Quantum phase transition of dynamical resistance in a mesoscopic capacitor
Yuji Hamamoto, Thibaut Jonckheere, Takeo Kato, Thierry Martin
备注：
5 pages, 2 figures, proceeding of the 19th International Conference on the Application of High Magnetic Fields in Semiconductor Physics and Nanotechnology (HMF-19)
We study theoretically dynamic response of a mesoscopic capacitor, which consists of a quantum dot connected to an electron reservoir via a point contact and capacitively coupled to a gate voltage. A quantum Hall edge state with a filling factor nu is realized in a strong magnetic field applied perpendicular to the two-dimensional electron gas. We discuss a noise-driven quantum phase transition of the transport property of the edge state by taking into account an ohmic bath connected to the gate voltage. Without the noise, the charge relaxation for nu>1/2 is universally quantized at R_q=h/(2e^2), while for nu<1/2, the system undergoes the Kosterlitz-Thouless transtion, which drastically changes the nature of the dynamical resistance. The phase transition is facilitated by the noisy gate voltage, and we see that it can occur even for an integer quantum Hall edge at nu=1. When the dissipation by the noise is sufficiently small, the quantized value of R_q is shifted by the bath impedance.
We investigate theoretically a novel type of high frequency quantum detector based on the mesoscopic capacitor recently realized by Gabelli et al., [Science {\bf 313}, 499 (2006)], which consists of a quantum dot connected via a single channel quantum point contact to a single lead. We show that the state of a double quantum dot charge qubit capacitively coupled to this detector can be read out in the GHz frequency regime with near quantum limited efficiency. To leading order, the quantum efficiency is found to be universal owing to the universality of the charge relaxation resistance of the m…
We evaluate the distribution of waiting times between electrons emitted by a driven mesoscopic capacitor. Based on a wave packet approach we obtain analytic expressions for the electronic waiting time distribution and the joint distribution of subsequent waiting times. These semi-classical results are compared to a full quantum treatment based on Floquet scattering theory and good agreement is found in the appropriate parameter ranges. Our results provide an intuitive picture of the electronic emissions from the driven mesoscopic capacitor and may be tested in future experiments.
We calculate the frequency-dependent equilibrium noise of a mesoscopic capacitor in time-dependent density functional theory (TDDFT). The capacitor is modeled as a single-level quantum dot with on-site Coulomb interaction and tunnel coupling to a nearby reservoir. The noise spectra are derived from linear-response conductances via the fluctuation-dissipation theorem. Thereby, we analyze the performance of a recently derived exchange-correlation potential with time-nonlocal density dependence in the finite-frequency linear-response regime. We compare our TDDFT noise spectra with real-time pertu…
We consider a one dimensional mesoscopic capacitor in the presence of strong electron interactions and compute its admittance in order to probe the universal nature of the relaxation resistance. We use a combination of perturbation theory, renormalization group arguments, and quantum Monte Carlo calculation to treat the whole parameter range of dot-lead coupling. The relaxation resistance is universal even in the presence of strong Coulomb blockade when the interactions in the wire are sufficiently weak. We predict and observe a quantum phase transition to an incoherent regime for a Luttinger …
We present a theoretical analysis of low frequency dynamics of a single-channel mesoscopic capacitor, which is composed by a quantum dot connected to an electron reservoir via a single quantum channel. At low frequencies, it is known that the Wigner-Smith delay time $τ_W$ plays a dominant role and it can be interpreted as the time delay between the current leaving the dot and the current entering the dot. At higher frequencies, we find that another characteristic time $τ_S$ can also be important. It describes the deformation of the leaving current to the entering one and hence can be referred …
We investigate the shot noise generated by particle emission from a mesoscopic capacitor into an edge state reflected and transmitted at a quantum point contact (QPC). For a capacitor subject to a periodic voltage the resulting shot noise is proportional to the number of particles (both electrons and holes) emitted during a period. It is proportional to the product of transmission and reflection probability of the QPC independent of the applied voltage but proportional to the driving frequency. If two driven capacitors are coupled to a QPC at different sides then the resulting shot noise is ma…
We propose an alternative derivation for the dynamic admittance of a gated quantum dot connected by a single-channel lead to an electron reservoir. Our derivation, which reproduces the result of Prêtre, Thomas, and Büttiker for the universal charge-relaxation resistance, shows that at low frequencies, the current leaving the dot lags after the entering one by the Wigner-Smith delay time. We compute the capacitance when interactions are taken into account only on the dot within the Hartree-Fock approximation and study the Coulomb-blockade oscillations as a function of the Fermi energy in the re…
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We review the latest progress in understanding the fundamental noise properties of a coherent single electron emitter known as the mesoscopic capacitor. The system consists of a sub-micron cavity connected to a two-dimensional electron gas via a quantum point contact. When subject to periodic gate voltage modulations, the mesoscopic capacitor absorbs and re-emits single electrons at giga-hertz frequencies as it has been demonstrated experimentally. Recent high-frequency noise measurements have moreover allowed for a precise characterization of the device in different operating regimes. Here we…
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We present an analysis of the effect of dephasing on the single channel charge relaxation resistance of a mesoscopic capacitor in the linear low frequency regime. The capacitor consists of a cavity which is via a quantum point contact connected to an electron reservoir and Coulomb coupled to a gate. The capacitor is in a perpendicular high magnetic field such that only one (spin polarized) edge state is (partially) transmitted through the contact. In the coherent limit the charge relaxation resistance for a single channel contact is independent of the transmission probability of the contact an…
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 realization of single-electron sources in integer quantum Hall systems has paved the way for exploring electronic quantum optics experiments in solid-state devices. In this work, we characterize a single Kramers pair emitter realized by a driven antidot embedded in a two-dimensional topological insulator, where spin-momentum locked edge states can be exploited for generating entanglement. Contrary to previous proposals, the antidot is coupled to both edges of a quantum spin Hall bar, thus enabling this mesoscopic capacitor to emit an entangled two-electron state. We study the concurrence $…
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The symmetry properties of the resistance of mesoscopic samples in the quantum Hall regime are investigated. In addition to the reciprocity relation, our samples obey new symmetries, that relate resistances measured with different contact configurations. Different kinds of symmetries are identified, depending on whether the magnetic field value is such that the system is above, or below, a quantum Hall transition. Related symmetries have recently been reported for macroscopic samples in the quantum Hall regime by Ponomarenko {\it et al.} (Solid State Commun. {\bf 130}, 705 (2004)), and Karmaka…
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It was aimed to determine whether plasma processing could contribute to enhanced capacitance and energy density of activated carbon electrode based electrochemical capacitors, through the formation of additional surface charges. While an increase of up to 35% of the gravimetric capacitance, along with ~ 20% decrease in resistance, was obtained through optimal plasma processing, increased plasma exposure yielded a drastic reduction (/increase) in the capacitance (/resistance). It was also found that the capacitance and resistance modulation was a sensitive function of sample processing as well …
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A brief overview is presented of recent work which investigates the time-dependent relaxation of charge and its spontaneous fluctuations on mesoscopic conductors in the proximity of gates. The leading terms of the low frequency conductance are determined by a capacitive or inductive emittance and a dissipative charge relaxation resistance. The charge relaxation resistance is determined by the ratio of the mean square dwell time of the carriers in the conductor and the square of the mean dwell time. The contribution of each scattering channel is proportional to half a resistance quantum. We dis…
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A discussion of recent work on time-dependent transport in mesoscopic structures is presented. The discussion emphasizes the use of time-dependent transport to gain information on the charge distribution and its collective dynamics. We discuss the RC-time of mesoscopic capacitors, the dynamic conductance of quantum point contacts and dynamic weak localization effects in chaotic cavities. We review work on adiabatic quantum pumping and photon-assisted transport, and conclude with a list which demonstrates the wide range of problems which are of interest.
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Quantitative thermoelectric measurements in the mesoscopic regime require accurate knowledge of temperature, thermovoltage, and device energy scales. We consider the effect of a finite load resistance on thermovoltage measurements of InAs/InP heterostructure nanowires. Load resistance and ac attenuation distort the measured thermovoltage therefore complicating the evaluation of device performance. Understanding these effects improves experimental design and data interpretation.
We report electrical and magneto transport measurements in mesoscopic size, two-dimensional (2D) electron gas in a GaAs quantum well. Remarkably, we find that the probe configuration and sample geometry strongly affects the temperature evolution of local resistance. We attribute all transport properties to the presence of hydrodynamic effects. Experimental results confirm the theoretically predicted significance of viscous flow in mesoscopic devices.
We review the first experiment on dynamic transport in a phase-coherent quantum conductor. In our discussion, we highlight the use of time-dependent transport as a means of gaining insight into charge relaxation on a mesoscopic scale. For this purpose, we studied the ac conductance of a model quantum conductor, i.e. the quantum RC circuit. Prior to our experimental work, M. Büttiker, H. Thomas and A. Prêtre first worked on dynamic mesoscopic transport in the 1990s. They predicted that the mesoscopic RC circuit can be described by a quantum capacitance related to the density of states in the ca…
The controlled and accurate emission of coherent electronic wave packets is of prime importance for future applications of nano-scale electronics. Here we present a theoretical and experimental analysis of the finite-frequency noise spectrum of a periodically driven single electron emitter. The electron source consists of a mesoscopic capacitor that emits single electrons and holes into a chiral edge state of a quantum Hall sample. We compare experimental results with two complementary theoretical descriptions: On one hand, the Floquet scattering theory which leads to accurate numerical result…
We investigate in a nonperturbative way the dynamics of a correlated quantum capacitor. We find that the many-body correlations do not disturb the universal low-frequency relaxation resistance per channel, $R_q(ω=0) = h/4e^2$ ensured by the Korringa-Shiba rule whereas the interpretation of the quantum capacitance $C_q$ in terms of the density of states fails when strong correlations are present. The AC resistance $R_q(ω)$ shows huge peaks (with values larger than $h/4e^2$) at $\hbarω\approx \pm Γ^*$, where $Γ^*$ is the renormalized level broadening. These peaks are merged to a single one at $ω…
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This review illustrates how Local Fermi Liquid (LFL) theories describe the strongly correlated and coherent low-energy dynamics of quantum dot devices. This approach consists in an effective elastic scattering theory, accounting exactly for strong correlations. Here, we focus on the mesoscopic capacitor and recent experiments achieving Coulomb-induced quantum state transfer. Extending to out-of-equilibrium regimes, aiming at triggered single electron emission, we illustrate how inelastic effects become crucial, requiring approaches beyond LFLs, shedding new light on past experimental data, by …
We propose a quantum Hamiltonian for a transmission line with charge discreteness. The periodic line is composed of an inductance and a capacitance per cell. In every cell the charge operator satisfies a nonlinear equation of motion because of the discreteness of the charge. In the basis of one-energy per site, the spectrum can be calculated explicitly. We consider briefly the incorporation of electrical resistance in the line.
We investigate the origin of the resistance fluctuations of mesoscopic samples, near transitions between Quantum Hall plateaus. These fluctuations have been recently observed experimentally by E. Peled et al. [Phys. Rev. Lett. 90, 246802 (2003); ibid 90, 236802 (2003); Phys. Rev. B 69, R241305 (2004)]. We perform realistic first-principles simulations using a six-terminal geometry and sample sizes similar to those of real devices, to model the actual experiment. We present the theory and implementation of these simulations, which are based on the linear response theory for non-interacting elec…
In a mesoscopic conductor electric resistance is detected even if the device is defect-free. We engineer and study a cold-atom analog of a mesoscopic conductor. It consists of a narrow channel connecting two macroscopic reservoirs of fermions that can be switched from ballistic to diffusive. We induce a current through the channel and find ohmic conduction, even for a ballistic channel. An analysis of in-situ density distributions shows that in the ballistic case the chemical potential drop occurs at the entrance and exit of the channel, revealing the presence of contact resistance. In contras…
We present electrical transport experiments performed on submicron hybrid devices made of a ferromagnetic conductor (Co) and a superconducting (Al) electrode. The sample was patterned in order to separate the contributions of the Co conductor and of the Co-Al interface. We observed a strong influence of the Al electrode superconductivity on the resistance of the Co conductor. This effect is large only when the interface is highly transparent. We characterized the dependence of the observed resistance decrease on temperature, bias current and magnetic field. As the differential resistance of th…
The electron waiting time is the time that passes between two subsequent charge transfers in an electronic conductor. Recently, theories of electron waiting times have been devised for quantum transport in Coulomb-blockade structures and for mesoscopic conductors, however, so far a proper description of a detector has been missing. Here we develop a quantum theory of a waiting time clock capable of measuring the distribution of waiting times between electrons above the Fermi sea in a mesoscopic conductor. The detector consists of a mesoscopic capacitor coupled to a quantum two-level system who…
