Charge and heat transfer through a nanoscale conductor is not only determined by the transmission properties of the electrons, but can also be strongly impacted by coupling to other degrees of freedom in the environment of the conductor. Here, we analyze the influence of the electromagnetic environment on a simple, yet significant thermoelectric property, the thermopower, in the simple transport scenario of single-charge transfer across a tunnel junction. Considering both thermal and out-of-equilibrium steady-state environments, we find that the thermopower can be strongly affected by the environmental state and can, in turn, act as a sensitive probe of environmental properties.
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 have studied the temperature dependent thermopower of gate-defined, lateral quantum dots in the Coulomb blockade regime using an electron heating technique. The line shape of the thermopower oscillations depends strongly on the contributing tunneling processes. Between 1.5 K and 40 mK a crossover from a pure sawtooth- to an intermitted sawtooth-like line shape is observed. The latter is attributed to the increasing dominance of cotunneling processes in the Coulomb blockade regime at low temperatures.
We study the conductance spectrum of graphene quantum dots, both single and multiple cases. The single electron tunneling phenomenon is investigated and the periodicity, amplitude and line shape of the Coulomb blockade oscillations at low temperatures are obtained. Further, we discuss the transport behavior when multiple dots are assembled in array and find a phase transition of conductance spectra from individual Coulomb blockade to collective Coulomb blockade.
We study the mechanism of nuclear spin relaxation in quantum dots due to the electron exchange with 2D gas. We show that the nuclear spin relaxation rate is dramatically affected by the Coulomb blockade and can be controlled by gate voltage. In the case of strong spin-orbit coupling the relaxation rate is maximal in the Coulomb blockade valleys whereas for the weak spin-orbit coupling the maximum of the nuclear spin relaxation rate is near the Coulomb blockade peaks.
We study theoretically the spin-dependent transport in ferromagnet/normal-metal/ferromagnet double tunnel junctions by special attention to cotunneling in the Coulomb blockade region. The spin accumulation caused by cotunneling squeezes the Coulomb blockade region when the magnetizations in the ferromagnetic electrodes are antiparallel. Outside the squeezed Coulomb blockade region, we propose a new anomalous region, where the sequential tunneling in one of the spin bands is suppressed by the Coulomb blockade and that in the other is not. In this region, the tunnel magnetoresistance oscillates …
We report on Coulomb blockade and Coulomb diamond measurements on an etched, tunable single-layer graphene quantum dot. The device consisting of a graphene island connected via two narrow graphene constrictions is fully tunable by three lateral graphene gates. Coulomb blockade resonances are observed and from Coulomb diamond measurements a charging energy of ~3.5 meV is extracted. For increasing temperatures we detect a peak broadening and a transmission increase of the nanostructured graphene barriers.
We present a theory of zero-bias anomalies and dephasing rates for a Coulomb-blockaded quantum dot, driven out of equilibrium by coupling to voltage biased source and drain leads. We interpret our results in terms of the statistics of voltage fluctuations in the system.
We develop the two-instanton approximation to the current-voltage characteristic of a single electron transistor within the Ambegaokar-Eckern-Schön model. We determine the temperature and gate voltage dependence of the Coulomb blockade oscillations of the conductance and the effective charge. We find that a small (in comparison with the charging energy) bias voltage leads to significant suppression of the Coulomb blockade oscillations and to appearance of the bias-dependent phase shift.
We study the Coulomb blockade in a chaotic cavity connected to a lead by a perfectly transmitting quantum channel. In contrast to the previous theories, we show that the quantum fluctuations of charge, resulting from the perfect transmission, do not destroy the Coulomb blockade completely. The oscillatory dependence of all the observable characteristics on the gate voltage persists, its period is not affected; however, phases of the oscillations are random, reflecting the chaotic electron motion in the cavity. Because of this randomness, the Coulomb blockade shows up not in the averages but in…
We report the observation of Coulomb blockade in a quantum dot contacted by two quantum point contacts each with a single fully-transmitting mode, a system previously thought to be well described without invoking Coulomb interactions. At temperatures below 50 mK we observe a periodic oscillation in the conductance of the dot with gate voltage that corresponds to a residual quantization of charge. From the temperature and magnetic field dependence, we infer the oscillations are Mesoscopic Coulomb Blockade, a type of Coulomb blockade caused by electron interference in an otherwise open system.
We study conductance through a quantum dot under Coulomb blockade conditions in the presence of an external periodic perturbation. The stationary state is determined by the balance between the heating of the dot electrons by the perturbation and cooling by electron exchange with the cold contacts. We show that Coulomb blockade peak can have a peculiar shape if heating is affected by dynamic localization, which can be an experimental signature of this effect.
We demonstrate single electron shuttling through two coupled nanomechanical pendula. The pendula are realized as nanopillars etched out of the semiconductor substrate. Coulomb blockade is found at room temperature, allowing metrological applications. By controlling the mechanical shuttling frequency we are able to validate the different regimes of electron shuttling.
I. Introduction (Preface, Basic properties of semiconductor nanostructures). II. Theory of Coulomb-blockade oscillations (Periodicity of the oscillations, Amplitude and lineshape). III. Experiments on Coulomb-blockade oscillations (Quantum dots, Disordered quantum wires, Relation to earlier work on disordered quantum wires). IV. Quantum Hall effect regime (The Aharonov-Bohm effect in a quantum dot, Coulomb blockade of the Aharonov-Bohm effect, Experiments on quantum dots, Experiments on disordered quantum wires).
We study Coulomb charging effects for transport through a topologically nontrivial superconducting wire, where Majorana bound states are present at the interface to normal-conducting leads. We construct the general Keldysh functional integral representation, and provide detailed results for the nonlinear current-voltage relation under weak Coulomb blockade conditions.
We demonstrate experimentally a precise realization of Coulomb Blockade Thermometry (CBT) working at temperatures up to 60 K. Advances in nano fabrication methods using electron beam lithography allow us to fabricate a uniform arrays of sufficiently small tunnel junctions to guarantee an overall temperature reading uncertainty of about 1\%
Coulomb blockade resonances are measured in a GaAs quantum dot in which both shape deformations and interactions are small. The parametric evolution of the Coulomb blockade peaks shows a pronounced pair correlation in both position and amplitude, which is interpreted as spin pairing. As a consequence, the nearest-neighbor distribution of peak spacings can be well approximated by a smeared bimodal Wigner surmise, provided that interactions which go beyond the constant interaction model are taken into account.
The distribution of Coulomb blockade peak heights as a function of magnetic field is investigated experimentally in a Ge-Si nanowire quantum dot. Strong spin-orbit coupling in this hole-gas system leads to antilocalization of Coulomb blockade peaks, consistent with theory. In particular, the peak height distribution has its maximum away from zero at zero magnetic field, with an average that decreases with increasing field. Magnetoconductance in the open-wire regime places a bound on the spin-orbit length ($l_{so}$ < 20 nm), consistent with values extracted in the Coulomb blockade regime ($l_{s…
A new field electron emission (FE) mechanism, which includes Coulomb blockade and quantum confinement effects, is revealed for heterostructured emitters composed of quantum dots and nanowires self-assembled at diamond nanotips. The total energy distributions of the emitted electrons show multiple peaks attributed to the discrete electronic states of the quantum-confined emitter with the corresponding energy levels oscillating as a function of the applied voltage due to the Coulomb blockade. The FE current-voltage characteristics exhibit a modified Coulomb staircase with additional steps becomi…
A tunable directional coupler based on Coulomb Blockade effect is presented. Two electron waveguides are coupled by a quantum dot to an injector waveguide. Electron confinement is obtained by surface Schottky gates on single GaAs/AlGaAs heterojunction. Magneto-electrical measurements down to 350 mK are presented and large transconductance oscillations are reported on both outputs up to 4.2 K. Experimental results are interpreted in terms of Coulomb Blockade effect and the relevance of the present design strategy for the implementation of an electronic multiplexer is underlined.
We extend the theory of Coulomb blockade oscillations to quantum dots which are deformed by the confining potential. We show that shape deformations can generate sequences of conductance resonances which carry the same internal wavefunction. This fact may cause strong correlations of neighboring conductance peaks. We demonstrate the relevance of our results for the interpretation of recent experiments on semiconductor quantum dots.
We develop a theory of the reversible switching of the magnetic state of the ferromagnet-insulator-normal metalferromagnet (FINF) nanostructure. The switching is controlled by tuning the Coulomb blockade strength via the gate voltage on the normal metal granule. The proposed mechanism allows for realizing the switching without passing a dissipative current through the structure.
A magnet with precessing magnetization pumps a spin current into adjacent leads. As a special case of this spin pumping, a precessing macrospin (magnetization) can assist electrons in tunneling. In small systems, however, the Coulomb blockade effect can block the transport of electrons. Here, we investigate the competition between macrospin-assisted tunneling and Coulomb blockade for the simplest system where both effects meet; namely, for a single tunnel junction between a normal metal and a metallic ferromagnet with precessing magnetization. By combining Fermi's golden rule with magnetizatio…
What quantity controls the Coulomb blockade oscillations if the dot--lead conductance is essentially frequency--dependent ? We argue that it is the ac dissipative conductance at the frequency given by the effective charging energy. The latter may be very different from the bare charging energy due to the interface--induced capacitance (or inductance). These observations are supported by a number of examples, considered from the weak and strong coupling (perturbation theory vs. instanton calculus) perspectives.
We report the observation of Coulomb blockade in field electron emission (FE) from single-wall carbon nanotubes (SWCNTs), which is manifested as pronounced steps in the FE current-voltage curves and oscillatory variations in the energy distribution of emitted electrons. The appearance of the Coulomb blockade is explained by the formation of nanoscale protrusions at the apexes of SWCNTs due to the electric field-assisted surface diffusion of adsorbates and carbon adatoms. The proposed adsorbate-assisted FE mechanism is substantially different from the well-known resonant tunneling associated wi…
Signatures of "mesoscopic Coulomb blockade" are reported for quantum dots with one fully transmitting point-contact lead, T1 = 1, T2 << 1. Unlike Coulomb blockade (CB) in weak-tunneling devices (T1, T2 << 1), one-channel CB is a mesoscopic effect requiring quantum coherence. Several distinctive features of mesoscopic CB are observed, including a reduction in CB upon breaking time-reversal symmetry with a magnetic field, relatively large fluctuations of peak position as a function of magnetic field, and strong temperature dependence on the scale of the quantum level spacing.
By using bosonization method and unitary transformation, we give a general relation between the dimensionless tunneling conductance and the fractional Coulomb blockade conductance peak splitting which is valid both for weak and strong transmission between two quantum dots, and show that the tunneling conductance has a linear temperature dependence in the low energy and low temperature limit.
We have investigated one and two dimensional (1D and 2D) arrays of tunnel junctions in partial Coulomb blockade regime. The absolute accuracy of the Coulomb blockade thermometer is influenced by the external impedance of the array, which is not the same in the different topologies of 1D and 2D arrays. We demonstrate, both by experiment and by theoretical calculations in simple geometries, that the 1D structures are better in this respect. Yet in both 1D and 2D, the influence of the environment can be made arbitrarily small by making the array sufficiently large.
We investigate temperature errors of Coulomb blockade thermometer (CBT) arising from inevitable non-uniformities in tunnel junction arrays. The errors are proportional to the junction resistance variance in the universal operation regime and this result holds approximately also beyond this originally studied high temperature range. We present both analytical and numerical results, and discuss briefly their implications on achievable uniformity based on state-of-the-art fabrication of sensors.
We determine the zero-bias anomaly of the conductance of tunnel junctions by an approach unifying the conventional Coulomb blockade theory for ultrasmall junctions with the diffusive anomalies in disordered conductors. Both, electron-electron interactions within the electrodes and electron-hole interactions between the electrodes are taken into account nonperturbatively. Explicit results are given for one- and two-dimensional junctions, and the crossover to ultrasmall junctions is discussed.
We propose that recent transport experiments revealing the existence of an energy gap in graphene nanoribbons may be understood in terms of Coulomb blockade. Electron interactions play a decisive role at the quantum dots which form due to the presence of necks arising from the roughness of the graphene edge. With the average transmission as the only fitting parameter, our theory shows good agreement with the experimental data.
The quantum theory for mesoscopic electric circuit is briefly described. The uncertainty relation for electric charge and current modifies the tranditional Heisenberg uncertainty relation. The mesoscopic ring is regarded as a pure L-design, and the persistent current is obtained explicitly. The Coulomb blockade phenomenon appears when applying to the pure C-design.
We study conductance through a quantum dot under Coulomb blockade conditions in the presence of an external periodic perturbation. The stationary state is determined by the balance between the heating of the dot electrons by the perturbation and cooling. We analyze two cooling mechanisms: electron exchange with the cold contacts and emission of phonons. Together with the usual linear Ohmic heating of the dot electrons we consider possible effects of dynamic localization. The combination of the abovementioned factors may result in a drastic change of the shape of the Coulomb blockade peak with …
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…
We discuss the possibility to generate in Coulomb-blockade systems steady states that violate detailed balance. This includes both voltage biased and non-biased scenarios. The violation of detailed balance yields that the charge-transfer statistics for electrons tunneling into an island experiencing strong Coulomb interaction is different from the statistics for tunneling out. This can be experimentally tested by time-resolved measurement of the island's charge state. We demonstrate this claim for two model systems.
We study the Coulomb blockade in a grain coupled to a lead via a resonant impurity level. We show that the strong energy dependence of the transmission coefficient through the impurity level can have a dramatic effect on the quantization of the grain charge. In particular, if the resonance is sufficiently narrow, the Coulomb staircase shows very sharp steps even if the transmission through the impurity at the Fermi energy is perfect. This is in contrast to the naive expectation that perfect transmission should completely smear charging effects.
The role of the discontinuity of the exchange-correlation potential of density functional theory is studied in the context of electron transport and shown to be intimately related to Coulomb blockade. By following the time evolution of an interacting nanojunction attached to biased leads, we find that, instead of evolving to a steady state, the system reaches a dynamical state characterized by correlation-induced current oscillations. Our results establish a dynamical picture of Coulomb blockade manifesting itself as a periodic sequence of charging and discharging of the nanostructure.
We investigate the two-terminal nonlinear conductance of a Coulomb-blockaded quantum dot attached to chiral edge states. Reversal of the applied magnetic field inverts the system chirality and leads to a different polarization charge. As a result, the current--voltage characteristic is not an even function of the magnetic field. We show that the corresponding magnetic-field asymmetry arises from single-charge effects and vanishes in the limit of high temperature.
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.
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…
Scanning-probe magnetometry is a valuable experimental tool to investigate magnetic phenomena at the micro- and nanoscale. We theoretically analyze the possibility of measuring magnetic fields via the electrical current flowing through quantum dots. We characterize the shot-noise-limited magnetic-field sensitivity of two devices: a single dot in the Coulomb blockade regime, and a double dot in the Pauli blockade regime. Constructing such magnetometers using carbon nanotube quantum dots would benefit from the large, strongly anisotropic and controllable g tensors, the low abundance of nuclear s…
We observe the suppression of the finite frequency shot-noise produced by a voltage biased tunnel junction due to its interaction with a single electromagnetic mode of high impedance. The tunnel junction is embedded in a quarter wavelength resonator containing a dense SQUID array providing it with a characteristic impedance in the kOhms range and a resonant frequency tunable in the 4-6 GHz range. Such high impedance gives rise to a sizeable Coulomb blockade on the tunnel junction (roughly 30% reduction in the differential conductance) and allows an efficient measurement of the spectral density…
We investigate Coulomb blockade thermometers (CBT) in an intermediate temperature regime, where measurements with enhanced accuracy are possible due to the increased magnitude of the differential conductance dip. Previous theoretical results show that corrections to the half width and to the depth of the measured conductance dip of a sensor are needed, when leaving the regime of weak Coulomb blockade towards lower temperatures. In the present work, we demonstrate experimentally that the temperature range of a CBT sensor can be extended by employing these corrections without compromising the pr…
We have investigated how the Coulomb blockade of a mesoscopic Josephson junction in a high-impedance environment is suppressed by shot noise from an adjacent junction. The presented theoretical analysis is an extension of the phase correlation theory for the case of a non-Gaussian noise. Asymmetry of the non-Gaussian noise should result in the shift of the conductance minimum from zero voltage and the ratchet effect (nonzero current at zero voltage), which have been experimentally observed. The analysis demonstrates that a Coulomb blockaded tunnel junction in a high impedance environment can b…
We report on a systematic study of the Coulomb blockade effects in nanofabricated narrow constrictions in thin (Ga,Mn)As films. Different low-temperature transport regimes have been observed for decreasing constriction sizes: the ohmic, the single electron tunnelling (SET) and a completely insulating regime. In the SET, complex stability diagrams with nested Coulomb diamonds and anomalous conductance suppression in the vicinity of charge degeneracy points have been observed. We rationalize these observations in the SET with a double ferromagnetic island model coupled to ferromagnetic leads. It…
We observed the recently predicted quantum suppression of dynamical Coulomb blockade on short coherent conductors by measuring the conductance of a quantum point contact embedded in a tunable on-chip circuit. Taking advantage of the circuit modularity we measured most parameters used by the theory. This allowed us to perform a reliable and quantitative experimental test of the theory. Dynamical Coulomb blockade corrections, probed up to the second conductance plateau of the quantum point contact, are found to be accurately normalized by the same Fano factor as quantum shot noise, in excellent …
We report measurements of spin transitions for GaAs quantum dots in the Coulomb blockade regime, and compare ground and excited state transport spectroscopy to direct measurements of the spin polarization of emitted current. Transport spectroscopy reveals both spin-increasing and spin-decreasing transitions as well as higher-spin ground states, and allows g-factors to be measured down to a single electron. The spin of emitted current in the Coulomb blockade regime, measured using spin-sensitive electron focusing, is found to be polarized along the direction of the applied magnetic field regard…
In this work we discuss the combined effects of finite-range electron-electron interaction and finite-range tunneling on the transport properties of ultrasmall tunnel junctions. We show that the Coulomb blockade phenomenon is deeply influenced by the interplay between the geometry and the screening properties of the contacts. In particular if the interaction range is smaller than the size of the tunneling region a "weakly correlated" regime emerges in which the Coulomb blockade gap $\D$ is significantly reduced. In this regime $\D$ is not simply given by the conventional charging energy of the…
We study the effect of the exchange interaction on the Coulomb blockade peak height statistics in chaotic quantum dots. Because exchange reduces the level repulsion in the many body spectrum, it strongly affects the fluctuations of the peak conductance at finite temperature. We find that including exchange substantially improves the description of the experimental data. Moreover, it provides further evidence of the presence of high spin states (S>1) in such systems.
We show that the low temperature electron transport properties of chemically functionalized graphene can be explained as sequential tunneling of charges through a two dimensional array of graphene quantum dots (GQD). Below 15 K, a total suppression of current due to Coulomb blockade through GQD array was observed. Temperature dependent current-gate voltage characteristics show Coulomb oscillations with energy scales of 6.2-10 meV corresponding to GQD sizes of 5-8 nm while resistance data exhibit an Efros-Shklovskii variable range hopping arising from structural and size induced disorder.
We study Coulomb blockade effects in the thermodynamic quantities of a weakly disordered metallic grain coupled to a metallic lead by a tunneling contact with a large conductance $g_T$. We consider the case of broken time-reversal symmetry and obtain expressions for both the {\em ensemble averaged} amplitude of the Coulomb blockade oscillations of the thermodynamic potential and the correlator of its {\em mesoscopic fluctuations} for a finite mean level spacing $δ$ in the grain. We develop a novel method which allows for an exact evaluation of the functional integral arising from disorder aver…
We show how a fine, multiple-peak structure can arise in the off-resonance, zero-bias conductance of Coulomb blockade systems. In order to understand how this effect comes about one must abandon the orthodox, mean-field understanding of the Coulomb blockade phenomenon and consider quantum fluctuations in the occupation of the single-particle electronic levels. We illustrate such an effect with a spinless Anderson-like model for multi-level systems and an equation-of-motion method for calculating Green's functions that combines two simple decoupling schemes.
We show that randomness of the electron wave functions in a quantum dot contributes to the fluctuations of the positions of the conductance peaks. This contribution grows with the conductance of the junctions connecting the dot to the leads. It becomes comparable with the fluctuations coming from the randomness of the single particle spectrum in the dot while the Coulomb blockade peaks are still well-defined. In addition, the fluctuations of the peak spacings are correlated with the fluctuations of the conductance peak heights.
We analyze the current-voltage characteristic of a quantum conduction channel coupled to an electromagnetic environment of arbitrary frequency-dependent impedance. In the weak blockade regime the correction to the ohmic behavior is directly related to the channel current fluctuations vanishing at perfect transmission in the same way as shot noise. This relation can be generalized to describe the environmental Coulomb blockade in a generic mesoscopic conductor coupled to an external impedance, as the response of the latter to the current fluctuations in the former.
We analyze an interplay between Coulomb blockade and quantum fluctuations in a coherent conductor (with dimensionless conductance $g \gtrsim 1$) attached to an Ohmic shunt. We demonstrate that at T=0 the system can be either an insulator or a metal depending on whether its total resistance is larger or smaller than $h/e^2\approx 25.8$ k$Ω$. In a metallic phase the Coulomb gap is fully suppressed by quantum fluctuations. We briefly discuss possible relation of this effect to recent experiments indicating the presence of a metal-insulator phase transition in 2d disordered systems.
Transport measurements are presented on a class of electrostatically defined lateral dots within a high mobility two dimensional electron gas (2DEG). The new design allows Coulomb Blockade(CB) measurements to be performed on a single lateral dot containing 0, 1 to over 50 electrons. The CB measurements are enhanced by the spin polarized injection from and into 2DEG magnetic edge states. This combines the measurement of charge with the measurement of spin through spin blockade spectroscopy. The results of Coulomb and spin blockade spectroscopy for first 45 electrons enable us to construct the a…
We study cotunneling in a double junction Coulomb blockade device under the influence of time dependent potentials. It is shown that the ac-bias leads to photon assisted cotunneling which in some cases may dominate the transport. We derive a general non-perturbative expression for the tunneling current in the presence of oscillating potentials and give a perturbative expression for the photon assisted cotunneling current.
