Tunneling Regime Research Articles

Threshold Condition of Energy Splitting for Some Classes of Symmetric Double Well Potential

The double-well potential (DWP) is a prevalent mathematical model for systems with 2 force centers, widely applied in quantum physics. Often expressed as a function with multiple parameters, the DWP can exhibit either single-well or double-well behavior depending on these parameters. Within the tunneling regime, optical properties are primarily characterized by the energy difference resulting from energy splitting (ES). Thus, formulating boundary conditions for the DWP and quantifying ES are critical but understudied areas. This research explores the threshold conditions for the existence of DWPs and ES in 2 common classes of symmetric DWPs: The extensively studied Razavy potentials and the more recently introduced Dong potentials. Utilizing quasi-exact solutions for Razavy potentials and the filter method for Dong potentials, we analyze the dependence of ES on DWP parameters. Our findings align well with existing numerical data, eigenfunction analysis and energy difference approaches. This innovative methodology allows for the examination of threshold conditions for higher ES, and provides an opportunity to control ES in DWPs by adjusting structural parameters. HIGHLIGHTS For symmetric-hyperbolicus double well potentials there are some threshold condition,.i.e.: (i) threshold for existence DWP, (ii) threshold for existence DWP with first-level energy splitting rE12 characterized by ε2 = Vmax, and (iii) Threshold for existence DWP with higher-level energy splitting rEij characterized by εj = Vmax. The method has been applied in the Razavy and Dong class potentials. The eigen-energies are determined through quasi-exact solutions for Razavy potentials and numerically using the filter method for Dong potentials. We find the the critical condition as a function od structural parameters. Our findings are in good agreement with the eigenfunction and energy difference approaches. GRAPHICAL ABSTRACT

Atomistic first-principles modeling of single donor spin-qubit

Using an impurity atom in crystal silicon as a spin-1/2 qubit has been made experimentally possible recently where the impurity atom acts as a quantum dot (QD). Quantum transport in and out of such a donor QD occurs in the sequential tunneling regime where a physical quantity of importance is the charging (addition) energy, which measures the energy necessary for adding an electron into the donor QD. In this work, we present a first-principles method to quantitatively predict the addition energy of the donor QD. Using density functional theory (DFT), we determine the impurity states that serve as the basis set for subsequent exact diagonalization calculation of the many-body states and energies of the donor QD. Due to the large effective Bohr radius of the conduction electrons in Si, very large supercells containing more than 10 000 atoms must be used to obtain accurate results. For the donor QD of a phosphorus impurity in bulk Si, the combined DFT and exact diagonalization predicts the first addition energy to be 53 meV, in good agreement with the corresponding experimental value. For the donor QD of an arsenic impurity in Si, the first addition energy is predicted to be 44.2 meV. The calculated many-body wave functions provide a vivid electronic picture of the donor QD.

Gradual Change between Coherent and Incoherent Tunneling Regimes Induced by Polarizable Halide Substituents in Molecular Tunnel Junctions.

This paper describes a gradual transition of charge transport across molecular junctions from coherent to incoherent tunneling by increasing the number and polarizability of halide substituents of phenyl-terminated aliphatic monolayers of the form S(CH2)10OPhXn, X = F, Cl, Br, or I; n = 0, 1, 2, 3, or 5. In contrast to earlier work where incoherent tunneling was induced by introducing redox-active groups or increasing the molecular length, we show that increasing the polarizability, while keeping the organization of the monolayer structure unaltered, results in a gradual change in the mechanism of tunneling of charge carriers where the activation energy increased from 23 meV for n = 0 (associated with coherent tunneling) to 257 meV for n = 5 with X = Br (associated with incoherent tunneling). Interestingly, this increase in incoherent tunneling rate with polarizability resulted in an improved molecular diode performance. Our findings suggest an avenue to improve the electronic function of molecular devices by introducing polarizable atoms.

Generalized analytical description of relativistic strong-field ionization

A relativistic analytical theory of strong-field ionization applicable across the regimes of deep tunneling up to over-the-barrier ionization (OTBI) is developed, accounting also for the bound-state polarization and the Stark shift beyond perturbation theory. The latter improvement with respect to the state-of-the-art quasiclassical theory of Perelomov-Popov-Terent'ev (PPT) for strong-field ionization is essential to describe analytically the ionization in the OTBI regime and to resolve the order-of-magnitude discrepancy of the ionization yield in the relativistic regime with respect to PPT theory that has remained unexplained since the numerical result using the Klein-Gordon equation of Hafizi []. The predictions of the present relativistic model, in deviation to PPT theory, are shown to be observable using ultrashort laser pulses of relativistic intensities. Published by the American Physical Society 2024

Enhancing the excitation gap of a quantum-dot-based Kitaev chain

Connecting double quantum dots via a semiconductor-superconductor hybrid segment offers a platform for creating a two-site Kitaev chain that hosts Majorana zero modes at a finely tuned sweet spot. However, the effective couplings mediated by Andreev bound states in the hybrid are generally weak in the tunneling regime. As a consequence, the excitation gap is limited in size, presenting a formidable challenge for using this platform to demonstrate non-Abelian statistics and realize topological quantum computing. Here we systematically study the effects of increasing the dot-hybrid coupling. In particular, the proximity effect transforms the dot orbitals into Yu-Shiba-Rusinov states, and as the coupling strength increases, the excitation gap is significantly enhanced and sensitivity to local perturbation is reduced. We also discuss how the strong-coupling regime shows in experimentally accessible quantities, such as conductance, and provide a protocol for tuning a double-dot system into a sweet spot with a large excitation gap.

Marcus Theory and Long-Range Activationless Transport in Molecular Junctions.

Intrachain transport in molecular junctions (MJs) longer than 5 nm has been modeled within the theoretical framework of Marcus theory. We show that in oligo(bisthienylbenzene)-based MJs, electronic transport involves polarons, localized on three monomers that are close to 4 nm in length. They hop and tunnel between adjacent localized sites with reorganization energies λ close to 400-600 meV and electronic coupling parameters Hab close to λ/2. As a consequence, the activation energy for intrachain transport, given by the equation ΔG* = (λ/4)(1 - 2Hab/λ)2, is close to zero, and transport along the chain is activationless, in agreement with experimental observation. On the contrary, similar calculations on conjugated oligonaphthalenefluoreneimine wires show that Hab is much less than λ/2 and predict that the activation energies for intrachain hopping between adjacent sites, close to λ/4, are ∼115 meV. This work proposes a new perspective for understanding long-range activationless transport in MJs beyond the tunneling regime.

Nanoironing van der Waals Heterostructures toward Electrically Controlled Quantum Dots.

Assembling two-dimensional van der Waals (vdW)-layered materials into heterostructures is an exciting development that sparked the discovery of rich correlated electronic phenomena. vdW heterostructures also offer possibilities for designer device applications in areas such as optoelectronics, valley- and spintronics, and quantum technology. However, realizing the full potential of these heterostructures requires interfaces with exceptionally low disorder which is challenging to engineer. Here, we show that thermal scanning probes can be used to create pristine interfaces in vdW heterostructures. Our approach is compatible at both the material- and device levels, and monolayer WS2 transistors show up to an order of magnitude improvement in electrical performance from this technique. We also demonstrate vdW heterostructures with low interface disorder enabling the electrical formation and control of quantum dots that can be tuned from macroscopic current flow to the single-electron tunneling regime.

Nonstatistical Unimolecular Decay of the CH2OO Criegee Intermediate in the Tunneling Regime.

Unimolecular decay of the formaldehyde oxide (CH2OO) Criegee intermediate proceeds via a 1,3 ring-closure pathway to dioxirane and subsequent rearrangement and/or dissociation to many products including hydroxyl (OH) radicals that are detected. Vibrational activation of jet-cooled CH2OO with two quanta of CH stretch (17-18 kcal mol-1) leads to unimolecular decay at an energy significantly below the transition state barrier of 19.46 ± 0.25 kcal mol-1, refined utilizing a high-level electronic structure method HEAT-345(Q)Λ. The observed unimolecular decay rate of 1.6 ± 0.4 × 106 s-1 is 2 orders of magnitude slower than that predicted by statistical unimolecular reaction theory using several different models for quantum mechanical tunneling. The nonstatistical behavior originates from excitation of a CH stretch vibration that is orthogonal to the heavy atom motions along the reaction coordinate and slow intramolecular vibrational energy redistribution due to the sparse density of states.

Quantum Circuits with Multiterminal Josephson-Andreev Junctions

We explore superconducting quantum circuits where several leads are simultaneously connected beyond the tunneling regime, such that the fermionic structure of Andreev bound states in the resulting multiterminal Josephson junction influences the states of the full circuit. Using a simple model of single-channel contacts and a single level in the middle region, we discuss different circuit configurations where the leads are islands with finite capacitance and/or form loops with finite inductance. We find situations of practical interest where the circuits can be used to define noise-protected qubits, which map to the bifluxon and 0−π qubits in the tunneling regime. We also point out the subtleties of the gauge choice for a proper description of these quantum circuit dynamics. Published by the American Physical Society 2024

A personal perspective of the present status and future challenges facing thermal reaction rate theory.

Reaction rate theory has been at the center of physical chemistry for well over one hundred years. The evolution of the theory is not only of historical interest. Reliable and accurate computation of reaction rates remains a challenge to this very day, especially in view of the development of quantum chemistry methods, which predict the relevant force fields. It is still not possible to compute the numerically exact rate on the fly when the system has more than at most a few dozen anharmonic degrees of freedom, so one must consider various approximate methods, not only from the practical point of view of constructing numerical algorithms but also on conceptual and formal levels. In this Perspective, I present some of the recent analytical results concerning leading order terms in an ℏ2m series expansion of the exact rate and their implications on various approximate theories. A second aspect has to do with the crossover temperature between tunneling and thermal activation. Using a uniform semiclassical transmission probability rather than the "primitive" semiclassical theory leads to the conclusion that there is no divergence problem associated with a "crossover temperature." If one defines a semiclassical crossover temperature as the point at which the tunneling energy of the instanton equals the barrier height, then it is a factor of two higher than its previous estimate based on the "primitive" semiclassical approximation. In the low temperature tunneling regime, the uniform semiclassical theory as well as the "primitive" semiclassical theory were based on the classical Euclidean action of a periodic orbit on the inverted potential. The uniform semiclassical theory wrongly predicts that the "half-point," which is the energy at which the transmission probability equals 1/2, for any barrier potential, is always the barrier energy. We describe here how augmenting the Euclidean action with constant terms of order ℏ2 can significantly improve the accuracy of the semiclassical theory and correct this deficiency. This also leads to a deep connection with and improvement of vibrational perturbation theory. The uniform semiclassical theory also enables an extension of the quantum version of Kramers' turnover theory to temperatures below the "crossover temperature." The implications of these recent advances on various approximate methods used to date are discussed at length, leading to the conclusion that reaction rate theory will continue to challenge us both on conceptual and practical levels for years to come.

Quantum information scrambling and chemical reactions

The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Out-of-time-order correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a double-well reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the early-time OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the low-temperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.

Semiclassical reaction rate constant of non-adiabatic system by means of initial value representation

We applied the semiclassical initial value representation (SC-IVR) method with the classical electron analog to deal with electronically non-adiabatic reactive barriers and calculated the thermal reaction rate constant. The symmetric form of the flux–flux correlation function is used, and the matrix element of the Boltzmannized flux operator is derived using imaginary-time path integral techniques. This combined use of non-adiabatic SC-IVR and non-adiabatic path-integral sampling (NA-IVR&PI) is beyond the treatment of mean-field, and we analyze its performance in comparison with some existing mean-field methods for different scenarios of potential energy surface. We found a systematically better performance. One exception is the deep tunneling regime, where the mean-field ring-polymer instanton is superior. In the golden rule limit, where all these mean-field methods break down, the significant advantage of NA-IVR&PI is shown by using the electronic states for description of the dividing surface.

Nuclear Quantum Effects in Hydroxide Hydrate Along the H-Bond Bifurcation Pathway.

Path integral (PI) simulations are used to explore nuclear quantum effects (NQEs) in hydroxide hydrate and its perdeuterated isotopomer along the H-bond bifurcation pathway. Toward this, a new potential energy surface using the symmetric gradient domain machine learning method with ab initio data at the CCSD(T)/aug-cc-pVTZ level is built. From PI umbrella sampling (US) simulations, free energy profiles along the bifurcation coordinate are explored as a function of temperature. At ambient temperature, the bifurcation barrier is increased upon inclusion of NQEs. At low temperatures in the deep tunneling regime, the barrier is strongly decreased and flattened. These trends are examined, and the role of the O-O distance is also investigated through two-dimensional US simulations.

Dielectric-Modulated Junctionless Carbon Nanotube Field-Effect Transistor as a Label-Free DNA Nanosensor: Achieving Ultrahigh Sensitivity in the Band-to-Band Tunneling Regime

Dielectric-Modulated Junctionless Carbon Nanotube Field-Effect Transistor as a Label-Free DNA Nanosensor: Achieving Ultrahigh Sensitivity in the Band-to-Band Tunneling Regime

Quantum plasmonics pushes chiral sensing limit to single molecules: a paradigm for chiral biodetections

Chiral sensing of single molecules is vital for the understanding of chirality and their applications in biomedicine. However, current technologies face severe limitations in achieving single-molecule sensitivity. Here we overcome these limitations by designing a tunable chiral supramolecular plasmonic system made of helical oligoamide sequences (OS) and nanoparticle-on-mirror (NPoM) resonator, which works across the classical and quantum regimes. Our design enhances the chiral sensitivity in the quantum tunnelling regime despite of the reduced local E-field, which is due to the strong Coulomb interactions between the chiral OSs and the achiral NPoMs and the additional enhancement from tunnelling electrons. A minimum of four molecules per single-Au particle can be detected, which allows for the detection of an enantiomeric excess within a monolayer, manifesting great potential for the chiral sensing of single molecules.

Point-Contact Spectroscopy in Bulk Samples of Electron-Doped Cuprate Superconductors.

Point-contact spectroscopy was performed on bulk samples of electron-doped high temperature superconductor Nd2-xCexCuO4-δ. The samples were characterized using X-ray diffraction and scanning electron microscopy equipped with a wavelength-dispersive spectrometer and an electron backscatter diffraction detector. Samples with Ce content x = 0.15 showed the absence of spurious phases and randomly oriented grains, most of which had dimensions of approximately 220 µm2. The low-bias spectra in the tunneling regime, i.e., high-transparency interface, exhibited a gap feature at about ±5 meV and no zero-bias conductance, despite the random oriented grains investigated within our bulk samples, consistent with most of the literature data on oriented samples. High-bias conductance was also measured in order to obtain information on the properties of the barrier. A V-shape was observed in some cases, instead of the parabolic behavior expected for tunnel junctions.

Renormalized chemical kinetics and benchmark quantum mechanical rates: activation energies and tunnelling transitivities for the reactions of fluorine atoms with H2 and HD

Experimental, theoretical and computational chemical kinetics contribute to progress both in molecular and materials sciences and in biochemistry, exploring the gap between elementary processes and complex systems. Stationary state quantum mechanics and statistical thermodynamics provide interpretive tools and instruments for classical molecular dynamics simulations for stable or metastable structures and near-equilibrium situations. Chemical reaction kinetics plays a key role at the mesoscales: time-dependent and evolution problems are typically tackled phenomenologically, and reactions through intermediates and transition states need be investigated and modelled. In this paper, scaling and renormalization procedures are developed beyond the Arrhenius equation and the Transition State Theory, regarding two key observables in reaction kinetics, the rate “constant” as a function of temperature (and its reciprocal, the generalised lifetime), and the apparent activation energy (and its reciprocal, the transitivity function). Coupled first-order equations—dependent on time and on temperature—are formulated in alternative coupling scheme they link experimental results to effective modelling, or vice versa molecular dynamics simulations to predictions. The passage from thermal to tunnelling regimes is uniformly treated and applied to converged quantum mechanical calculations of rate constants available for the prototypical three-atom reactions of fluorine atoms with both H2 and HD: these are exothermic processes dominated by moderate tunnel, needing formal extension to cover the low-temperature regime where aspects of universal behaviour are shown to emerge. The results that have been validated towards experimental information in the 10–350 K temperature range, document the complexity of commonly considered “elementary” chemical reactions: they are relevant for modelling atmospheric and astrophysical environments. Perspectives are indicated of advances towards other types of transitions and to a global generality of processes of interest in applied chemical kinetics in biophysics and in astrochemistry.

X-ray Spectroscopy of a Rare-Earth Molecular System Measured at the Single Atom Limit at Room Temperature.

We investigate the limit of X-ray detection at room temperature on rare-earth molecular films using lanthanum and a pyridine-based dicarboxamide organic linker as a model system. Synchrotron X-ray scanning tunneling microscopy is used to probe the molecules with different coverages on a HOPG substrate. X-ray-induced photocurrent intensities are measured as a function of molecular coverage on the sample, allowing a correlation of the amount of La ions with the photocurrent signal strength. X-ray absorption spectroscopy shows cogent M4,5 absorption edges of the lanthanum ion originated by the transitions from the 3d3/2 and 3d5/2 to 4f orbitals. X-ray absorption spectra measured in the tunneling regime further reveal an X-ray excited tunneling current produced at the M4,5 absorption edge of the La ion down to the ultimate atomic limit at room temperature.

Self-consistent numerical solution of quantum regime with exchange-correlation effects of space charges for electron field emission in a nano-gap

The quantum effects of space charge on electron field emission have been widely investigated since the last century. When electrons energy and their mean spacing approach the Hartree level and the de Broglie wavelength respectively, the influence of the quantum effects on the field emission current becomes significant. In this work, by developing an in-house software, we self-consistently solve the one-dimensional Poisson-Schrödinger equation together with the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) model for metal-vacuum-metal nanogaps, after considering the anode screening effect, space charge Coulomb potential and exchange-correlation effects simultaneously. Employing the method, the electron field emission characteristics were studied by varying the nanogap spacing (D) and the electric field strength (F), and four different emission regimes including quantum regime (QR), space charge limited regime (SCLR), direct tunnelling regime (DTR) and field emission regime (FER) are defined. The influences of space charge field components on the field emission characteristics and space charge distribution are analyzed for different emission regimes in nanogap. In addition, the impact of using different exchange-correlation functionals (LDA, GGA and meta-GGA) on Jacob’s ladder for describing the quantum effects of space charge on the electron emission current density was analyzed. Finally, electron field emission properties of one-dimensional (1-D) nanogaps consisting of refractory metals (W and Mo) as well as the three-dimensional (3-D) nano-tip are discussed to elucidate the impact of the exchange-correlation effects on the enhanced field emission process at nanoscale.

Molecular Thermoelectricity in EGaIn-Based Molecular Junctions.

ConspectusUnderstanding the thermoelectric effects that convert energy between heat and electricity on a molecular scale is of great interest to the nanoscience community. As electronic devices continue to be miniaturized to nanometer scales, thermoregulation on such devices becomes increasingly critical. In addition, the study of molecular thermoelectricity provides information that cannot be accessed through conventional electrical conductance measurements. The field of molecular thermoelectrics aims to explore thermoelectric effects in electrode-molecule-electrode tunnel junctions and draw inferences on how the (supra)molecular structure of active molecules is associated with their thermopower. In this Account, we introduce a convenient and useful junction technique that enables thermovoltage measurements of one molecule thick films, self-assembled monolayers (SAMs), with reliability, and discuss the atomic-detailed structure-thermopower relations established by the technique. The technique relies on a microelectrode composed of non-Newtonian liquid metal, eutectic gallium-indium (EGaIn) covered with a native gallium oxide layer. The EGaIn electrode makes it possible to form thermoelectric contacts with the delicate structure of SAMs in a noninvasive fashion. A defined interface between SAM and the EGaIn electrode allows time-effective collection of large amounts of thermovoltage data, with great reproducibility, efficiency, and reliable interpretation and statistical analysis of the data. We also highlight recent efforts to utilize the EGaIn technique for probing molecular thermoelectricity and structure-thermopower relations. Using the technique, it was possible to unravel quantum-chemical mechanisms of thermoelectric functions, based on the Mott formula, in SAM-based large-area junctions, which in turn led us to set various hypotheses to boost the Seebeck coefficient. By validating the hypotheses again with the EGaIn technique, we revealed that the thermopower of junction increases through the reduction of the energy offset between accessible molecular orbital energy level and Fermi level or the tuning of broadening of the orbital energy level. Such alterations in the shape of energy topography of junction could be achieved through structural modifications in anchoring group and molecular backbone of SAM, and the bottom electrode. Molecular thermoelectrics offers a unique opportunity to build a well-defined nanoscale system and isolate an effect of interest from others, advancing fundamental understanding of charge transport across individual molecules and molecule-electrode interfaces. In the Account, we showed our recent work involving carefully designed molecular system that are relevant to answering the question of how thermopower differs between the tunneling and thermal-hopping regimes. The field of molecular thermoelectrics needs to address practical application-related issues, particularly molecular degradation in thermal environments. In this regard, we summarized the results highlighting the thermal instability of SAM-based junctions based on a traditional thiol anchor group and how to circumvent this problem. We also discussed the power factor (PF)─a practical parameter representing the efficiency for converting heat into electricity─of SAMs, evaluated using the EGaIn technique. In the Conclusion section of this Account, we present future challenges and perspectives.