Observation of Quantum Fluctuations of Charge on a Quantum Dot

Berman, David H.; Zhitenev, Nikolai B.; Ashoori, R. C.; Shayegan, M.

doi:10.1103/physrevlett.82.161

Cited by 88 publications

(107 citation statements)

References 26 publications

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“…For a weakly-coupled dot, at low temperatures, this function generally exhibits sharp steps, resulting in the "Coulomb staircase". We emphasize the fact that a direct measurement of the average dot charge can be performed with sensitivity well below a single charge [4].In this Letter, we investigate the shape of the steps of the Coulomb staircase in the presence of spin-flip assisted tunneling. The setup we examine consists of a (large) dot or grain coupled to a reservoir through a smaller dot (Fig.1).…”

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Smearing of charge fluctuations in a grain by spin-flip assisted tunneling

Hur

Simon

2003

Phys. Rev. B

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We investigate the charge fluctuations of a grain coupled to a lead via a small quantum dot in the Kondo regime. We show that the strong entanglement of charge and spin flips in this setup can result in a stable SU(4) Kondo fixed point, which considerably smears out the Coulomb staircase behavior already in the weak tunneling limit. This behavior is robust enough to be experimentally observable.PACS numbers: 75.20.Hr,71.27.+a,73.23.Hk Recently, quantum dots have attracted a considerable interest due to their potential applicability as single electron transistors or as basic building blocks (qubits) in the fabrication of quantum computers [1]. One of their most important features is the Coulomb blockade phenomenon, i.e., as a result of the strong repulsion between electrons, the charge of a quantum dot is quantized in units of the elementary charge e. Even when the quantum dot is weakly-coupled to a bulk lead, so that electrons can hop from the lead to the dot and back, the dot charge remains to a large extent quantized. This quantization has been thoroughly investigated both theoretically [2] and experimentally [3]. The quantity of interest here is the average dot charge as a function of the voltage applied to a back-gate. For a weakly-coupled dot, at low temperatures, this function generally exhibits sharp steps, resulting in the "Coulomb staircase". We emphasize the fact that a direct measurement of the average dot charge can be performed with sensitivity well below a single charge [4].In this Letter, we investigate the shape of the steps of the Coulomb staircase in the presence of spin-flip assisted tunneling. The setup we examine consists of a (large) dot or grain coupled to a reservoir through a smaller dot (Fig.1). We assume that the smaller dot contains an odd number of electrons and acts as an S=1/2 Kondo impurity [5]. A different limit where the small dot rather acts as a resonant level has been partially studied in Ref. 6 where it was shown that the resonant level can smear the Coulomb blockade (nevertheless, for a narrow resonance at the Fermi energy, the effect is weak). Furthermore, the charge of the grain in such a device can be used to measure the occupation of the dot [6].In the following analysis, we focus on the regime where the back-gate voltage is such that the charging states of the grain with 0 or 1 electron are degenerate. We show below that in this case, the charge degrees of freedom of the grain become strongly entangled with the spin degrees of freedom of the small dot resulting in a stable fixed point with an SU(4) symmetry. The major consequence of this enlarged symmetry in our setup is that the dot's capacitance exhibits instead of a logarithmic singularity [2]-a strongly reduced peak as a function of the back-gate voltage, smearing charging effects in the grain considerably. The Coulomb staircase behavior becomes smeared out already in the weak tunneling limit due to the prominence of spin-flip assisted tunneling. The possibility of a strongly correlated ground state possessing...

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confidence: 99%

Smearing of charge fluctuations in a grain by spin-flip assisted tunneling

Hur

Simon

2003

Phys. Rev. B

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“…First, the quasi-period of the rings against the density increment approximately corresponds to the addition of a single-electron charge over the maximal correlated area of the structure. Second, as noted above, the peaks often overshoot the level of zero yielding negative transparency, as is seen in the capacitance measurements under Coulomb blockade conditions [10].…”

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confidence: 96%

Single-electron states in the quantum Hall effect

Zhitenev¹,

Fulton²,

Yacoby³

et al. 2000

Physica E: Low-dimensional Systems and Nanostructures

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Spatially localized electronic states in a two-dimensional electron gas in the quantum Hall regime are imaged using a scanning single-electron-transistor probe. Two di erent regimes of localization are identiÿed depending on the strength of the built-in long-range density uctuations. In the smoother regions localized states merge into dielectric-like blobs a few m in extent. In the places with a stronger density gradient complex patterns occur which change markedly with an addition of a single electron. The simplest appearance of the latter is a ring collapsing toward the center as an electron is added to the area. ?

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“…2 (b)]. This is a clear distinction between the localized and delocalized phases which in principle should be accessible experimentally [2].…”

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confidence: 99%

“…A quantum dot can be viewed as a simple artificial atom exhibiting charge quantization [1], and its charge can now be measured with a very high accuracy with the aid of an electrometer based on a single-electron transistor [2]. The coupling of the quantum dot to a macroscopic reservoir of electrons inevitably produces quantum charge fluctuations on the dot.…”

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confidence: 99%

Unification of electromagnetic noise and Luttinger liquid via a quantum dot

Hur

2005

Phys. Rev. B

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We investigate the effect of dissipation on a small quantum dot (resonant level) tunnel-coupled to a chiral Luttinger liquid (LL) with the LL parameter K. The dissipation stems from the coupling of the dot to an electric environment, being characterized by the resistance R, via Coulomb interactions. We show that this problem can be mapped onto a Caldeira-Leggett model where the (ohmic) bath of harmonic oscillators is governed by the effective dissipation strength α = (2K) −1 withK −1 = K −1 + 2R/RK and RK = h/e 2 the quantum of resistance. Experimental consequences are discussed and the limit K = 1/2 + is thoroughly studied at small R/RK through the spin-boson-fermion model. PACS numbers: 73.23.Hk, 71.10.Pm, 72.70.+m A quantum dot can be viewed as a simple artificial atom exhibiting charge quantization [1], and its charge can now be measured with a very high accuracy with the aid of an electrometer based on a single-electron transistor [2]. The coupling of the quantum dot to a macroscopic reservoir of electrons inevitably produces quantum charge fluctuations on the dot. This generic phenomenon has been vividly investigated theoretically both in the case of a large metallic box with a very dense spectrum [3] and in the opposite limit of a two-level system [4]. The reservoir of electrons may be a two-dimensional (2D) Fermi-liquid lead [3,5] or a 1D structure [6,7] [e.g., a fractional quantum Hall edge state (FQHES)or a quantum wire] where interacting electrons form TomonagaLuttinger liquid (LL). Some recent endeavors have been accomplished by Cedraschi et al. [4] and by one of us [8] to understand the role of dissipation-coming from the capacitive coupling of the dot to an electric environment with an ohmic resistance-on the charge quantization of a quantum dot, but with the limitation of free electrons in the reservoir lead. In this Letter, we explore dissipation effects on the small quantum dot (resonant level) coupled to a chiral LL (CLL) which has been previously introduced by Furusaki and Matveev [6]. We seek to provide a unified picture of the role of interactions in the onechannel conductor and of the zero-point fluctuations of the electric environment generalizing the case of a single junction [9]. Of interest to us is to understand the nature of the quantum phases emerging through the dissipative mesoscopic structure shown in Fig. 1 and hence to discuss physical implications for the occupation probability on the quantum dot. We highlight that the physics explored here is sufficiently appealing to experimentalists to carry out activities similar to those already existing on superconducting qubits capacitively coupled to lossy transmission lines in GaAs/AlGaAs heterostructures [10].The quantum dot of interest in Fig. 1 is small enough such that we can only restrict ourselves to the highestoccupied level. This leads to a two-level system [4]. The gate voltage V g is fixed such that the two states in which the level is occupied (|1 ) or not (|0 ) are almost degener- ate. We can thus resort to an orbital s...

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Observation of Quantum Fluctuations of Charge on a Quantum Dot

Cited by 88 publications

References 26 publications

Smearing of charge fluctuations in a grain by spin-flip assisted tunneling

Smearing of charge fluctuations in a grain by spin-flip assisted tunneling

Single-electron states in the quantum Hall effect

Unification of electromagnetic noise and Luttinger liquid via a quantum dot

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