Controlling charge quantization with quantum fluctuations
S. Jezouin, Z. Iftikhar, A. Anthore, F. D. Parmentier, U. Gennser, A. Cavanna, A. Ouerghi, I. P. Levkivskyi, E. Idrisov, E. V. Sukhorukov, L. I. Glazman, F. Pierre
备注：
Letter and Methods; See also Nature News & Views: Y. Nazarov, Nature 536, 38 (2016)
In 1909, Millikan showed that the charge of electrically isolated systems is quantized in units of the elementary electron charge e. Today, the persistence of charge quantization in small, weakly connected conductors allows for circuits where single electrons are manipulated, with applications in e.g. metrology, detectors and thermometry. However, quantum fluctuations progressively reduce the discreteness of charge as the connection strength is increased. Here we report on the full quantum control and characterization of charge quantization. By using semiconductor-based tunable elemental conduction channels to connect a micrometer-scale metallic island, the complete evolution is explored while scanning the entire range of connection strengths, from tunnel barrier to ballistic contact. We observe a robust scaling of charge quantization as the square root of the residual electron reflection probability across a quantum channel when approaching the ballistic critical point, which also applies beyond the regimes yet accessible to theory. At increased temperatures, the thermal fluctuations result in an exponential suppression of charge quantization as well as in a universal square root scaling, for arbitrary connection strengths, in agreement with expectations. Besides direct applications to improve single-electron functionalities and for the metal-semiconductor hybrids emerging in the quest toward topological quantum computing, the knowledge of the quantum laws of electricity will be essential for the quantum engineering of future nanoelectronic devices.
We investigate a Zeeman-split quantum dot (QD) containing a single spin 1/2 weakly coupled to a helical Luttinger liquid (HLL) within a generalized master equation approach. The HLL induces a tunable magnetization direction on the QD controlled by an applied bias voltage when the quantization axes of the QD and the HLL are noncollinear. The backscattering conductance (BSC) in the HLL is finite and shows a resonance feature when the bias voltage equals the Zeeman energy in magnitude. The observed BSC asymmetry in bias voltage directly reflects the quantization axis of the HLL spin.
In this paper we show how the stochastic quantization method developed by Parisi and Wu can be used to obtain Casimir forces. Both quantum and thermal fluctuations are taken into account by a Langevin equation for the field. The method allows the Casimir force to be obtained directly, derived from the stress tensor instead of the free energy. It only requires the spectral decomposition of the Laplacian operator in the given geometry. The formalism provides also an expression for the fluctuations of the force. As an application we compute the Casimir force on the plates of a finite piston of ar…
We would like to point out the blind spots of the approach combining the spin pumping theory proposed by Tserkovnyak et al. with the Landau-Lifshitz-Gilbert equation; this method has been widely used for interpreting vast experimental results. The essence of the spin pumping effect is the quantum fluctuation. Thus, localized spin degrees of freedom should be quantized, i.e. be treated as magnons not as classical variables. Consequently, the precessing ferromagnet can be regarded as a magnon battery. This point of view will be useful for further progress of spintronics.
We develop a theory of the valley Hall effect in high-quality graphene samples, in which strain fluctuation-induced random gauge potentials have been suggested as the dominant source of disorder. We find a near-quantized value of valley Hall conductivity in the band transport regime, which originates from an enhanced side jump of a Dirac electron when it scatters off the gauge potential. By assuming a small residue charge density our theory reproduces qualitatively the temperature- and gap-dependence of the observed valley Hall effect at the charge neutral point. Our study suggests that the va…
We consider a magnetic skyrmion adiabatically driven by a spin-polarized electrical current periodic in both space and time and asymmetric in space, and also subject to a random magnetic field representing the thermal fluctuations. We show that when the random magnetic field is low enough, while the time variation of the driving current is slow enough, the skyrmion flow is an integer multiply of the ratio between the space and time periods, the integer being a topological invariant called Chern number. This result is also demonstrated by numerically solving the stochastic Landau-Lifshitz-Gilbe…
Recent investigations of fractal conductance fluctuations (FCF) in electron billiards reveal crucial discrepancies between experimental behavior and the semiclassical Landauer-Buttiker (SLB) theory that predicted their existence. In particular, the roles played by the billiard's geometry, potential profile and the resulting electron trajectory distribution are not well understood. We present measurements on two custom-made devices - a 'disrupted' billiard device and a 'bilayer' billiard device - designed to probe directly these three characteristics. Our results demonstrate that intricate proc…
Measuring heat flow through nanoscale systems poses formidable practical difficulties as there is no `ampere meter' for heat. We propose to overcome this problem by realizing heat transport through a chain of trapped ions. Laser cooling the chain edges to different temperatures induces a current of local vibrations (vibrons). We show how to efficiently control and measure this current, including fluctuations, by coupling vibrons to internal ion states. This demonstrates that ion crystals provide a suitable platform for studying quantum transport, e.g., through thermal analogues of quantum wire…
Recently, a method based on stochastic quantization has been proposed to compute the Casimir force and its fluctuations in arbitrary geometries. It relies on the spectral decomposition of the Laplacian operator in the given geometry. Both quantum and thermal fluctuations are considered. Here we use such method to compute the Casimir force on the plates of a finite piston of arbitrary cross section. Asymptotic expressions valid at low and high temperatures and short and long distances are obtained. The case of a piston with triangular cross section is analysed in detail. The regularization of t…
We study the Coulomb blockade in a chaotic quantum dot connected to a lead by a single channel at nearly perfect transmission. We take into account quantum fluctuations of the dot charge and a finite level spacing for electron states within the dot. Mesoscopic fluctuations of thermodynamic and transport properties in the Coulomb blockade regime exist at any transmission coefficient. In contrast to the previous theories, we show that by virtue of these mesoscopic fluctuations, the Coulomb blockade is not destroyed completely even at perfect transmission. The oscillatory dependence of all the ob…
We provide theory and formal insight on the Green function quantization method for absorptive and dispersive spatial-inhomogeneous media in the context of dielectric media. We show that a fundamental Green function identity, which appears, e.g., in the fundamental commutation relation of the electromagnetic fields, is also valid in the limit of non-absorbing media. We also demonstrate how the zero-point field fluctuations yields a non-vanishing surface term in configurations without absorption, when using a more formal procedure of the Green function quantization method. We then apply the pres…
We consider the Coulomb blockade on a superconductive quantum dot strongly coupled to a lead through a tunnelling barrier and/or normal diffusive metal. Andreev transport of the correlated pairs leads to quantum fluctuations of the charge on the dot. These fluctuations result in exponential renormalization of the effective charging energy. We employ two complimentary ways to approach the problem, leading to the coinciding results: the instanton and the functional RG treatment of the non-linear sigma model. We also derive the charging energy renormalization in terms of arbitrary transmission ma…
Fluctuation engineering in cavity quantum materials
Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质与结构动力学研究所）；Center for Free-Electron Laser Science (CFEL)（自由电子激光科学中心）；Department of Physics, Columbia University（哥伦比亚大学物理系）；Institute for Quantum Electronics, ETH Zürich（苏黎世联邦理工学院量子电子学研究所）；Quantum Center, ETH Zürich（苏黎世联邦理工学院量子中心）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Department of Physics, University of Erlangen-Nürnberg（埃尔朗根-纽伦堡大学物理系）；Joint Quantum Institute, University of Maryland（马里兰大学联合量子研究所）
We report a theoretical investigation on the conductance and its fluctuation of three-dimensional topological insulators (3D TI) in $Bi_2Se_3$ and $Sb_2Te_3$ in the presence of disorders. Extensive numerical simulations are carried out. We find that in the diffusive regime the conductance is quantized with fractional value. Importantly, the conductance fluctuation is also quantized with a universal value. For 3D TI connected by two terminals, three independent conductances $G_{zz}$, $G_{xx}$ and $G_{zx}$ are identified where z is the normal direction of quintuple layer of 3D TI (see inset of F…
We theoretically investigate the noise of a single-electron transistor in the regime of large quantum fluctuation of charge out of equilibrium. We show that the charge noise is suppressed due to the charge renormalization caused by the quantum fluctuation. However the fluctuation is not strong enough to wash out the charge quantization. We find that the renormalization effect reduces the performance of a single-electron electrometer.
It is shown that an account of the Berry phase (a topological $θ$-term) together with a dissipative term in the effective action $S[ϕ]$ of the tunnel contacts induces a strong quantization of the tunnel current at low temperatures. This phenomenon like the Coulomb blockade reflects a discrete charge structure of the quantum shot noise and can ensure a quantization of the tunnel current without a capacitive charging energy $E_C$, when the latter is strongly suppressed by quantum fluctuations. Since a value of the $θ$-parameter is determined by the gate voltage, this effect allows to control a c…
We probe local charge fluctuations in a semiconductor via laser spectroscopy on a nearby self-assembled quantum dot. We demonstrate that the quantum dot is sensitive to changes in the local environment at the single charge level. By controlling the charge state of localized defects, we are able to infer the distance of the defects from the quantum dot with +-5 nm resolution. The results identify and quantify the main source of charge noise in the commonly-used optical field-effect devices. Based on this understanding we achieve routinely close-totransform-limited quantum dot optical linewidths…
The topological terms of the bulk effective action for the integer quantum Hall effect, capturing the dynamics of gauge and gravitational fluctuations, reveal a curiosity, namely, the Abelian potential for the magnetic field appears in a particular combination with the Abelian spin connection. This seems to hold for quantum Hall effect on complex projective spaces of arbitrary dimensions. An interpretation of this in terms of the algebra of symplectic transformations is given. This can also be viewed in terms of the metaplectic correction in geometric quantization.
We have investigated the conductance of long quantum wires formed in GaAs/AlGaAs heterostructures. Using realistic fluctuation potentials from donor layers we have simulated numerically the conductance of four different kinds of wires. While ideal wires show perfect quantization, potential fluctuations from random donors may give rise to strong conductance oscillations and degradation of the quantization plateaux. Statistically there is always the possibility of having large fluctuations in a sample that may effectively act as a microconstriction. We therefore introduce microconstrictions in t…
We report here direct measurements of the destruction of charge quantization in a single electron box, the first over the full range of box-to-lead conductance values from G ~ 0 to the conductance quantum G_q = 2e^2/h, using a sensitive single-electron transistor (SET) electrometer. The sensitivity of the electrometer is measured to be dq ~ 6 x 10^-5 e/sqrt{Hz} and its superiority to conductance measurements of charge fluctuations is clearly demonstrated. As the rate of quantum mechanical tunneling from the box to its lead is increased, the quantization of charge is destroyed, disappearing ent…
Zero resistance, diamagnetism (Meissner effect) and the energy gap in the excitation spectrum are the fundamental attributes of superconductivity. In nanoparticles with characteristic size 10 nm superconductivity is suppressed by the quantization of the electron energy spectrum. In narrow quasi-1D superconducting channels thermal fluctuations enable zero resistance only at temperatures noticeably below the critical temperature Tc, while quantum fluctuations suppress the dissipationless electric current in ultra-narrow superconducting nanowires even at temperatures close to T=0. Here we demonst…
