Sequential Tunneling Research Articles

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.

Spectrum of Tunneling Transport through Phonon-Coupled Defect States in a Carbon-Doped Hexagonal Boron Nitride Barrier.

Defects in hexagonal boron nitride (h-BN) play important roles in tunneling transport through the h-BN barrier. Here, using carbon-doped h-BN (h-BN:C) as a tunnel barrier containing defects in a controlled manner, we investigated tunneling transport through defects in the h-BN:C/graphene heterostructures. Defect-assisted tunneling through a specific kind of carbon-related defect was observed in all measured devices, where the defect level was always located at ∼0.1 eV above the graphene's charge neutrality point. We revealed a phonon-assisted inelastic process in the defect-assisted tunneling, in which carriers tunnel through the defect with phonon emission. Furthermore, when the h-BN:C barrier was thick (12 layers, ∼4 nm), sequential tunneling through two defects became dominant, where the phonon-assisted inelastic process shows substantial effects between the two defects. This study reveals the contribution of phonons to defect-assisted tunneling transport, which is essential for the development of defect-related van der Waals (vdW) electronic techniques.

Nonlinear Charge Transport and Excitable Phenomena in Semiconductor Superlattices.

Semiconductor superlattices are periodic nanostructures consisting of epitaxially grown quantum wells and barriers. For thick barriers, the quantum wells are weakly coupled and the main transport mechanism is a sequential resonant tunneling of electrons between wells. We review quantum transport in these materials, and the rate equations for electron densities, currents, and the self-consistent electric potential or field. Depending on superlattice configuration, doping density, temperature, voltage bias, and other parameters, superlattices behave as excitable systems, and can respond to abrupt dc bias changes by large transients involving charge density waves before arriving at a stable stationary state. For other parameters, the superlattices may have self-sustained oscillations of the current through them. These oscillations are due to repeated triggering and recycling of charge density waves, and can be periodic in time, quasiperiodic, and chaotic. Modifying the superlattice configuration, it is possible to attain robust chaos due to wave dynamics. External noise of appropriate strength can generate time-periodic current oscillations when the superlattice is in a stable stationary state without noise, which is called the coherence resonance. In turn, these oscillations can resonate with a periodic signal in the presence of sufficient noise, thereby displaying a stochastic resonance. These properties can be exploited to design and build many devices. Here, we describe detectors of weak signals by using coherence and stochastic resonance and fast generators of true random sequences useful for safe communications and storage.

Geostress-associated settlements of a raft-foundation building due to shield tunnelling in soft ground

The stress state of soil may affect the building settlements induced by tunnelling, which, however, has not been well understood. In this study, 3D numerical analyses combined with in-situ measurements were performed to investigate the geostress-associated settlements of a raft-foundation building due to tunnelling in soft ground. Basically, two types of geostress fields were investigated: the first type considered the effect of additional stress generated in the foundation soil (FAS) due to building weight; while in the second type, a sequential twin tunnelling was presumed, and the effect of additional soil stress induced by the first tunnel (TAS) on the building response to the second tunnel was considered. The results indicated that FAS may aggravate the stress release of the foundation soil, and thus gave rise to a larger building settlement or inclination. In the sequential tunnelling process, the effect of TAS can be more complex: when the first tunnel lowered the stress of foundation soil, TAS effect of the first tunnel may help reduce the building settlements induced by the second tunnel; otherwise, it may aggravate building settlements. In addition to TAS effect, the sheltering effect was also found to play an important part in twin tunnelling.

Quantum fidelity and Von Neumann entropy of a Bose-Fermi Mixture in 1D double well potential

Abstract The time evolution of probability density, the ground-state fidelity and the entanglement of a Bose-Fermi mixture in a 1D double well potential, are studied through the two-mode approximation.

We found that the behavior of the quantum return probability shows three distinct regions. The first region is characterized by a complete miscibility, and correlated tunneling of bosons and fermion. The second region is characterized by correlated sequential tunneling and in the last region we found an increase in the tunneling frequency of the two species.

Through the Von Neumann entropy, we found that the boson-fermion coupling allows a maximum entanglement of quantum correlations of bosons and fermions in the same value. \textcolor{red}{Finally, Considering variations in the interaction between pairs of fermions $\lambda_{FF}$, pairs of bosons $\lambda_{BB}$, and variations in the interaction between particles of different species $\lambda_{BF}$, we calculated the fidelity in the $\lambda_{FF}-\lambda_{BF}$ and $\lambda_{BB}-\lambda_{BF}$ planes and we found that the drop of the two fidelities becomes deeper and deeper as the boson-fermion interaction decreases.}

Penetration of arbitrary double potential barriers with probability unity: Implications for testing the existence of a minimum length

Quantum tunneling across double potential barriers is studied. With the assumption that the real space is a continuum, it is rigorously proved that large barriers of arbitrary shapes can be penetrated by low-energy particles with a probability of unity, i.e., realization of resonant tunneling (RT), by simply tuning the interbarrier spacing. The results are demonstrated by tunneling of electrons and protons, in which resonant and sequential tunneling are distinguished. The critical dependence of tunneling probabilities on the barrier positions not only demonstrates the crucial role of phase factors but also points to the possibility of ultrahigh accuracy measurements near resonance. By contrast, the existence of a nonzero minimum length puts upper bounds on the barrier size and particle mass, beyond which effective RT ceases. A scheme is suggested for dealing with the practical difficulties arising from the delocalization of particle position due to the uncertainty principle. This work opens a possible avenue for experimental tests of the existence of a minimum length based on atomic systems. Published by the American Physical Society 2024

The effects of excavating twin tunnels during cyclic loading on the progressive settlement of existing footing

Tunnels may be constructed in a pair undercrossing existing geotechnical structures exposed to cyclic loading. Such construction changes the stress state in the ground in different ways regarding the tunnelling sequence and would lead to large settlement or even failure to those structures under cyclic loading. Large physical model tests were carried out to examine the impact of excavating twin tunnels during cyclic loading on the progressive settlement of footings. The vertical soil stress, footing settlement and ground deformation were analysed regarding different construction sequences and spacings between twin tunnels. The results indicate that previous cyclic loading history affects the alteration of soil stress caused by tunnelling activity. Compared with excavating twin tunnels successively, excavating the tunnels in sequence leads to greater settlement caused by the subsequent cyclic loading. The change in the relative density of soil is invalid to explain the enlargement of the settlement. Finite element analysis was performed to investigate the mechanism of the effects of excavating twin tunnels during cyclic loading on the footing settlement. It was found that the increase of footing settlement in the subsequent cyclic loading and the greater settlement in the sequential tunnelling case are attributed to the greater stress ratio (q/p) in the ground.

Investigation of Peak-to-Valley Current Ratio of GaN/AlN Resonant Tunneling Diodes

Peak-to-valley current ratios (PVCRs) achie-ved in GaN/AlN resonant tunneling diodes (RTDs) are less than 2, significantly less than their counterparts, such as InGaAs/AlAs RTDs (e.g., PVCR <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim$</tex-math> </inline-formula> 12). This has hindered their high-speed applications because the maximum self-oscillation frequency and minimum switching time generally increase and decrease with PVCR. In this article, we investigate the problem of low PVCR in GaN/AlN RTDs with both modeling and experiments. Firstly, we developed a Schrödinger equation-based solver for RTD simulations. While the solver gives reasonable agreement with the experimental current–voltage ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> ) characteristics, such as the positions of resonant peaks, it predicts a much higher PVCR. Then, we conducted temperature dependence studies on GaN/AlN RTDs and compared them with InGaAs/AlAs RTDs. The similarities observed suggest that sequential tunneling with phase randomization, resulting from scattering processes such as optical phonon and interface roughness scattering, is responsible for the large valley currents in GaN/AlN RTDs.

Hydration shell effects in ac-driven single-molecule junctions

We propose a quantum-mechanical model to calculate the current through a single molecular junction immersed in a solvent and surrounded by a thin shell of bound water under an applied ac voltage. The solvent plus hydration shell are captured by a dielectric continuum model for which the resulting spectral density is determined. Here the dielectric properties, e.g., the Debye relaxation time and the dielectric constant, of the bulk solvent and the hydration shell as well as the shell thickness directly enter. We determine the charge current through the molecular junction under an ac voltage in the sequential tunneling regime where we solve a quantum master equation by a real-time diagrammatic technique. Interestingly, the Fourier components of the charge current show an exponential-like decline when the hydration shell thickness increases. Finally, we apply our findings to binary solvent mixtures with varying volume fractions and find that the current is highly sensitive to both the hydration shell thickness as well as the volume fraction of the solvent mixture, giving rise to possible applications as shell and concentration sensors on the molecular scale.

Optical gain reduction caused by nonrelevant subbands in narrow-period terahertz quantum cascade laser designs

The recent designs of terahertz quantum cascade lasers usually employ the short periodic length and also the tall barriers for high-temperature operation. In this work, the effect of high-energy lying non-relevant subbands is studied based on nonequilibrium Green’s function formalisms model, demonstrating those subbands are probable to play a minor role on the population inversion, but play a major role on the optical gain at high temperatures. The phenomenon can be ascribed to the appearance of leakages crossing neighboring periods via sequential resonant tunneling, and those leakages are inherently created by the specific features of the two-well configuration in this design that the phonon well should be wide enough for performing the phonon scattering to depopulate the lower-laser subband. The narrower periodic length design can strengthen this inter-period leakage. A parasitic absorption between the first high-lying nonrelevant subbands from two laser wells can closely overlap the gain shape and thus significantly reduce the peak gain.

Gate-tunable step-like current through a single-molecule junction

Using the kinetic approach, analytical expressions are obtained for the sequential and direct tunneling components of the current in a molecular junction, where the molecule acts as a mediator for interelectrode electron transfer. Within the framework of the modified HOMO-LUMO model, it is shown that the current components are not independent even with weak interaction of the molecule with the electrodes but are interrelated kinetically through processes that lead to the occupation of the electronic states of a charged and neutral molecule. As an application of the theory, the critical voltages determining the ranges of resonant steplike electron transfer through a junction with a planar ZnPc molecule are estimated. The values of the gate voltages at which the junction is capable of performing the functions of photoemitter are presented.

Hyperchaos, Intermittency, Noise and Disorder in Modified Semiconductor Superlattices.

Weakly coupled semiconductor superlattices under DC voltage bias are nonlinear systems with many degrees of freedom whose nonlinearity is due to sequential tunneling of electrons. They may exhibit spontaneous chaos at room temperature and act as fast physical random number generator devices. Here we present a general sequential transport model with different voltage drops at quantum wells and barriers that includes noise and fluctuations due to the superlattice epitaxial growth. Excitability and oscillations of the current in superlattices with identical periods are due to nucleation and motion of charge dipole waves that form at the emitter contact when the current drops below a critical value. Insertion of wider wells increases superlattice excitability by allowing wave nucleation at the modified wells and more complex dynamics. Then hyperchaos and different types of intermittent chaos are possible on extended DC voltage ranges. Intrinsic shot and thermal noises and external noises produce minor effects on chaotic attractors. However, random disorder due to growth fluctuations may suppress any regular or chaotic current oscillations. Numerical simulations show that more than 70% of samples remain chaotic when the standard deviation of their fluctuations due to epitaxial growth is below 0.024 nm (10% of a single monolayer) whereas for 0.015 nm disorder suppresses chaos.

Charge-State Dependent Vibrational Relaxation in a Single-Molecule Junction.

The outcome of an electron-transfer process is determined by the quantum-mechanical interplay between electronic and vibrational degrees of freedom. Nonequilibrium vibrational dynamics are known to direct electron-transfer mechanisms in molecular systems; however, the structural features of a molecule that lead to certain modes being pushed out of equilibrium are not well understood. Herein, we report on electron transport through a porphyrin dimer molecule, weakly coupled to graphene electrodes, that displays sequential tunneling within the Coulomb-blockade regime. The sequential transport is initiated by current-induced phonon absorption and proceeds by rapid sequential transport via a nonequilibrium vibrational distribution of low-energy modes, likely related to torsional molecular motions. We demonstrate that this is an experimental signature of slow vibrational dissipation, and obtain a lower bound for the vibrational relaxation time of 8ns, a value dependent on the molecular charge state.

The hydrogen bond rotation of confined water affected by quantum resonance tunnelling

In this work, we report quantum tunnelling effects on the confined water chain flipping, different from the spatial size and even electronic correlation effects of the confinement environment. First-principles calculations and analyses confirm that quantum tunnelling from the water chain itself enhances the hydrogen bond rotation. Importantly, the neglected resonant tunnelling can result in tunnelling rotation of hydrogen bonds with a probability close to 1 through the provided 0.6 eV energy, while the probability of generally recognized sequential tunnelling is only 10−6. Not only that, compared to sequential tunnelling, resonant tunnelling leads to a 20 K higher flipping temperature of the water chain. Additionally, the ratio of the resonant tunnelling probability to the thermal disturbance probability at 200 K is at least ten times larger than that of sequential tunnelling, which further illustrates the enhancement of hydrogen bond rotation brought about by resonant tunnelling.

Nonrelevant quantum levels effecting on the current in 2-well terahertz quantum cascade lasers

Recent renewed operating temperatures in terahertz quantum cascade lasers emphasize on narrowing the periodic length in a 2-well resonant-phonon design for a clean quantum level structure, in which the depopulation energy is significantly higher than one longitudinal phonon. In this study, various depopulation energies (small and large) are engineered in a 2-well design; the effect of the high-lying nonrelevant levels on the currents are systematically studied by using the non-equilibrium Green’s function method. The engineering of the depopulation energy is unable to avoid the formation of leakage channels, which are activated within at least three neighboring periods via sequential close tunneling. However, a large depopulation energy relaxes the thermal backfilling process; as a result, the net leakages at high temperatures can be significantly suppressed. In addition, pre-alignment remains a critical issue in the design when using a large depopulation energy, which requires improved engineering for the barriers to obtain better laser dynamics.

Matrix product state simulations of quantum quenches and transport in Coulomb blockaded superconducting devices

Superconducting devices subject to strong charging energy interactions and Coulomb blockade are one of the key elements for the development of nanoelectronics and constitute common building blocks of quantum computation platforms and topological superconducting setups. The study of their transport properties is nontrivial and some of their nonperturbative aspects are hard to capture with the most ordinary techniques. Here we present a matrix product state approach to simulate the real-time dynamics of these systems. We propose a study of their transport based on the analysis of the currents after quantum quenches connecting such devices with external leads. Our method is based on the combination of a Wilson chain construction for the leads and a mean-field BCS description for the superconducting scatterers. In particular, we employ a quasiparticle energy eigenbasis which greatly reduces their entanglement growth and we introduce an auxiliary degree of freedom to encode the device's total charge. This approach allows us to treat nonperturbatively both their charging energy and coupling with external electrodes. We show that our construction is able to describe the Coulomb diamond structure of a superconducting dot with subgap states, including its sequential tunneling and cotunneling features. We also study the conductance zero-bias peaks caused by Majorana modes in a blockaded Kitaev chain and compare our results with common Breit-Wigner predictions.

Thermometry in dual quantum dot setup with staircase ground state configuration

We propose and investigate thermometry of a setup employing dual quantum dots with staircase ground state configuration. The stair-case ground state configuration actuates thermally controlled inelastic tunnelling, which translates into a temperature sensitive conductance, thereby inducing thermometry. The performance of the set-up is then analyzed employing quantum master equation (QME) for such systems in the sequential tunnelling regime. In particular, it is demonstrated that the system performance, in terms of temperature sensitivity and efficiency, is maximum in the regime of low temperature, making such system suitable for cryogenic thermometry. The proposed set-up can pave the path towards realization of high performance cryogenic nano temperature sensors.

Thermal transport driven by Coulomb interactions in quantum dots: Enhancement of thermoelectric and heat currents

We investigate thermal transport in a serial asymmetric double quantum dot (DQD) coupled to two electron reservoirs with different temperatures. The inter- and intra-Coulomb interactions are taken into account in a Coulomb blockade DQD where the electron sequential tunneling via four different master equation approaches is considered. In the absence of Coulomb interactions, a neglectable thermoelectric and heat currents is found identifying as the Coulomb blockade DQD regime. In the presence of Coulomb interactions, intra- and inter-Coulomb interactions, crossings energies between the intra- and the inter-dot many-body electron states are observed. The crossings induce extra channels in the energy spectrum of the DQD that enhance thermoelectric and heat currents. The extra channels form several peaks in the thermoelectric and heat currents in which intensity and position of the peaks depend on strength of the inter- and intra-dot Coulomb interactions. In addition, the problem of coherences and incoherences are studied using different approaches to the master equation, which are the first order von-Neumann, the Redfield, a first order Lindblad, and the Pauli methods. We find that all methods give almost similar thermal transport when the role of the coherences is irrelevant in the DQD.

Precession of entangled spin and pseudospin in double quantum dots

Quantum dot spin valves are characterized by exchange fields which induce spin precession and generate current spin resonances even in absence of spin splitting. Analogous effects have been studied in double quantum dots, in which the orbital degree of freedom, the pseudospin, replaces the spin in the valve configuration. We generalize, now, this setup to allow for arbitrary spin and orbital polarization of the leads, thus obtaining an even richer variety of current resonances, stemming from the precession dynamics of entangled spin and pseudospin. We observe for both vectors a delicate interplay of decoherence, pumping and precession which can only be understood by also considering the dynamics of the spin-pseudospin correlators. The numerical results are obtained in the framework of a generalized master equation within the cotunneling approximation and are complemented by the analytics of a coherent sequential tunneling model.

A Simple, Semiclassical Mechanism for Activationless, Long RangeCharge Transport in Molecular Junctions

Past reports on photocurrents in molecular junctions consisting of aromatic oligomers between electrical contacts reveal very low activation energies (<1 meV) and weak distance dependence for molecular layer thicknesses of 20–60 nm. Photocurrent transport mediated by sequential tunneling between adjacent subunit orbitals represents a “super highway” for charge transport with low activation barrier, field dependence and long range of at least 60 nm. In addition to photocurrents, such transport may be involved in dark currents for distances >10 nm, previously reported biological transport across μm in bacterial nanowires, and >1 cm in cable bacteria.