arXiv:cond-mat/9612180 · Physical Review Letters

Single-Electron Box and the Helicity Modulus of an Inverse SquareXYModel

Walter Hofstetter, W. Zwerger

Published May 12, 1997• 57 citations

Abstract

We calculate the average number of electrons on a metallic single-electron box as a function of the gate voltage for arbitrary values of the tunneling conductance. In the vicinity of the plateaus the problem is equivalent to calculating the helicity modulus of a classical inverse square XY model in one dimension. By a combination of perturbation theory, a two-loop renormalization group calculation, and a Monte Carlo simulation in the intermediate regime we provide a complete description of the smearing of the Coulomb staircase at zero temperature with increasing conductance.

DOI: 10.1103/physrevlett.78.3737

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arXiv:cond-mat/9612180 · Physical Review Letters

Single-Electron Box and the Helicity Modulus of an Inverse SquareXYModel

Walter Hofstetter, W. Zwerger

Published May 12, 1997• 57 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.78.3737

Related papers

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E_C^*

in the limit of very small tunneling resistance. While previous Monte Carlo simulations were restricted to the weak and intermediate tunneling regimes, our method extends the range of

E_C^*

-values by more than 30 orders of magnitude. This allows us to clearly observe the exponential suppression of

E_C^*

with increasing tunneling conductance

α

. For large, but fixed

α

, the correction to the leading exponential behavior exhibits a crossover from an intermediate temperature behavior at

βE_C^* \ll 1

, to zero temperature behavior at

βE_C^*\gg 1

. We determine this correction in both regimes and compare the numerical results to the numerous and controversial theoretical predictions for the strong tunneling limit.

The two-dimensional

S=1/2

XY model is investigated with an extensive quantum Monte Carlo simulation. The helicity modulus is precisely estimated through a continuous-time loop algorithm for systems up to

128 \times 128

near and below the critical temperature. The critical temperature is estimated as

T_{\rm KT} = 0.3427(2)J

. The obtained estimates for the helicity modulus are well fitted by a scaling form derived from the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.

A Monte Carlo simulation of the helicity modulus and the specific heat of the classical

\mathrm{XY}

model in two dimensions is presented. In particular, we have investigated the dependence of these quantities with the size of the Monte Carlo sample. The height of the specific-heat peak is found to saturate as the infinite-volume limit is approached. The peak height of the derivative of the helicity modulus is found to grow rapidly with the increase in the size of the system and is located only 7% below the temperature at which the specific heat has the maximum.