As a possible physical realization of a quantum information processor, a system with stacked self-assembled InAs quantum dots buried in GaAs in adjacent to the channel of a spin field-effect transistor has been proposed. In this system, only one of the stacked qubits, i.e. the edge qubit (the qubit closest to the channel), is measurable via "spin-blockade measurement." It is shown that the state tomography of the whole chain of the qubits is still possible even under such a restricted accessibility. The idea is to make use of the entangling dynamics of the qubits. A recipe for the two-qubit system is explicitly constructed and the effect of an imperfect fidelity of the measurement is clarified. A general scheme for multiple qubits based on repeated measurements is also presented.
We incorporate an Al-AlO_x-Al single-electron transistor as the gate of a narrow (~100 nm) metal-oxide-semiconductor field-effect transistor (MOSFET). Near the MOSFET channel conductance threshold, we observe oscillations in the conductance associated with Coulomb blockade in the channel, revealing the formation of a Si single-electron transistor. Abrupt steps present in sweeps of the Al transistor conductance versus gate voltage are correlated with single-electron charging events in the Si transistor, and vice versa. Analysis of these correlations using a simple electrostatic model demonstrat…
We report finite-bias characteristics of electrical transport through phosphorus donors in silicon nanoscale transistors, in which we observe inelastic-cotunneling current in the Coulomb blockade region. The cotunneling current appears like a resonant-tunneling current peak emerging from the excited state at the crossover between blockade and non-blockade regions. These cotunneling features are unique, since the inelastic-cotunneling currents have so far been reported either as a broader hump or as a continuous increment of current. This finding is ascribed purely due to excitation-related ine…
Current-driven vibrational non-equilibrium induces vibrational sidebands in single-molecule transistors which arise from tunneling processes accompanied by absorption of vibrational quanta. Unlike conventional sidebands, these absorption sidebands occur in a regime where the current is nominally Coulomb blockaded. Here, we develop a detailed and analytical theory of absorption sidebands, including current-voltage characteristics as well as shot noise. We discuss the relation of our predictions to recent experiments.
We investigate vibron-assisted electron transport in single-molecule transistors containing an individual Fe4 Single-Molecule Magnet. We observe a strong suppression of the tunneling current at low bias in combination with vibron-assisted excitations. The observed features are explained by a strong electron-vibron coupling in the framework of the Franck-Condon model supported by density-functional theory.
We demonstrate a tunable negative differential resistance controlled by spin blockade in single electron transistors. The single electron transistors containing a few electrons and spin polarized source and drain contacts were formed in GaAs/GaAlAs heterojunctions using metallic gates. Coulomb blockade measurements performed as a function of applied source-drain bias, electron number and magnetic field reveal well defined regimes where a decrease in the current is observed with increasing bias. We establish that the origin of the negative differential regime is the spin-polarized detection of …
Single-electron transistors embedded in a suspended nanobeam or carbon nanotube may exhibit effects originating from the coupling of the electronic degrees of freedom to the mechanical oscillations of the suspended structure. Here, we investigate theoretically the consequences of a capacitive electromechanical interaction when the supporting beam is brought close to the Euler buckling instability by a lateral compressive strain. Our central result is that the low-bias current blockade, originating from the electromechanical coupling for the classical resonator, is strongly enhanced near the Eu…
We have fabricated and measured superconducting single-electron transistors with Al leads and Nb islands. At bias voltages below the gap of Nb we observe clear signatures of resonant tunneling of Cooper pairs, and of Coulomb blockade of the subgap currents due to linewidth broadening of the energy levels in the superconducting density of states of Nb. The experimental results are in good agreement with numerical simulations.
We have measured the Cooper Pair Transistor (CPT) in a tunable electromagnetic environment consisting of four one-dimensional SQUID arrays. The transport properties of the CPT in the high impedance limit, Z_env>>R_Q=6.45~kΩ, are studied for different ratios of the Josephson coupling energy to the charging energy. As the impedance of the environment is increased, the current-voltage characteristic (IVC) of the CPT develops a Coulomb blockade of Cooper pair tunneling and the measured IVCs agree qualitatively with a theory based on quasicharge dynamics for a CPT. Increasing the impedance of the e…
We investigate a silicon single-electron transistor (SET) in a metal-oxide-semiconductor (MOS) structure by applying a magnetic field perpendicular to the sample surface. The quantum dot is defined electrostatically in a point contact channel and by the potential barriers from negatively charged interface traps. The magnetic field dependence of the excitation spectrum is primarily driven by the Zeeman effect. In the two-electron singlet-triplet (ST) transition, electron-electron Coulomb interaction plays a significant role. The evolution of Coulomb blockade peaks with magnetic field B is also …
We have fabricated quantum dot single electron transistors, based on AlGaAs/GaAs heterojunctions without modulation doping, which exhibit clear and stable Coulomb blockade oscillations. The temperature dependence of the Coulomb blockade peak lineshape is well described by standard Coulomb blockade theory in the quantum regime. Bias spectroscopy measurements have allowed us to directly extract the charging energy, and showed clear evidence of excited state transport, confirming that individual quantum states in the dot can be resolved.
In order to illustrate the emergence of Coulomb blockade from coherent quantum phase-slip processes in thin superconducting wires, we propose and theoretically investigate two elementary setups, or "devices". The setups are derived from Cooper-pair box and Cooper-pair transistor, so we refer to them as QPS-box and QPS-transistor, respectively. We demonstrate that the devices exhibit sensitivity to a charge induced by a gate electrode, this being the main signature of Coulomb blockade. Experimental realization of these devices will unambiguously prove the Coulomb blockade as an effect of cohere…
Single electron transistors (SETs) made from single wall carbon nanotubes (SWCNTs) are promising for quantum electronic devices operating with ultra-low power consumption and allow fundamental studies of electron transport. We report on SETs made by registered in-plane growth utilizing tailored nanoscale catalyst patterns and chemical vapor deposition. Metallic SWCNTs have been removed by an electrical burn-in technique and the common gate hysteresis was removed using PMMA and baking, leading to field effect transistors with large on/off ratios up to 10^5. Further segmentation into 200 nm shor…
We present a new mechanism for a spin blockade effect associated with a change in the type of magnetic anisotropy over oxidation state in a single molecule transistor, by taking an example of an individual Eu$_{2}$(C$_{8}$H$_{8}$)$_{3}$ molecule weakly coupled to non-magnetic electrodes without linker groups. The molecule switches its magnetization direction from in-plane to out-of-plane when it is charged. In other words, the magnetic anisotropy of the molecule changes from easy plane to easy axis when the molecule is charged. By solving the master equation based on model Hamiltonian, we find…
Influence of forced mechanical vibrations of a suspended single-electron transistor on electron tunneling through the quantum dot limited by the Coulomb blockade is investigated. It is shown that mechanical oscillations of the quantum dot lead to the Coulomb blockade breakdown, shown in sharp resonant peaks in the transistor conductance dependence on the excitation frequency at values corresponding to the mechanical oscillations eigen modes. Physical mechanism of the observed effect is considered. It is presumably connected with oscillations of the mutual electrical capacitances between the qu…
The magnetopolaronic generalization of a Majorana-resonant-level (MRL) model is considered for a single-level vibrating quantum dot coupled to two half-infinite $g=1/2$ Tomonaga-Luttinger liquid (TLL) leads. A qualitatively new non-trivial formula for the effective transmission coefficient and differential conductance for resonant magnetopolaron-assisted tunneling is obtained under the assumption about a fermion-boson factorization of corresponding averages. This approach is valid for the case of weak magnetopolaronic coupling in a system. Surprisingly, it is found that despite a supposed weak…
We present a theory of a single-electron transistor exchange-coupled to a localized spin. We show how to gain detailed quantitative knowledge about the attached spin such as spin size, exchange coupling strength, Landé g-factor, and spin decay time $T_1$ by utilizing a robust blockade phenomenon of DC magnetotransport with accompanying noise enhancement. Our studies are of particular relevance to spin-resolved scanning single-electron transistor microscopy, electronic transport through nanomagnets, and the effect of hyperfine interaction on transport electrons by surrounding nuclear spins.
Coulomb blockade-like transport and enhanced memory in organic transistors embedded with sub-nm Pt nanoparticles for neuromorphic computing
Department of Physics and Astronomy, University of Missouri（密苏里大学物理与天文学系）；MU Materials Science and Engineering Institute, University of Missouri（密苏里大学材料科学与工程研究所）；Department of Electrical Engineering and Computer Science, University of Missouri（密苏里大学电气与计算机工程系）
Metallic nanoparticles offer possibilities to build basic electric devices with new functionality and improved performance. Due to the small volume and the resulting low self-capacitance, each single nanoparticle exhibits a high charging energy. Thus, a Coulomb-energy gap emerges during transport experiments that can be shifted by electric fields, allowing for charge transport whenever energy levels of neighboring particles match. Hence, the state of the device changes sequentially between conducting and non-conducting instead of just one transition from conducting to pinch-off as in semicondu…
It is known that the quantum-mechanical ground state of a nano-scale junction has a significant impact on its electrical transport properties. This becomes particularly important in transistors consisting of a single molecule. Due to strong electron-electron interactions and the possibility to access ground states with high spins, these systems are eligible hosts of a current-blockade phenomenon called ground-state spin blockade. This effect arises from the inability of a charge carrier to account for the spin difference required to enter the junction, as that process would violate the spin se…
We study the low temperature electrical transport behaviour of a silicon single electron transistor. The island and leads are defined by patterned phosphorus doped regions achieved by ion implantation through a polymer resist mask. In the device a 50 nm diameter island, containing ~600 donors and having a metallic density of states, is separated from source and drain leads by undoped silicon tunnel barriers. The central island and tunnel barriers are covered by a surface gate in a field effect transistor geometry allowing the coupling between the leads and island to be controlled. Coulomb bloc…
We develop a method of theoretically investigating the charge, energy and heat transport in the presence of the charge Kondo correlations. The Coulomb blockade oscillations of heat conductance in the single electron transistor exhibiting the charge Kondo effects are investigated. We explore the Wiedemann Franz ratio in both charge-single channel and charge-two channel Kondo regime. The close connections of our findings with the recent experiments on multi-channel charge Kondo effects are discussed.
Low temperature electron transport measurements of single electron transistors fabricated in advanced CMOS technology with polysilicon gates not only exhibit clear Coulomb blockade behavior but also show a large number of additional conductance fluctuations in the nonlinear regime. By comparison with simulations these features are quantitatively attributed to the effects of discretely charged islands in the polysilicon gates.
Effects of the single-electron tunneling and the Coulomb blockade in a cluster structure (the molecular transistor) are investigated theoretically. In the framework of the particle-in-a-box model for the spherical and disk-shaped gold clusters, the electron spectrum, the temperature dependence of the chemical potential and the residual charge are calculated. We show that the residual charge is equal to the non-integer value of elementary charge $e$ and depends on the cluster's shape. The equations for the analysis of the current-voltage characteristic are used under conservation condition for …
The distribution of nearest-neighbour spacings of Coulomb blockade oscillation peaks in normal conducting aluminum single electron transistors is found to be non-Gaussian. A pronounced tail to reduced spacings is observed, which we attribute to impurity-specific parametric charge rearrangements close to the transistor. Our observation may explain the absence of a Wigner-Dyson distribution in the experimental nearest-neighbour spacing distributions in semiconductor quantum dots.
We study interaction effects on transport through a small metallic cluster connected to two ferromagnetic leads (a single-electron spin-valve transistor) in the "orthodox model" for the Coulomb blockade. The non-local exchange between the spin accumulation on the island and the ferromagnetic leads is shown to affect the transport properties such as the electric current and spin-transfer torque as a function of the magnetic configuration, gate voltage, and applied magnetic field.
A single hole transistor is patterned in a p-Si/SiGe quantum well by applying voltages to nanostructured top gate electrodes. Gating is achieved by oxidizing the etched semiconductor surface and the mesa walls before evaporation of the top gates. Pronounced Coulomb blockade effects are observed at small coupling of the transistor island to source and drain.
We investigate the effect of Zeeman-splitting on quasiparticle transport in normal-superconducting-normal (NSN) aluminum single electron transistors (SETs). In the above-gap transport the interplay of Coulomb blockade and Zeeman-splitting leads to spin-dependence of the sequential tunneling. This creates regimes where either one or both spin species can tunnel onto or off the island. At lower biases, spin-dependence of the single quasiparticle state is studied and operation of the device as a bipolar spin filter is suggested.
We use a simultaneous flow of ethylene and hydrogen gases to grow single wall carbon nanotubes by chemical vapor deposition. Strong coupling to the gate is inferred from transport measurements for both metallic and semiconducting tubes. At low-temperatures, our samples act as single-electron transistors where the transport mechanism is mainly governed by Coulomb blockade. The measurements reveal very rich quantized energy level spectra spanning from valence to conduction band. The Coulomb diamonds have similar addition energies on both sides of the semiconducting gap. Signatures of subbands po…
We consider Coulomb blockade oscillations of thermoelectric coefficients of a single electron transistor based on a quantum dot strongly coupled to one of the leads. Analytic expression for the thermopower as a function of temperature $T$ and the reflection amplitude $r$ in the quantum point contact is obtained. Two regimes can be identified: $T \ll E_C|r|^2$ and $T \gg E_C |r|^2$, where $E_C$ is the charging energy of the dot. The former regime is characterized by weak logarithmic dependence of the thermopower on the reflection coefficient, in the latter the thermopower is linear in the refle…
We integrate ambipolar quantum dots in silicon fin field-effect transistors using exclusively standard complementary metal-oxide-semiconductor fabrication techniques. We realize ambipolarity by replacing conventional highly-doped source and drain electrodes by a metallic nickel silicide with Fermi level close to the silicon mid-gap position. Such devices operate in a dual mode, either as classical field-effect or single-electron transistor. We implement a classical logic NOT gate at low temperature by tuning two interconnected transistors into opposite polarities. In the quantum regime, we dem…
We propose and analyze a scheme for conditional state transfer in a Heisenberg $XXZ$ spin chain which realizes a quantum spin transistor. In our scheme, the absence or presence of a control spin excitation in the central gate part of the spin chain results in either perfect transfer of an arbitrary state of a target spin between the weakly coupled input and output ports, or its complete blockade at the input port. We also present a possible realization of the corresponding spin chain with a one-dimensional ensemble of cold atoms with strong contact interactions.
The shot noise of the current through a single electron transistor (SET), coupled capacitively with an electronic box, is calculated, using the master equation approach. We show that the noise may be sub-Poissonian or strongly super-Poissonian, depending mainly on the box parameters and the gate. The study also supports the idea that not negative differential conductance, but charge accumulation in the quantum dot, responds for the super-Poissonian noise observed.
We study transport in ferromagnetic single-electron transistors. The non- equilibrium spin accumulation on the island caused by a finite current through the system is described by a generalized theory of the Coulomb blockade. It enhances the tunnel magnetoresistance and has a drastic effect on the time- dependent transport properties. A transient decay of the spin accumulation may reverse the electric current on time scales of the order of the spin-flip relaxation time. This can be used as an experimental signature of the non- equilibrium spin accumulation.
Silicon quantum dots are attractive candidates for the development of scalable, spin-based qubits. Pauli spin blockade in double quantum dots provides an efficient, temperature independent mechanism for qubit readout. Here we report on transport experiments in double gate nanowire transistors issued from a CMOS process on 300 mm silicon-on-insulator wafers. At low temperature the devices behave as two few-electron quantum dots in series. We observe signatures of Pauli spin blockade with a singlet-triplet splitting ranging from 0.3 to 1.3 meV. Magneto-transport measurements show that transition…
We present an experimental realization of a Coulomb blockade refrigerator (CBR) based on a single - electron transistor (SET). In the present structure, the SET island is interrupted by a superconducting inclusion to permit charge transport while preventing heat flow. At certain values of the bias and gate voltages, the current through the SET cools one of the junctions. The measurements follow theoretical model down to about 80 mK, which was the base temperature of the current measurements. The observed cooling increases rapidly with decreasing temperature in agreement with the theory, reachi…
Single-electron transistors embedded in a vibrating nanoresonator such as a doubly-clamped carbon nanotube exhibit effects stemming from the coupling between electronic and vibrational degrees of freedom. In particular, a capacitive electromechanical coupling induces a blockade of the current at low bias voltage. It has been recently shown theoretically within a sequential-tunneling approximation that this current blockade can be enhanced by orders of magnitude when the suspended structure is brought to the Euler buckling instability. Here, we investigate the role of cotunneling on the predict…
Current-voltage characteristics of a single-electron transistor with a vibrating quantum dot were calculated assuming vibrons to be in a coherent (non-equilibrium) state. For a large amplitude of quantum dot oscillations we predict strong suppression of conductance and the lifting of polaronic blockade by bias voltage in the form of steps in $I-V$ curves. The height of the steps differs from the prediction of the Franck-Condon theory (valid for equilibrated vibrons) and the current saturates at lower voltages then for the case, when vibrons are in equilibrium state.
We have systematically measured the shot noise in a single electron transistor (SET) as a function of bias and gate voltages. By embedding a SET in a resonance circuit we have been able to measure its shot noise at the resonance frequency 464 MHz, where the 1/f noise is negligible. We can extract the Fano factor which varies between 0.5 and 1 depending on the amount of Coulomb blockade in the SET, in very good agreement with the theory.
Transistors play a vital role in classical computers, and their quantum mechanical counterparts could potentially be as important in quantum computers. Where a classical transistor is operated as a switch that either blocks or allows an electric current, the quantum transistor should operate on quantum information. In terms of a spin model the in-going quantum information is an arbitrary qubit state (spin-1/2 state). In this paper, we derive a model of four qubits with Heisenberg interactions that works as a quantum spin transistor, i.e. a system with perfect state transfer or perfect blockade…
We investigate single molecule magnet transistors (SMMTs) with ligands that support transport resonances. We find the lowest unoccupied molecular orbitals of Mn12-benzoate SMMs (with and without thiol or methyl-sulfide termination) to be on ligands, the highest occupied molecular orbitals being on the Mn12 magnetic core. We predict gate controlled switching between Coulomb blockade and coherent resonant tunneling in SMMTs based on such SMMs, strong spin filtering by the SMM in both transport regimes, and that if such switching is observed then the magnetic easy axis of the SMM is parallel to t…
We report on the observation of Kondo and split Kondo peaks in single-molecule transistors containing a single spin transition molecule with a Fe2+ ion. Coulomb blockade characteristics reveal a double quantum dot behavior in a parallel configuration, making our system a molecular equivalent to a semiconducting double-quantum-dot system. As the gate voltage is increased the charging of the second dot by an additional electron induces a splitting of the Kondo peak. We discuss possible origins of this effect including a spin transition into a high-spin state.
A single-hole transistor is patterned in a p-type, C-doped GaAs/AlGaAs heterostructure by AFM oxidation lithography. Clear Coulomb blockade resonances have been observed at T=300 mK. A charging energy of ~ 1.5 meV is extracted from Coulomb diamond measurements, in agreement with the lithographic dimensions of the dot. The absence of excited states in Coulomb diamond measurements, as well as the temperature dependence of Coulomb peak heights indicate that the dot is in the multi-level transport regime. Fluctuations in peak spacings larger than the estimated mean single-particle level spacing ar…
Single electron charging effects in a surface-gated InSb/AlInSb QW structure are reported. This material, due to its large g-factor and light effective mass, offers considerable advantages over more commonly used materials, such as GaAs, for quantum information processing devices. However, differences in material and device technology result in significant processing challenges. Simple Coulomb blockade and quantised confinement models are considered to explain the observation of conductance oscillations in these structures. The charging energy is found to be comparable with the energy spectrum…
We study electron transport through single-electron spin-valve transistors in the presence of non-local exchange between the ferromagnetic leads and the central normal-metal island. The Coulomb interaction is described with the orthodox model for Coulomb blockade and we allow for noncollinear lead magnetization directions. Two distinct exchange mechanisms that have been discussed in the literature are shown to be of comparable strength and are taken into account on equal footing. We present results for the linear conductance as a function of gate voltage and magnetic configuration, and discuss…
We use Kelvin Force Microscopy (KFM) to study the electrostatic properties of single-walled Carbon Nanotube Field Effect Transistor devices (CNTFETs) with backgate geometry at room temperature. We show that KFM maps recorded as a function of the device backgate polarization enable a complete phenomenological determination of the averaging effects associated with the KFM probe side capacitances, and thus, to obtain KFM measurements with quantitative character. The value of the electrostatic lever arm of the CNTFET is determined from KFM measurements, and found in agreement with transport measur…
We study transport properties of a single electron transistor based on elastic nanotube. Assuming that an external compressive force is applied to the nanotube, we focus on the vicinity of the Euler buckling instability. We demonstrate that in this regime the transport through the transistor is extremely sensitive to elastic disorder. In particular, built-in curvature (random or regular) leads to the ``elastic curvature blockade'': appearance of threshold bias voltage in the $I$-$V$ curve which can be larger than the Coulomb-blockade-induced one. In the case of a random curvature, an additiona…
Based on the Ambegaokar-Eckern-Schon approach to the Coulomb blockade we develop a complete quantum theory of the single electron transistor. We identify a previously unrecognized physical observable q^\prime in the problem that, unlike the usual average charge (Q) on the island, is robustly quantized for any finite value of the tunneling conductance as the temperature goes to absolute zero. This novel quantity is fundamentally related to the non-symmetrized noise of the system. We present a unifying scaling diagram in the q^\prime - g^\prime plane where g^\prime denotes the conductance of the…
We consider nanojunctions in the single-electron tunnelling regime which, due to a high degree of spatial symmetry, have a degenerate many body spectrum. As a consequence, interference phenomena which cause a current blocking can occur at specific values of the bias and gate voltage. We present here a general formalism to give necessary and sufficient conditions for interference blockade also in the presence of spin polarized leads. As an example we analyze a triple quantum dot single electron transistor (SET). For a set-up with parallel polarized leads, we show how to selectively prepare the …
We report on DC and microwave electrical transport measurements in silicon-on-insulator CMOS nano-transistors at low and room temperature. At low source-drain voltage, the DC current and RF response show signs of conductance quantization. We attribute this to Coulomb blockade resulting from barriers formed at the spacer-gate interfaces. We show that at high bias transport occurs thermionically over the highest barrier: Transconductance traces obtained from microwave scattering-parameter measurements at liquid helium and room temperature is accurately fitted by a thermionic model. From the fits…
We propose a novel method for suppression of quasiparticle poisoning in Al Coulomb blockade devices. The method is based on creation of a proper energy gap profile along the device. In contrast to the previously used techniques, the energy gap is controlled by the film thickness. Our transport measurements confirm that the quasiparticle poisoning is suppressed and clear 2$e$ periodicity is observed only when the island is made much thinner than the leads. This result is consistent with the existing model and provides a simple method to suppress quasiparticle poisoning.
We theoretically investigate quantum fluctuation of charge between even and odd states of a normal-superconducting-normal single-electron tunneling transistor. It is shown that due to the superconducting gap, the charge fluctuation in the Coulomb blockade regime for even state is larger than that for odd state. We show that large energy correction in the former regime caused by charge fluctuation can be explained by considering the charging energy renormalization.
Recently, Coulomb blockade physics was observed at room temperature in a carbon nanotube single-electron transistor (H. W. Ch. Postma, et. al., Science 293, 76 (2001)). In this work, we suggest that these devices may be promising for studying the Kondo effect. In particular, they could allow for a detailed investigation of the 2-channel Kondo fixed point. Moreover, fabricating a similar device in a short nanotube could be promising for studying the effect of a magnetic impurity in an ultrasmall metallic grain. Experimental signatures of the Kondo effect in these systems is discussed.
We report a study of transport blockade features in a quantum dot single-electron transistor, based on an undoped AlGaAs/GaAs heterostructure. We observe suppression of transport through the ground state of the dot, as well as negative differential conductance at finite source-drain bias. The temperature and magnetic field dependence of these features indicate the couplings between the leads and the quantum dot states are suppressed. We attribute this to two possible mechanisms: spin effects which determine whether a particular charge transition is allowed based on the change in total spin, an…
We study thermal conductance and thermopower of a metallic single-electron transistor beyond the limit of weak tunnel coupling. Employing both a systematic second-order perturbation expansion and a non-perturbative approximation scheme, we find, in addition to sequential and cotunneling contributions, terms that are associated with the renormalization of system parameters due to quantum fluctuations. The latter can be identified by their logarithmic temperature dependence that is typical for many-channel Kondo correlations. In particular, the temperature dependence of thermopower, which provid…
We study the thermopower of a quantum dot weakly coupled to two reservoirs by tunnel junctions. At low temperatures the transport through the dot is suppressed by charging effects (Coulomb blockade). As a result the thermopower shows an oscillatory dependence on the gate voltage. We study this dependence in the limit of low temperatures where the transport through the dot is dominated by the processes of inelastic cotunneling. We also obtain a crossover formula for intermediate temperatures which connects our cotunneling results to the known sawtooth behavior in the sequential tunneling regime…
