Direct observation of macroscopic charge quantization

Lafarge, P.; Pothier, H.; Williams, Edwin R.; Estève, D.; Urbina, C.; Devoret, M. H.

doi:10.1007/bf01307627

Cited by 263 publications

(175 citation statements)

References 14 publications

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“…As a basic example, we consider a single-electron box (SEB) [24][25][26][27], which is somewhat related to the quantum-dot circuit discussed above. However, here we focus on a metallic system, where the only energy relevant for the system Hamiltonian is the Coulomb energy, and 'particle-in-box' quantum effects can be fully ignored.…”

Section: Fluctuation Relationsmentioning

confidence: 99%

Towards quantum thermodynamics in electronic circuits

2015

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Section: Fluctuation Relationsmentioning

confidence: 99%

Towards quantum thermodynamics in electronic circuits

2015

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“…In this letter, we discuss the fundamental question how quantum fluctuations influence Coulomb blockade phenomena at zero temperature, i.e., we analyze the smearing of E 0 (n x ) and N (n x ) in the whole regime from weak to strong tunneling up to T ∼ 50 (in recent experiments T ∼ 33 was achieved [4]). Another quantity of recent interest is the second derivative of the energy E 0 , E * C (n x ) = 1 2…”

mentioning

confidence: 99%

Strong Tunneling in the Single-Electron Box

König

Schoeller

1998

Phys. Rev. Lett.

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We study strong tunneling (i.e. transmission h/e 2 RT ≫ 1) in the single-electron box with many transverse modes at zero temperature. We develop a new renormalization group method which includes all charge states and requires no initial or final energy cutoff. We determine the ground-state energy, the average charge and the renormalized charging energy. The covered range for the coupling constant and the gate voltage is much increased in comparison to recent perturbative approaches, poor man scaling methods and Quantum Monte Carlo simulations. We reach the regime where Coulomb blockade become practically unobservable.73.23. Hk,73.40.Gk,73.30.Rw Introduction. Metallic nanostructures with junctions of low capacitance show quantization of electric charge and Coulomb blockade phenomena due to large charging energy [1-3]. The simplest system in which one can see Coulomb blockade effects is the single-electron box. Electrons enter or leave a small metallic island via a tunnel junction with many transverse channels. The junction is characterized by a resistance R T and a capacitance C. The charge on the island is controlled by a capacitively (with C G ) coupled external voltage V G . In the "weak tunneling" regime, i.e., when the transmission T = h/e 2 R T of the barrier is much less than unity, the average charge of the box can be described within the "orthodox theory" [1] which treats tunneling in lowest order perturbation theory (golden rule). This means that the energy for charge N on the island is given by the classical expression

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“…They can be used as devices which rely on the discreteness of the electron charge, for example highly sensitive electrometers [2][3][4][5], or single electron pumps as a possible current standard [6]. Furthermore, SETs defined in a two-dimensional electron gas (2DEG) of a semiconductor heterostructure are also known as "quantum dots", and can be seen as tunable artificial atoms with interacting electrons.…”

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confidence: 99%

In-plane gate single-electron transistor in Ga[Al]As fabricated by scanning probe lithography

Lüscher

Fuhrer

Held

et al. 1999

Applied Physics Letters

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A single-electron transistor has been realized in a Ga [Al]As heterostructure by oxidizing lines in the GaAs cap layer with an atomic force microscope. The oxide lines define the boundaries of the quantum dot, the in-plane gate electrodes, and the contacts of the dot to source and drain. Both the number of electrons in the dot as well as its coupling to the leads can be tuned with an additional, homogeneous top gate electrode. Pronounced Coulomb blockade oscillations are observed as a function of voltages applied to different gates. We find that, for positive top-gate voltages, the lithographic pattern is transferred with high accuracy to the electron gas. Furthermore, the dot shape does not change significantly when in-plane voltages are tuned.

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Direct observation of macroscopic charge quantization

Cited by 263 publications

References 14 publications

Towards quantum thermodynamics in electronic circuits

Towards quantum thermodynamics in electronic circuits

Strong Tunneling in the Single-Electron Box

In-plane gate single-electron transistor in Ga[Al]As fabricated by scanning probe lithography

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