Controlling charge quantization with quantum fluctuations

Abstract

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 in which single electrons are manipulated, with applications in, for example, metrology, detectors and thermometry. However, as the connection strength is increased, the discreteness of charge is progressively reduced by quantum fluctuations. Here we report the full quantum control and characterization of charge quantization. By using semiconductor-based tunable elemental conduction channels to connect a micrometre-scale metallic island to a circuit, we explore the complete evolution of charge quantization while scanning the entire range of connection strengths, from a very weak (tunnel) to a perfect (ballistic) contact. We observe, when approaching the ballistic limit, that charge quantization is destroyed by quantum fluctuations, and scales as the square root of the residual probability for an electron to be reflected across the quantum channel; this scaling also applies beyond the different regimes of connection strength currently accessible to theory. At increased temperatures, the thermal fluctuations result in an exponential suppression of charge quantization and in a universal square-root scaling, valid for all connection strengths, in agreement with expectations. Besides being pertinent for the improvement of single-electron circuits and their applications, and for the metal-semiconductor hybrids relevant to topological quantum computing, knowledge of the quantum laws of electricity will be essential for the quantum engineering of future nanoelectronic devices.

Anyons in multichannel Kondo systems

“…76,77 Experimental signatures of the two-channel Kondo effect and, recently, even of the three-channel case are presently available using a charge pseudospin. [78][79][80][81] So far we have argued for the existence of quasiparticle fractionalization in NCK systems. Furthermore, we re- viewed the experimental relevance and feasibility of NCK in highly tunable and accessible devices.…”

Transmitting the quantum state of electrons across a metallic island with Coulomb interaction

“…However, independent absorption and emission of electrons result in fluctuations of the total island charge Q, with a characteristic charging energy E C = e 2 2C (with C the geometrical capacitance of the island and e the elementary electron charge). At low temperatures T ≪ E C k B (with k B the Boltzmann constant) this energy is not available, and the macroscopic quantum charge state Q is effectively frozen [8,9] (although not quantized in units of e as long as one channel is perfectly connected [10][11][12]). Consequently, correlations develop between absorbed and emitted elec- * These authors contributed equally to this work.…”

Nonlinear Seebeck effect of SU(N) Kondo impurity

“…(21) with the chemical potentials as specified in Eqs. (12) and (13) we obtain K 0 =e∆V , K 1 = (πT L ) 2 −(πT R ) 2 −3C(e∆V ) 2 /6 and…”

“…The many-body Kondo resonance at the Fermi level opens an effective path towards the enhancement of thermoelectric production at the nano scale level [9]. Recent experiments [10][11][12][13][14][15] have further expanded the scope of transport measurements in Kondo correlated nano scale systems. Most of these studies have been focused on the transport measurement for the spin S=1/2 Kondo impurity described by the SU(2) symmetry group.…”

“…Here the occupancy factor m takes all possible values starting from 1 to N −1. The paradigmatic SU(4) Kondo physics has been experimentally studied in CNTs [12,[19][20][21][22][23], double QDs [24] and single-atom transistor [25]. Various theoretical works [26][27][28][29][30][31] have contributed towards better understanding of SU(4) Kondo physics over past years.…”