Electronic correlations and disorder in transport through one-dimensional nanoparticle arrays

Abstract

We analyze and clarify the transport properties of a one-dimensional metallic nanoparticle array with interaction between charges restricted to charges placed in the same conductor. We study the threshold voltage, the I-V curves and the potential drop through the array and their dependence on the array parameters including the effect of charge and resistance disorder. We show that very close to threshold the current depends linearly on voltage with a slope independent on the array size. At intermediate bias voltages, for which a Coulomb staircase is observed we find that the average potential drop through the array oscillates with position. At higher voltages I-V curves are linear but have a finite offset voltage. We show that the slope is given by the inverse of the resistances added in series and estimate the voltage at which this linear regime is reached. We also calculate the offset voltage and relate it to the potential drop through the array. Nanoparticle arrays made of metallic 1,2,3,4,5,6,7,8,9,10 , semiconducting 10,11,12,13,14,15,16 , magnetic 17,18,19 or combined 20,21,22 materials and with radii of the order of 2-7 nm can be now synthesized. The transport properties of these systems are influenced by the ratio between the energy level spacing, the charging energy of the nanoparticles, and the temperature. The first two quantities depend on the material and the size of the nanoparticle. In the case of metallic nanoparticles, at not too low temperatures, the level spacing is much smaller than the temperature and does not play any role in the transport 23 . On the contrary, the charging energy is of the order of 0.1 eV. Strong interactions between the electric charges and the possibility of tuning interparticle coupling make nanoparticles arrays an ideal system to study correlated motion 24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42 .Experimentally, these arrays are strongly influenced by disorder 43,44,45 . Local charging disorder is present in all arrays due to randomly dispersed charged impurities lodged in the substrate or in the materials that separate and surround the nanoparticles. Because of the exponential dependence of the tunneling resistance, even a small dispersion in the distance between nanoparticles results in large variations in the tunneling resistances of the junctions. Differences in the island sizes and voids in the lattice can be other sources of disorder 3 .Due to the combination of disorder and charging effects the current in voltage biased arrays is blocked up to a threshold voltage 31,35,43,46,47,48,49,50,51,52 V T . For bias voltages larger than V T current is in general non-linear in voltage with a power-law dependence 43,49,53 close to threshold, a linear dependence recovered at high-voltages and frequently a step-like behavior, called a Coulomb staircase, at intermediate voltages. Most studies have focused on the statistical analysis of the threshold voltage and on the power-law behavior of the current close to this threshold. This exponent depends on the dimensi...

Single‐Electron Effects for Probing Local Electrical Polarization Changes and Charge Hopping

“…The electrostatic free energy of the system is given by where we follow ref. and introduce as disorder potential on the particles in order to be able to take background charge induced local variations of the potential into account. is understood to be the component ( i , j ) of the inverse Maxwell capacitance matrix of the system including the electrodes.…”

Robustness of the magnetoresistance of nanoparticle arrays

“…The value of δ does not influence the results as soon as δ T . The current is calculated by means of a Monte Carlo simulation described elsewhere 16,17,19 . Simulations become increasingly costly with increasing temperature.…”

“…For finite range of the interactions and in the absence of charge disorder, once a charge has entered the array it is able to flow, even in the absence of charge gradient. The threshold voltage is strongly reduced and given by the voltage which allows an electron to enter the array or a hole to leave it 17,21 . The role played by the spin accumulation on the transport is expected to decrease if the interactions are long range.…”

“…The specific device configuration determines the transport characteristics and even regions with weak negative differential conductance or oscillations in the TMR can be found [9][10][11][12][13][14][15] . Charging effects are known to be enhanced in nanoparticle arrays 5,[16][17][18] . The threshold voltage increases, being proportional to the number of islands when interactions are restricted to charges in the same conductor or when there is charge disorder 17,18 .…”

“…Charging effects are known to be enhanced in nanoparticle arrays 5,[16][17][18] . The threshold voltage increases, being proportional to the number of islands when interactions are restricted to charges in the same conductor or when there is charge disorder 17,18 . For onsite interactions all the voltage drop happens at the contact junctions, between islands and electrodes.…”