We investigate the effects of Majorana bound states on the ac response of a quantum resistor-capacitor circuit which is composed of a topological superconducting wire whose two ends are tunnel-coupled to a lead and a spinless quantum dot, respectively. The Majorana states formed at the two ends of the wire are found to suppress completely or enhance greatly the dissipation, depending on the strength of the overlap between two Majorana modes and/or the dot level. We compare the relaxation resistance and the quantum capacitance of the system with those of non-Majorana counterparts to find that the effects of the Majorana state on the ac response are genuine and cannot be reproduced in ordinary fermonic systems.
We investigate the mesoscopic resistor-capacitor circuit consisting of a quantum dot coupled to spatially separated Majorana fermion modes in a chiral topological superconductor. We find substantially enhanced relaxation resistance due to the nature of Majorana fermions, which are their own anti-particles and composed of particle and hole excitations in the same abundance. Further, if only a single Majorana mode is involved, the zero-frequency relaxation resistance is completely suppressed due to a destructive interference. As a result, the Majorana mode opens an exotic dissipative channel on …
We determined the frequency dependent effective permittivity of a large ternary network of randomly positioned resistors, capacitors, and diodes. A linear circuit analysis of such systems is shown to match the experimental dielectric response of single-walled carbon nanotube (SWCNT) filled polymers. This modeling method is able to reproduce the two most important features of SWCNT filled composites, i.e. the low frequency dispersion and dipolar relaxation. As a result of the modeling important physical conclusion proved by the experimental data was done: the low frequency behavior of SWCNT-fil…
Can we change the average state of a resistor by simply applying white noise? We show that the answer to this question is positive if the resistor has memory of its past dynamics (a memristive system). We also prove that, if the memory arises only from the charge flowing through the resistor -- an ideal memristor -- then the current flowing through such memristor can not charge a capacitor connected in series, and therefore cannot produce useful work. Moreover, the memristive system may skew the charge probability density on the capacitor, an effect which can be measured experimentally.
For sufficiently strong in-plane magnetic field a $ν_T=1$ bilayer quantum Hall pseudo-ferromagnet is expected to exhibit a soliton lattice. For sufficiently close layers and large in-plane field, we predict this incommensurate ``planar'' phase $P_I$ to undergo a reentrant pseudo-spin canting transition to an incommensurate state $C_I$, with a finite out-of-plane pseudo-magnetization component, corresponding to an interlayer charge imbalance in regions between solitons. At $T>0$ the transition is in the 2d compressible Ising universality class, and at T=0, the quantum transition is in heretofor…
What is the complex impedance of a fully coherent quantum resistance-capacitance (RC) circuit at GHz frequencies in which a resistor and a capacitor are connected in series? While Kirchhoff's laws predict addition of capacitor and resistor impedances, we report on observation of a different behavior. The resistance, here associated with charge relaxation, differs from the usual transport resistance given by the Landauer formula. In particular, for a single mode conductor, the charge relaxation resistance is half the resistance quantum, regardless of the transmission of the mode. The new mesosc…
We consider an interacting quantum dot working as a coherent source of single electrons. The dot is tunnel coupled to a reservoir and capacitively coupled to a gate terminal with an applied ac potential. At low frequencies, this is the quantum analog of the RC circuit with a purely dynamical response. We investigate the quantized dynamics as a consequence of ac pulses with large amplitude. Within a Keldysh-Green function formalism we derive the time-dependent current in the Coulomb blockade regime. Our theory thus extends previous models that considered either noninteracting electrons in nonli…
The capacitance of an arbitrarily shaped object is calculated with the same second-kind integral equation method used for computing static and dynamic polarizabilities. The capacitance is simply the dielectric permittivity multiplied by the area of the object and divided by the squared norm of the Neumann-Poincaré operator eigenfunction corresponding to the largest eigenvalue. The norm of this eigenfunction varies slowly with shape thus enabling the definition of two scale-invariant shape factors and perturbative calculations of capacitance. The result is extended to a special class of capacit…
Three types of metallic nanostructures comprising niobium were investigated experimentally; in all three types, electric transport at very low temperatures was governed by Coulomb blockade effects. 1. Thin film strips of niobium could be tuned into resistor strips by an electrochemical anodisation process, using microfabricated masks and in situ resistance monitoring. These resistors showed a transition from superconducting to insulating behaviour with increasing sheet resistance, occurring at a value approximately equal to the quantum resistance for Cooper pairs, h/(4e^2). 2. Combining the an…
We describe a measurement method that enables the correct estimation of the charging energy of an unintentional quantum dot (QD) in the channel of a metal-oxide-semiconductor field-effect transistor (MOSFET). If the channel has a dominant QD with a large charging energy and an array of stray QDs with much weaker charging, this method eliminates the additional voltage drops due to stray QDs by regarding the stray QDs as series resistors. We apply this method to a short-channel MOSFET and find that the charging energy of the dominant QD can indeed be smaller than the size of the Coulomb diamond.
We suggest electronic circuits with memristors (resistors with memory) that operate as memcapacitors (capacitors with memory) and meminductors (inductors with memory). Using a memristor emulator, the suggested circuits have been built and their operation has been demonstrated, showing a useful and interesting connection between the three memory elements.
A standard method for picoammeter calibrations is the capacitor charging technique, which allows generating traceable currents in the sub-nA range. However, its accuracy is limited by the ac-dc differences of the capacitances involved. The Ultrastable Low-noise Current Amplifier (ULCA) is a novel high-precision amperemeter for direct current measurements in the pA range, developed at PTB. Its amplifier stages, based on resistor networks and op-amps, can be calibrated traceably with a cryogenic current comparator (CCC) system. We compare the results from both independent calibration routes for …
Electronic ratchets transduce local spatial asymmetries into directed currents in the absence of a global drain bias, by rectifying temporal signals that reside far from thermal equilibrium. We show that the absence of a drain bias can provide distinct energy advantages for computation, specifically, reducing static dissipation in a logic circuit. Since the ratchet functions as a gate voltage-controlled current source, it also potentially reduces the dynamic dissipation associated with charging/discharging capacitors. In addition, the unique charging mechanism eliminates timing related constra…
We present a tutorial on the properties of the new ideal circuit element, a memristor. By definition, a memristor M relates the charge q and the magnetic flux $ϕ$ in a circuit, and complements a resistor R, a capacitor C, and an inductor L as an ingredient of ideal electrical circuits. The properties of these three elements and their circuits are a part of the standard curricula. The existence of the memristor as the fourth ideal circuit element was predicted in 1971 based on symmetry arguments, but was clearly experimentally demonstrated just this year. We present the properties of a single m…
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the m…
We build on the study of single-photon heat conduction in electronic circuits taking into account the back-action of the superconductor--insulator--normal-metal thermometers. In addition, we show that placing capacitors, resistors, and superconducting quantum interference devices (SQUIDs) into a microwave cavity can severely distort the spatial current profile which, in general, should be accounted for in circuit design. The introduction of SQUIDs also allows for in situ tuning of the photonic power transfer which could be utilized in experiments on superconducting quantum bits.
We propose a model for nanoscale supercapacitor consisting of two-dimensional insulating BN layers placed between two commensurate and metallic graphene layers. First-principles Density Functional calculations of structure optimized total energy and self-consistent field potential performed on these nanoscale capacitors for different levels of charging and different number of BN layers mark the values of capacitance per unit mass, which are larger than those measured values for the supercapacitors made from other carbon based materials. Our theoretical study also compares results obtained for …
The Hodgkin-Huxley model describes the behavior of the cell membrane in neurons, treating each part of it as an electric circuit element, namely capacitors, memristors, and voltage sources. We focus on the activation channel of potassium ions, due to its simplicity, while keeping most of the features displayed by the original model. This reduced version is essentially a classical memristor, a resistor whose resistance depends on the history of electric signals that have crossed it, coupled to a voltage source and a capacitor. Here, we will consider a quantized Hodgkin-Huxley model based on a q…
