The quantum transport of electrons in an artificial atom, such as a quantum dot (QD), is governed by the Coulomb blockade (CB) effects, revealing the ground-state charge configuration of the electronic system under interplays of the on-site strong Coulomb interactions. In a coherently-coupled QD array, i.e. artificial molecules, the phenomenon of collective CB (CCB) was predicted by theoretical studies circa two decades ago but its evidence remains controversial. Here, we present direct evidence for the observation of CCB in a six-quantum-dot array (QDA) under high magnetic fields at 20 mK. The coherent inter-dot coupling is enhanced and mediated via the Quantum Hall edge states of the GaAs sample substrate. Two continuously fine-tuned gate voltages enable the quantum dot conductance spectrum to undergo a localization to delocalization transition process which manifests as an emergence and a collapse of CCB. The transition between these two distinct quantum phases is analogous to the Mott-Hubbard metal-insulator transition. The gate-voltage-dependent conductance map thus obtained makes it possible to utilize QDA as an on-chip laboratory for studying CCB and Mott physics. Our QDA device provides a platform for developing engineered QD materials, qubit systems and artificial molecular devices in the future.
We study many-body corrections to the cotunneling current via a localized state with energy $ε_d$ at large bias voltages $V$. We show that the transfer of {\em electron pairs}, enabled by the Coulomb repulsion in the localized level, results in ionization resonance peaks in the third derivative of the current with respect to $V$, centered at $eV=\pm 2ε_d/3$. Our results predict the existence of previously unnoticed structure within Coulomb-blockade diamonds.
The charging of a quantum box connected to a lead by a single-mode point contact is solved for arbitrary temperatures, tunneling amplitudes, and gate voltages, using a variant of Wilson's numerical renormalization group. The charge inside the box and the capacitance of the junction are calculated on equal footing for all physical regimes, including weak tunneling, near perfect transmission, and the crossover regime in between. At the charge plateaus, perturbation theory is found to break down at fairly small tunneling amplitudes. Near perfect transmission, we confirm Matveev's scenario for the…
Carbon nanotubes provide a new class of molecular wires that display new and exciting mesoscopic transport properties. We provide a detailed theoretical description for transport in multi-wall nanotubes, where both disorder and strong interactions are important. The interplay of both aspects leads to a particularly effective intrinsic Coulomb blockade for tunneling. The relation to recent experiments is discussed.
We derive a closed expression for the linear conductance through a quantum dot in the Coulomb-blockade regime in the presence of a constant exchange interaction. With this expression we calculate the temperature dependence of the conductance peak-height and peak-spacing statistics. Using a realistic value of the exchange interaction, we find significantly better agreement with experimental data as compared with the statistics obtained in the absence of an exchange interaction.
In this paper, we ask the question: How well can Coulomb blockade experiments correctly identify and distinguish between different topological orders in quantum Hall states? We definitively find the answer to be: Quite poorly. In particular, we write the general expression for the spacing of resonance peaks in a simple form that explicitly displays its dependence on the conformal scaling dimensions of the systems' edge modes. This form makes transparent the general argument that the Coulomb blockade peak spacings do not provide a strongly indicative signature of the topological order of the sy…
The non-linear current-voltage characteristic of a tunnel junction between two Luttinger systems is calculated for an interaction with finite range. Coulomb blockade features are found. The dissipative resistance, the capacitance and the external impedance, which were introduced ad hoc in earlier theories, are obtained in terms of the electron-electron interaction. The frequency dependence of the impedance is given by the excitation spectrum of the electrons.
Above the Kondo temperature, the Kohn-Sham zero-bias conductance of an Anderson junction has been shown to completely miss the Coulomb blockade. Within a standard model for the spectral function, we deduce a parameterization for both the onsite exchange-correlation potential and the bias drop as a function of the site occupation that applies for all correlation strengths. We use our results to sow doubt on the common interpretation of such corrections as arising from dynamical exchange-correlation contributions.
We discuss some recent results on the statistics of the Coulomb Blockade in disordered quantum dots containing spinless interacting fermions using the self-consistent Hartree-Fock approximation. We concentrate on the regime r_s >~1, with finite dimensionless conductance g. We present significantly different results for the cases of a Coulomb and a nearest-neighbour bare interaction. We show that neglecting rearrangements when the particle number is changed (Koopmans' approximation) can lead to large errors, and show how the spectral statistics of the self-consistent single particle orbitals ev…
We use chiral Luttinger liquid theory to study transport through a quantum dot in the fractional quantum Hall effect regime and find rich non-Fermi-liquid tunneling characteristics. In particular, we predict a remarkable Coulomb-blockade-type energy gap that is quantized in units of the noninteracting level spacing, new power-law tunneling exponents for voltages beyond threshold, and a line shape as a function of gate voltage that is dramatically different than that for a Fermi liquid. We propose experiments to use these unique spectral properties as a new probe of the fractional quantum Hall …
A new theoretical method is introduced to study coherent electron transport in an interacting multilevel quantum dot. The method yields the correct behavior both in the limit of weak and strong coupling to the leads, giving a unified description of Coulomb blockade and the Kondo effect. Results for the density of states and the temperature dependent conductance for a two- level dot are presented. The relevance of these results in connection to recent experiments on the Kondo effect in semiconducting quantum dots is discussed.
We study the dissipation in a system consisting of a small metallic island coupled to a gate electrode and to a massive reservoir via single tunneling junction. The dissipation of energy is caused by a slowly oscillating gate voltage. We compute it in the regimes of weak and strong Coulomb blockade. We focus on the regime of not very low temperatures when electron coherence can be neglected but quantum fluctuations of charge are strong due to Coulomb interaction. The answers assume a particularly transparent form while expressed in terms of specially chosen physical observables. We discovered …
Tunneling spectroscopy measurements of single tunnel junctions formed between multiwalled carbon nanotubes (MWNTs) and a normal metal are reported. Intrinsic Coulomb interactions in the MWNTs give rise to a strong zero-bias suppression of a tunneling density of states (TDOS) that can be fitted numerically to the environmental quantum-fluctuation (EQF) theory. An asymmetric conductance anomaly near zero bias is found at low temperatures and interpreted as Fano resonance in the strong tunneling regime.
We study the interplay between Coulomb blockade and the Kondo effect in quantum dots. We use a self-consistent scheme which describes mesoscopic devices in terms of a collective phase variable (slave rotor) and quasiparticle degrees of freedom. In the strong Coulomb blockade regime, we recover the description of metallic islands in terms of a phase only action. For a dot with well-separated levels, our method leads to the Kondo effect. We identify the regime where a crossover between the Coulomb blockade regime at high temperatures and the formation of a Kondo resonance at lower temperature ta…
Signatures of the non-Abelian statistics of quasi-particles in the $ν=5/2$ quantum Hall state are predicted to be present in the current-voltage characteristics of tunneling through one or two quantum Hall puddles of Landau filling $ν_a$ embedded in a bulk of filling $ν_b$ with $(ν_a,ν_b)=(2,5/2)$ and $(ν_a,ν_b)=(5/2,2)$.
We investigate theorerically the non-equilibrium transport through a molecular quantum dot as a function of gate and bias voltage, taking into account the typical situation in molecular electronics. In this respect, our study includes asymmetries both in the capacitances and tunneling rates to the source and drain electrodes, as well as an infinitely large charging energy on the molecule. Our calculations are based on the out-of-equilibrium Non-Crossing-Approximation (NCA), which is a reliable technique in the regime under consideration. We find that Coulomb blockade edges and Kondo peaks disp…
We study the fluctuations of an energy level as a function of the number of electrons $m$ added to a Coulomb-blockade quantum dot. A microscopic calculation in the limit of Koopmans' theorem predicts that the standard deviation of these fluctuations behaves as $\sqrt{m}$ in the absence of surface charge but is linear in $m$ when the effect of a surface charge in a finite geometry is included. The microscopic results are compared to a parametric random-matrix approach. We estimate the number of electrons it takes to scramble the spectrum completely in terms of the interaction strength, the dime…
We report that the conductance of macroscopic multiwall nanotube (MWNT) bundles under pressure shows power laws in temperature and voltage, as corresponding to a network of bulk-bulk connected Tomonaga-Luttinger Liquids (LL). Contrary to individual MWNT, where the observed power laws are attributed to Coulomb blockade, the measured ratio for the end and bulk obtained exponents, ~2.4, can only be accounted for by LL theory. At temperatures characteristic of interband separation, it increases due to thermal population of the conducting sheets unoccupied bands.
We find that tunnel junctions are not needed to provide single electron effects in a metallic island. Eventually the tunnel junction may be replaced by an arbitrary scatterer. It is important that even a {\it diffusive} scatterer provides a sufficient isolation for single electron effects to persist. To formulate this in exact terms, we derive and analyze the effective action that describes an arbitrary scatterer. We also consider the fluctuations of the effective charging energy.
We explore electron transport through a quantum dot coupled to the source and drain charge reservoirs We trace the transition from the Coulomb blockade regime to Kondo regime in the electron transport through the dot occuring when we gradually strengthen the coupling of the dot to the charge reservoirs. The current-voltage $(I-V)$ characteristics are calculated using the equations of motion approach within the nonequilibrium Green's functions formalism (NEGF) beyond the Hartree-Fock approximation. We show that within the Coulomb blockade regime the $I-V$ characteristics for the quantum dot con…
Graphene nanodisk is a graphene derivative with a closed edge. The trigonal zigzag nanodisk with size $N$ has $N$-fold degenerated zero-energy states. We investigate electron-electron interaction effects in the zero-energy sector. We explicitely derive the direct and exchange interactions, which are found to have no SU($N$) symmetry. Then, regarding a nanodisk as a quantum dot with an internal degree of freedom, we analyze the nanodisk-lead system consisting of a nanodisk and two leads. Employing the standard Green function method, we reveal novel Coulomb blockade effects in the system. The oc…
We performed electronic transport measurements on 1D InAs quantum wires. In sufficiently disordered wires, transport is dominated by Coulomb blockade, and the conductance can be well described by tunneling through a quantum dot embedded between two one-dimensional Luttinger liquid wires. In contrast to previous experiments in other material systems, in our system the conductance difference between peak to valley decreases with decreasing temperature for several consecutive peaks. This phenomenon is theoretically expected to occur only for strongly interacting systems with small Luttinger inter…
Disordered granular systems, at temperatures where charging effects are important, are studied, by means of an effective medium approximation. The intragrain charging energy leads to insulating behavior at low temperatures, with a well defined Coulomb gap. Non equilibrium effects can give rise to a zero temperature transition between a metallic, gapless phase, and an insulating phase.
Motivated by the discovery of superconductivity in the infinite-layer nickelate family, we report an experimental endeavor to clean the surface of nickelate superconductor Pr0.8Sr0.2NiO2 films by Ar+ ion sputtering and subsequent annealing, and we study their electronic structures by cryogenic scanning tunneling microscopy and spectroscopy. The annealed surfaces are characterized by nano-sized clusters and Coulomb staircases with periodicity inversely proportional to the projected area of the nanoclusters, consistent with a double-barrier tunneling junction model. Moreover, the dynamical Coulo…
Physical properties of single-electron devices in the week Coulomb blockade regime are significantly dependent on non-perturbative effects. They arise as instanton solutions of equations of motion for the corresponding Ambegaokar-Eckern-Schoen action. In equilibrium those solutions are known as Korshunov instantons. In this paper we study non-equilibrium Ambegaokar-Eckern- Schoen action using Keldysh technique. We found instantons for the most general stationary out-of equilibrium state. We also found that action saddle-point value assumes a universal value irrespective of the stationary non-e…
We study transport through a strongly correlated quantum dot and show that Coulomb blockade can appear even in the presence of perfect contacts. This conclusion arises from numerical calculations of the conductance for a microscopic model of spinless fermions in an interacting chain connected to each lead via a completely open channel. The dependence of the conductance on the gate voltage shows well defined Coulomb blockade peaks which are sharpened as the interaction strength is increased. Our numerics is based on the embedding method and the DMRG algorithm. We explain the emergence of Coulom…
A theory of tunneling through a quantum dot is presented which enables us to study combined effects of Coulomb blockade and discrete energy spectrum of the dot. The expression of tunneling current is derived from the Keldysh Green's function method, and is shown to automatically satisfy the conservation at DC current of both junctions.
Using the conformal field theory partition function of a Coulomb-blockaded quantum dot, constructed by two quantum point contacts in a Laughlin quantum Hall bar, we derive the finite-temperature thermodynamic expression for the thermopower in the linear-response regime. The low-temperature results for the thermopower are compared to those for the conductance and their capability to reveal the structure of the single-electron spectrum in the quantum dot is analyzed.
We consider a metallic wire coupled to two metallic electrodes via two junctions placed nearby. A bias voltage applied to one of such junctions alters the electron distribution function in the wire in the vicinity of another junction thus modifying both its noise and the Coulomb blockade correction to its conductance. We evaluate such interaction corrections to both local and non-local conductances demonstrating non-trivial Coulomb anomalies in the system under consideration. Experiments on non-local electron transport with Coulomb effects can be conveniently used to test inelastic electron re…
A model of carbon nanotube at half filling is studied. The Coulomb interaction is assumed to be unscreened. It is shown that this allows to develop the adiabatic approximation which leads to considerable simplifications in calculations of the excitation spectrum. We give a detailed analysis of the spectrum and the phase diagram at half filling and discuss effects of small doping. At small doping several phases develop strong superconducting fluctuations corresponding to various types of pairing.
We investigate the transport characteristics of a redox system weakly coupled to leads in the Coulomb blockade regime. The redox system comprises a donor and acceptor separated by an insulating bridge in a solution. It is modeled by a two-site extended Hubbard model which includes on-site and inter-site Coulomb interactions and the coupling to a bosonic bath. The current voltage characteristics is calculated at high temperatures using a rate equation approach. For high voltages exceeding the Coulomb repulsion at the donor site the calculated transport characteristics exhibit pronounced deviati…
