Energy-dependent Tunneling Research Articles

Highly nonlinear transport across single-molecule junctions via destructive quantum interference.

To rival the performance of modern integrated circuits, single-molecule devices must be designed to exhibit extremely nonlinear current-voltage (I-V) characteristics1-4. A common approach is to design molecular backbones where destructive quantum interference (QI) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) produces a nonlinear energy-dependent tunnelling probability near the electrode Fermi energy (EF)5-8. However, tuning such systems is not straightforward, as aligning the frontier orbitals to EF is hard to control9. Here, we instead create a molecular system where constructive QI between the HOMO and LUMO is suppressed and destructive QI between the HOMO and strongly coupled occupied orbitals of opposite phase is enhanced. We use a series of fluorene oligomers containing a central benzothiadiazole10 unit to demonstrate that this strategy can be used to create highly nonlinear single-molecule circuits. Notably, we are able to reproducibly modulate the conductance of a 6-nm molecule by a factor of more than 104.

Direct Measurement of Electron Intervalley Relaxation in a Si/Si - Ge Quantum Dot

The presence of non-degenerate valley states in silicon can drastically affect electron dynamics in silicon-based heterostructures, leading to electron spin relaxation and spin-valley coupling. In the context of solid-state spin qubits, it is important to understand the interplay between spin and valley degrees of freedom to avoid or alleviate these decoherence mechanisms. Here we report the observation of relaxation from the excited valley state to the ground state in a Si/SiGe quantum dot, at zero magnetic field. Valley state read-out is aided by a valley-dependent tunneling effect, which we attribute to valley-orbit coupling. We find a long intervalley relaxation time of 12.0 $\pm$ 0.3 ms, a value that is unmodified when a magnetic field is applied. Furthermore, we compare our findings with the spin relaxation time and find that the spin-valley "hot spot" relaxation is roughly four times slower than intervalley relaxation, consistent with established theoretical predictions. The precision of this technique, adapted from electron spin read-out via energy-dependent tunneling, is an improvement over indirect valley relaxation measurements and could be a useful probe of valley physics in spin and valley qubit implementations.

Self-driven oscillation in Coulomb blockaded suspended carbon nanotubes

Suspended carbon nanotubes are known to support self-driven oscillations due to electromechanical feedback under certain conditions, including low temperatures and high mechanical quality factors. Prior reports identified signatures of such oscillations in Kondo or high-bias transport regimes. Here, we observe self-driven oscillations that give rise to significant conduction in normally Coulomb-blockaded low-bias transport. Using a master equation model, the self-driving is shown to result from strongly energy-dependent electron tunneling, and the dependencies of transport features on bias, gate voltage, and temperature are well reproduced.

Thermovoltage in quantum dots with attractive interaction

We study the linear and nonlinear thermovoltage of a quantum dot with effective attractive electron–electron interaction and weak, energy-dependent tunnel coupling to electronic contacts. Remarkably, we find that the thermovoltage shows signatures of repulsive interaction, which can be rationalized. These thermovoltage characteristics are robust against large potential and temperature differences well into the nonlinear regime, which we expect can be demonstrated in current state-of-the-art experiments. Furthermore, under nonlinear operation, we find extended regions of large power production at efficiencies on the order of the Curzon–Ahlborn bound interrupted only by a characteristic sharp dip.

Heat-flow allocator based on a triple quantum dot.

We theoretically propose a simple setup based on a three-terminal triple quantum dot in the Coulomb blockade regime as a heat-flow allocator to spatially separate heat flow along two different channels at arbitrary proportion. We show that a constant output heat-flow ratio can be obtained in a wide range of system parameters, and any ratio of the output heat flow, whether it is an integer ratio or a fractional ratio, can be obtained by directly adjusting the ratio of the energy-dependent tunneling rate.

Electrical-Driven Plasmon Source of Silicon Based on Quantum Tunneling

A silicon-based light source presents an unreached goal in the field of photonics due to silicon’s indirect electronic band structure preventing direct carrier recombination and subsequent photon emission. Here, we utilize inelastically tunneling electrons to demonstrate an electrically driven light emitting silicon-based tunnel junction operating at room temperature. We show that such a junction is a source for plasmons driven by the electrical tunnel current. We find that the emission spectrum is not given by the quantum condition where the emission frequency would be proportional to the applied voltage, but the spectrum is determined by the spectral overlap between the energy-dependent tunnel current and the modal dispersion of the plasmon. By coupling an internal electric field enhancement with an external k-vector matching grating, we were able to demonstrate a 10-fold increase in the internal efficiency and a 40-fold increase in overall quantum efficiency. Such an electron tunneling-based mechanism could lead to a new class of solid-state light sources with unique features such as down-scalability and temporal responses that are significantly shorter than that of light-emitting diodes.

Single-electron thermal devices coupled to a mesoscopic gate

We theoretically investigate the propagation of heat currents in a three-terminal quantum dot engine. Electron–electron interactions introduce state-dependent processes which can be resolved by energy-dependent tunneling rates. We identify the relevant transitions which define the operation of the system as a thermal transistor or a thermal diode. In the former case, thermal-induced charge fluctuations in the gate dot modify the thermal currents in the conductor with suppressed heat injection, resulting in huge amplification factors and the possible gating with arbitrarily low energy cost. In the latter case, enhanced correlations of the state-selective tunneling transitions redistribute heat flows giving high rectification coefficients and the unexpected cooling of one conductor terminal by heating the other one. We propose quantum dot arrays as a possible way to achieve the extreme tunneling asymmetries required for the different operations.

The fractional acoustoelectric current plateau induced by the energy-dependent tunnelling from dynamic quantum dots into an impurity dot

The fractional acoustoelectric (AE) current plateau in surface-acoustic-waves (SAW) single-electron transport devices is studied by measuring the current plateau as a function of the SAW power and gate bias as well as a function of perpendicular magnetic filed. Our investigation indicates that the fractional plateau is induced by the tunnelling effect from the dynamic quantum dots (QDs) into a static impurity dot. Rate equations are used to extract the tunnelling rates, which change a lot with the number of electrons in the dynamic QDs, the SAW power and gate bias. In addition, the current plateau evolves into a fractional structure, when a strong perpendicular magnetic field is applied to the system.

Characteristics of the resonant charge transfer in strongly coupled plasmas including quantum and shielding effects

The influence of quantum tunnelling and shielding on the resonant electron transfer process in strongly coupled plasmas is investigated. The screened atomic states and energy eigenvalues are employed to obtain the resonant electron transfer cross-section in strongly coupled plasmas. It is found that the classical resonant electron transfer cross-section increases with an increase of the ion-sphere radius. However, the energy-dependent quantum tunnelling resonant electron transfer cross-section is shown to decrease with increasing ion-sphere radius. It is demonstrated that an increase of the nuclear charge decreases the screening effect on the electron transfer cross-section while the quantum tunnelling effect enhances the resonant electron transfer cross-section in strongly coupled plasmas. In addition, it is shown that the effect of quantum tunnelling on the resonant electron transfer process decreases when both the collision energy and ion-sphere radius increase. The variation of shielding effect on the resonant electron transfer process in strongly coupled plasmas is also discussed.

Gate-controlled terahertz single electron photovoltaic effect in self-assembled InAs quantum dots

We have observed a terahertz (THz) induced single electron photovoltaic effect in self-assembled InAs quantum dots (QDs). We used a single electron transistor (SET) geometry that consists of a single InAs QD and nanogap electrodes coupled with a bowtie antenna. Under a weak, broadband THz radiation, a photocurrent induced by THz intersublevel transitions in the QD is generated even when no bias voltage is applied to the SET. The observed single electron photovoltaic effect is due to an energy-dependent tunneling asymmetry in the QD-SET. Moreover, the tunneling asymmetry changes not only with the shell but also with the electron number in the QD, suggesting the manybody nature of the electron wavefunctions. The THz photovoltaic effect observed in the present QD-SET system may have potential applications to nanoscale energy harvesting.

Measurement Back-Action in Stacked Graphene Quantum Dots.

We present an electronic transport experiment in graphene where both classical and quantum mechanical charge detector back-action on a quantum dot are investigated. The device consists of two stacked graphene quantum dots separated by a thin layer of boron nitride. This device is fabricated by van der Waals stacking and is equipped with separate source and drain contacts to both dots. By applying a finite bias to one quantum dot, a current is induced in the other unbiased dot. We present an explanation of the observed measurement-induced current based on strong capacitive coupling and energy dependent tunneling barriers, breaking the spatial symmetry in the unbiased system. This is a special feature of graphene-based quantum devices. The experimental observation of transport in classically forbidden regimes is understood by considering higher-order quantum mechanical back-action mechanisms.

Correlations of heat and charge currents in quantum-dot thermoelectric engines

We analyze the noise properties of both electric charge and heat currents as well as their correlations in a quantum-dot based thermoelectric engine. The engine is a three-terminal conductor with crossed heat and charge flows where heat fluctuations can be monitored by a charge detector. We investigate the mutual influence of charge and heat dynamics and how it is manifested in the current and noise properties. In the presence of energy-dependent tunneling, operating conditions are discussed where a charge current can be generated by heat conversion. In addition, heat can be pumped into the hot source by driving a charge current in the coupled conductor. An optimal configuration is found for structures in which the energy dependence of tunneling maximizes asymmetric transmission with maximal charge–heat cross-correlations. Remarkably, at a voltage that stalls the heat engine we find that in the optimal case the non-equilibrium state is maintained by fluctuations in the heat and charge currents only.

Probing the charge of a quantum dot with a nanomechanical resonator

We have used the mechanical motion of a carbon nanotube (CNT) as a probe of the average charge on a quantum dot. Variations of the resonance frequency and the quality factor are determined by the change in average charge on the quantum dot during a mechanical oscillation. The average charge, in turn, is influenced by the gate voltage, the bias voltage, and the tunnel rates of the barriers to the leads. At bias voltages that exceed the broadening due to tunnel coupling, the resonance frequency and quality factor show a double dip as a function of gate voltage. We find that increasing the current flowing through the CNT at the Coulomb peak does not increase the damping, but in fact decreases damping. Using a model with energy-dependent tunnel rates, we obtain quantitative agreement between the experimental observations and the model. We theoretically compare different contributions to the single-electron induced nonlinearity, and show that only one term is significant for both the Duffing parameter and the mode coupling parameter. We also present additional measurements which support the model we develop: Tuning the tunnel barriers of the quantum dot to the leads gives a 200-fold decrease of the quality factor. Single-electron tunneling through an excited state of the CNT quantum dot also changes the average charge on the quantum dot, bringing about a decrease in the resonance frequency. In the Fabry-P\'{e}rot regime, the absence of charge quantization results in a spring behaviour without resonance frequency dips, which could be used, for example, to probe the transition from quantized to continuous charge with a nanomechanical resonator.

Theory of STM junctions forπ-conjugated molecules on thin insulating films

A microscopic theory of the transport in a scanning tunnelling microscope (STM) set-up is introduced for \pi-conjugated molecules on insulating films, based on the density matrix formalism. A key role is played in the theory by the energy dependent tunnelling rates which account for the coupling of the molecule to the tip and to the substrate. In particular, we analyze how the geometrical differences between the localized tip and extended substrate are encoded in the tunnelling rate and influence the transport characteristics. Finally, using benzene as an example of a planar, rotationally symmetric molecule, we calculate the STM current voltage characteristics and current maps and analyze them in terms of few relevant angular momentum channels.

Noise calculations within the second-order von Neumann approach

We extend the second-order von Neumann approach within the generalized master equation formalism for quantum electronic transport to include the counting field. The resulting non-Markovian evolution equation for the reduced density matrix of the system resolved with respect to the number of transported charges enables the evaluation of the noise and higher-order cumulants of the full counting statistics. We apply this formalism to an analytically solvable model of a single-level quantum dot coupled to highly biased leads with Lorentzian energy-dependent tunnel coupling and demonstrate that, although reproducing exactly the mean current, the resonant tunneling approximation is not exact for the noise and higher-order cumulants. Even if it may fail in the regime of strongly non-Markovian dynamics, this approach generically improves results of lower-order and/or Markovian approaches.

Tunable Spin Loading andT1of a Silicon Spin Qubit Measured by Single-Shot Readout

We demonstrate single-shot readout of a silicon quantum dot spin qubit, and we measure the spin relaxation time T1. We show that the rate of spin loading can be tuned by an order of magnitude by changing the amplitude of a pulsed-gate voltage, and the fraction of spin-up electrons loaded can also be controlled. This tunability arises because electron spins can be loaded through an orbital excited state. Using a theory that includes excited states of the dot and energy-dependent tunneling, we find that a global fit to the loading rate and spin-up fraction is in good agreement with the data.

Pauli spin blockade and lifetime-enhanced transport in a Si/SiGe double quantum dot

We analyze electron transport data through a Si/SiGe double quantum dot in terms of spin blockade and lifetime-enhanced transport (LET), which is transport through excited states that is enabled by long spin relaxation times. We present a series of low-bias voltage measurements showing the sudden appearance of a strong tail of current that we argue is an unambiguous signature of LET appearing when the bias voltage becomes greater than the singlet-triplet splitting for the (2,0) electron state. We present eight independent data sets, four in the forward bias (spin-blockade) regime and four in the reverse bias (lifetime-enhanced transport) regime, and show that all eight data sets can be fit to one consistent set of parameters. We also perform a detailed analysis of the reverse bias (LET) regime, using transport rate equations that include both singlet and triplet transport channels. The model also includes the energy dependent tunneling of electrons across the quantum barriers, and resonant and inelastic tunneling effects. In this way, we obtain excellent fits to the experimental data, and we obtain quantitative estimates for the tunneling rates and transport currents throughout the reverse bias regime. We provide a physical understanding of the different blockade regimes and present detailed predictions for the conditions under which LET may be observed.

Spin- and Energy-Dependent Tunneling through a Single Molecule with Intramolecular Spatial Resolution

We investigate the spin- and energy-dependent tunneling through a single organic molecule (CoPc) adsorbed on a ferromagnetic Fe thin film, spatially resolved by low-temperature spin-polarized scanning tunneling microscopy. Interestingly, the metal ion as well as the organic ligand show a significant spin dependence of tunneling current flow. State-of-the-art abinitio calculations including also van der Waals interactions reveal a strong hybridization of molecular orbitals and substrate 3d states. The molecule is anionic due to a transfer of one electron, resulting in a nonmagnetic (S=0) state. Nevertheless, tunneling through the molecule exhibits a pronounced spin dependence due to spin-split molecule-surface hybrid states.

Modelling of Hot-Electron Energy in Short-Channel MOSFETs by Electrical Method

Channel hot-electron (HE) energy in short-channel metal–oxide–semiconductor field-effect transistors (MOSFETs) is estimated based on electrical characterization. The HE assisted gate leakage is monitored, and its energy dependent tunnelling probability is calculated, from which the excess energy of HE is estimated. The credibility of the proposed method is supported by the experimental and theoretical results, and its accuracy in ultra-small-feature-size device application is also discussed.

Resonance fluorescence in driven quantum dots: Electron and photon correlations

We study the counting statistics for electrons and photons being emitted from a driven two-level quantum dot. Our technique allows us to calculate their mutual correlations as well. We study different transport configurations by tuning the chemical potential of one of the leads to find that the electronic and photonic fluctuations can be externally manipulated by tuning the ac and transport parameters. We also propose special configurations where electron-photon correlation is maximal meaning that spontaneous emission of photons with a well-defined energy is regulated by single electron tunneling. Interesting features are also obtained for energy-dependent tunneling.