### Abstract

We theoretically investigate the current-voltage (I-V) property of two-dimensional Coulomb blockade (CB) arrays by conducting Monte Carlo simulations. The I-V property can be divided into three regions and we report the dependence of the aspect ratio δ (namely, the lateral size N _{y} over the longitudinal one N_{x}). We show that the average CB threshold obeys a power-law decay as a function of δ. Its exponent γ corresponds to a sensitivity of the threshold depending on δ, and is inversely proportional to N_{x} (i.e., δ at fixed N _{y}). Further, the power-law exponent ζ, characterizing the nonlinearity of the I-V property in the intermediate region, logarithmically increases as δ increases. Our simulations describe the experimental result ζ = 2:25 obtained by Parthasarathy et al. [Phys. Rev. Lett. 87 (2001) 186807]. In addition, the asymptotic I-V property of one-dimensional arrays obtained by Bascones et al. [Phys. Rev. B 77 (2008) 245422] is applied to two-dimensional arrays. The asymptotic equation converges to the Ohm's law at the large voltage limit, and the combined tunneling-resistance is inversely proportional to δ. The extended asymptotic equation with the first-order perturbation well describes the experimental result obtained by Kurdak et al. [Phys. Rev. B 57 (1998) R6842]. Based on our asymptotic equation, we can estimate physical values that it is hard to obtain experimentally.

Original language | English |
---|---|

Article number | 114704 |

Journal | journal of the physical society of japan |

Volume | 80 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 1 2011 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*journal of the physical society of japan*,

*80*(11), [114704]. https://doi.org/10.1143/JPSJ.80.114704

**Size dependence of current-voltage properties in Coulomb blockade networks.** / Narumi, Takayuki; Suzuki, Masaru; Hidaka, Yoshiki; Kai, Shoichi.

Research output: Contribution to journal › Article

*journal of the physical society of japan*, vol. 80, no. 11, 114704. https://doi.org/10.1143/JPSJ.80.114704

}

TY - JOUR

T1 - Size dependence of current-voltage properties in Coulomb blockade networks

AU - Narumi, Takayuki

AU - Suzuki, Masaru

AU - Hidaka, Yoshiki

AU - Kai, Shoichi

PY - 2011/11/1

Y1 - 2011/11/1

N2 - We theoretically investigate the current-voltage (I-V) property of two-dimensional Coulomb blockade (CB) arrays by conducting Monte Carlo simulations. The I-V property can be divided into three regions and we report the dependence of the aspect ratio δ (namely, the lateral size N y over the longitudinal one Nx). We show that the average CB threshold obeys a power-law decay as a function of δ. Its exponent γ corresponds to a sensitivity of the threshold depending on δ, and is inversely proportional to Nx (i.e., δ at fixed N y). Further, the power-law exponent ζ, characterizing the nonlinearity of the I-V property in the intermediate region, logarithmically increases as δ increases. Our simulations describe the experimental result ζ = 2:25 obtained by Parthasarathy et al. [Phys. Rev. Lett. 87 (2001) 186807]. In addition, the asymptotic I-V property of one-dimensional arrays obtained by Bascones et al. [Phys. Rev. B 77 (2008) 245422] is applied to two-dimensional arrays. The asymptotic equation converges to the Ohm's law at the large voltage limit, and the combined tunneling-resistance is inversely proportional to δ. The extended asymptotic equation with the first-order perturbation well describes the experimental result obtained by Kurdak et al. [Phys. Rev. B 57 (1998) R6842]. Based on our asymptotic equation, we can estimate physical values that it is hard to obtain experimentally.

AB - We theoretically investigate the current-voltage (I-V) property of two-dimensional Coulomb blockade (CB) arrays by conducting Monte Carlo simulations. The I-V property can be divided into three regions and we report the dependence of the aspect ratio δ (namely, the lateral size N y over the longitudinal one Nx). We show that the average CB threshold obeys a power-law decay as a function of δ. Its exponent γ corresponds to a sensitivity of the threshold depending on δ, and is inversely proportional to Nx (i.e., δ at fixed N y). Further, the power-law exponent ζ, characterizing the nonlinearity of the I-V property in the intermediate region, logarithmically increases as δ increases. Our simulations describe the experimental result ζ = 2:25 obtained by Parthasarathy et al. [Phys. Rev. Lett. 87 (2001) 186807]. In addition, the asymptotic I-V property of one-dimensional arrays obtained by Bascones et al. [Phys. Rev. B 77 (2008) 245422] is applied to two-dimensional arrays. The asymptotic equation converges to the Ohm's law at the large voltage limit, and the combined tunneling-resistance is inversely proportional to δ. The extended asymptotic equation with the first-order perturbation well describes the experimental result obtained by Kurdak et al. [Phys. Rev. B 57 (1998) R6842]. Based on our asymptotic equation, we can estimate physical values that it is hard to obtain experimentally.

UR - http://www.scopus.com/inward/record.url?scp=80755125891&partnerID=8YFLogxK

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U2 - 10.1143/JPSJ.80.114704

DO - 10.1143/JPSJ.80.114704

M3 - Article

AN - SCOPUS:80755125891

VL - 80

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 11

M1 - 114704

ER -