Coulomb blockade at almost perfect transmission

Матвеев, К. А.

doi:10.1103/physrevb.51.1743

Cited by 334 publications

(595 citation statements)

References 16 publications

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“…At the same time, at G > G m , there is at least one electron channel in the contact disk with almost perfect transparency. This guarantees [22,23] that the charging energy of every single NC, E c = e 2 /ε r d, is reduced to a value much smaller than δ (ε r is effective dielectric constant of the NC film). Accordingly, the Mott-Hubbard localization is eliminated at the same time as the Anderson localization.…”

Section: Critical Doping Concentration At Mitmentioning

confidence: 99%

“…This conductance can be easily understood with the help of the Landauer formula [22]. The number of conducting channels in the contact area is ∼ (k F ρ) 2 and each of them additively contributes ∼ e 2 /π to G. It was proven that the MIT occurs if the average conductance between two neighboring NCs G in an array of NCs is equal to the minimal conductance G m [23,24]:Substituting G from Eq. (3) into (4) yields the general criterion for the MIT…”

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confidence: 99%

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Metal–insulator transition in films of doped semiconductor nanocrystals

Chen¹,

Reich²,

Kramer³

et al. 2015

Nature Mater

109

134

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To fully deploy the potential of semiconductor nanocrystal films as low-cost electronic materials, a better understanding of the amount of dopants required to make their conductivity metallic is needed. In bulk semiconductors, the critical concentration of electrons at the metal-insulator transition is described by the Mott criterion. Here, we theoretically derive the critical concentration nc for films of heavily doped nanocrystals devoid of ligands at their surface and in direct contact with each other. In the accompanying experiments, we investigate the conduction mechanism in films of phosphorus-doped, ligand-free silicon nanocrystals. At the largest electron concentration achieved in our samples, which is half the predicted nc, we find that the localization length of hopping electrons is close to three times the nanocrystals diameter, indicating that the film approaches the metal-insulator transition.Semiconductor nanocrystals (NCs) have shown great potential in optoelectronics applications such as solar cells [1], light emitting diodes [2], and field-effect transistors [3,4] by virtue of their size-tunable optical and electrical properties [5] and low-cost solution-based processing techniques [6,7]. These applications require conducting NC films and the introduction of extra carriers through doping can enhance the electrical conduction. Several strategies for NC doping have been developed. Remote doping, the use of suitable ligands as donors in the vicinity of NC surface, increased the conductivity of PbSe NC films by 12 orders of magnitude [8]. Electrochemical doping, which tunes the carrier concentration accurately and reversibly, resulted in conducting NC films [9,10]. Lately, stoichiometric control has emerged as a strategy to dope lead chalcogenide NCs [11]. Finally, electronic impurity doping of NCs, originally impeded by synthetic challenges [12], was recently achieved in InAs [13] and CdSe [14] NCs.While many experimental studies have been directed towards increasing the conductivity of NC films, there is still no clear consensus on the fundamental question: what is the condition for the metal-insulator transition (MIT) in NC films [15][16][17]? In a bulk semiconductor, the critical electron concentration n M for the MIT depends on the Bohr radius a B according to the well-known Mott criterion [18] n M a 3 B 0.02, where a B = ε 2 /m * e 2 is the effective Bohr radius (in Gaussian units), ε is the dielectric constant of the semiconductor, and m * is the effective electron mass. It is obvious that a dense film of undoped semiconductor NCs is an insulator, while a film of touching metallic NCs with the same geometry is a conductor. Therefore, the MIT has to occur in semiconductor NC films at some criti-FIG. 1. The origin of the metal-to-insulator transition in semiconductor nanocrystal films. The figure shows the cross section of two nanocrystals in contact through facets with radius ρ. The blue spherical cloud represents an electron wave packet which moves through the contact. Such a compact wave pac...

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Section: Critical Doping Concentration At Mitmentioning

confidence: 99%

mentioning

confidence: 99%

Metal–insulator transition in films of doped semiconductor nanocrystals

Chen¹,

Reich²,

Kramer³

et al. 2015

Nature Mater

109

134

View full text Add to dashboard Cite

show abstract

“…7,8 In the strong-coupling limit (g → 1), a dramatic dependence of the peak splitting on N ch has already been found. In the cases of N ch = 1 and N ch = 2, the leading nontrivial terms have been found to be proportional to √ 1 − g and (1 − g) ln(1 − g), respectively, [4][5][6]9 and it has been hypothesized 10,11 that, for N ch > 2 but finite, the leading nontrivial term is proportional to (1 − g) N ch /2 . This last suggestion appears to correspond to calculations in the large-N ch limit, 12,13 where the effective charging energy has been found to be proportional to e −gtot/2 , which is equivalent to (1 − g tot /N ch ) N ch /2 in the limit N ch → ∞.…”

Section: Introductionmentioning

confidence: 99%

Higher-order results for the relation between channel conductance and the Coulomb blockade for two tunnel-coupled quantum dots

Golden

Halperin

1996

Phys. Rev. B

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We extend earlier results on the relation between the dimensionless tunneling channel conductance g and the fractional Coulomb blockade peak splitting f for two electrostatically equivalent dots connected by an arbitrary number N ch of tunneling channels with bandwidths W much larger than the two-dot differential charging energy U2. By calculating f through second order in g in the limit of weak coupling (g → 0), we illuminate the difference in behavior of the large-N ch and small-N ch regimes and make more plausible extrapolation to the strong-coupling (g → 1) limit. For the special case of N ch = 2 and strong coupling, we eliminate an apparent ultraviolet divergence and obtain the next leading term of an expansion in (1 − g). We show that the results we calculate are independent of such band structure details as the fraction of occupied fermionic single-particle states in the weak-coupling theory and the nature of the cut-off in the bosonized strong-coupling theory. The results agree with calculations for metallic junctions in the N ch → ∞ limit and improve the previous good agreement with recent two-channel experiments.

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“…1 may be regarded as a topologically nontrivial counterpart to the quantum RC circuit discussed in ordinary 2D electron systems. 9,10 The upper part of the device is in the QSHI regime (chemical potential µ inside the bulk gap), and contains a narrow constriction (a quantum point contact or QPC) that opens onto a quantum dot. A helical LL flows along the edges of the QSHI, as well as around the internal walls of the dot.…”

Section: Proposed Experimental Setupsmentioning

confidence: 99%

Noninvasive probes of charge fractionalization in quantum spin Hall insulators

Garate

Hur

2012

Phys. Rev. B

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When an electron with well-defined momentum tunnels into a nonchiral Luttinger liquid, it breaks up into two separate wave packets that carry fractional charges and move in opposite directions. A direct observation of this phenomenon has proven elusive, mainly due to single-particle and plasmon backscattering caused by measurement probes. This paper theoretically introduces two topological insulator devices that are naturally suited for detecting fractional charges and their velocities directly and in a noninvasive fashion.

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Coulomb blockade at almost perfect transmission

Cited by 334 publications

References 16 publications

Metal–insulator transition in films of doped semiconductor nanocrystals

Metal–insulator transition in films of doped semiconductor nanocrystals

Higher-order results for the relation between channel conductance and the Coulomb blockade for two tunnel-coupled quantum dots

Noninvasive probes of charge fractionalization in quantum spin Hall insulators

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