different values of the bias voltage and E r.

Nonadiabatic tunnelling in an ideal one-dimensional semi-infinite periodic potential system: an analytically solvable model

Nonadiabatic tunnelling in an ideal one-dimensional semi-infinite periodic potential system is analysed using our model. Using our simple analytically solvable model it is shown that an ideal one-dimensional semi-infinite periodic potential system can be thought as a model of molecular switch. The method is applicable to those systems where Green's function for the motion in the absence of coupling is known. The method has been applied to the problem where motion takes place on parabolic potentials, for which analytical expression of Green's function can be found.

Towards a new type of energy trap: Classical analog of quantum Landau-Zener tunneling

We present a novel type of an energy trap providing targeted energy transfer in a system of weakly coupled pendulums. Our approach is based on the analogy we revealed between the behavior of two weakly coupled classical parametric pendulums (in linear approximation) and the nonadiabatic Landau-Zener tunneling in a two-state quantum system. This analogy leads us to the prediction of an efficient irreversible transfer of vibration energy from one subsystem to another, when the eigenfrequency of at least one of them changes in time, so that the coupled subsystems pass through an internal resonance. The existence of such a phenomenon is not restricted to coupled pendulums, but is inherent to a wide class of both linear and nonlinear parametric oscillatory systems. This opens up the possibility of designing new types of energy traps and absorbers for the dynamic protection of various mechanical systems.

Dielectric breakdown in a Mott insulator: Many-body Schwinger-Landau-Zener mechanism studied with a generalized Bethe ansatz

The nonadiabatic quantum tunneling picture, which may be called the many-body Schwinger-Landau-Zener mechanism, for the dielectric breakdown of Mott insulators in strong electric fields is studied in the one-dimensional Hubbard model. The tunneling probability is calculated by a metod due to Dykhne-Davis-Pechukas with an analytical continuation of the Bethe-ansatz solution for excited states to a non-Hermitian case. A remarkable agreement with the time-dependent density matrix renormalization group result is obtained.