Depinning transition in Mott-Anderson insulators

Abstract

We have studied the I-V curves of amorphous insulators at very low temperature which exhibit a crossover from variable range hopping to a low-temperature activation law. Around a critical voltage V c , the current increases by several orders of magnitude. This is interpreted as resulting from an interplay between Coulomb interactions and disorder: below V c charges are collectively ''pinned,'' while above V c free charges exist. We find a critical scaling of the I-V curves near V c , at least when hysteretic effects can be neglected.In the last decades, taking into account both strong disorder and Coulomb interactions in the description of electronic transport turned out to be both a necessity and a tough challenge. This is particularly true in disordered insulators, where Coulomb interaction is poorly screened. In systems with a small number of electrons such as lightly doped semiconductors, disorder is thought to dominate over charging effects, leading to Mott's famous variable range hopping ͑VRH͒ law for the resistance at low temperature T: Rϰexp(T 0 /T) ␥ , where ␥ϭ1/(dϩ1). Electron-hole interactions were later included by Efros and Shklovskii ͑ES͒, 1 who argued that, at sufficiently low T, ␥ should take the value 1 2 . Very recently, this interplay between disorder and interactions was addressed within a rather different framework, in the context of quantum dots where the interaction is dominant, and leads to Coulomb blockage effects. Middleton and Wingreen 2 have shown that an array of such quantum dots should, in the presence of local disorder, undergo a depinning transition as the external voltage V is increased. For small voltages, the current I is zero ͑at Tϭ0͒, and increases from zero above a critical value V c of the voltage, with a nontrivial exponent: Iϰ(VϪV c ) ␤ . This prediction was rapidly corroborated by a series of experiments on model quantum dot systems. 3 The central point of the present paper is to show that this depinning transition could also be relevant in certain real samples-in our case sputtered films of Y x Si 1Ϫx . In such samples, some kind of small-scale granularity is unavoidable, in particular near the metal-insulator transition ͑MIT͒, leading to the presence of more metallic droplets within a more insulating matrix. If the charging energy of these droplets becomes large, Coulomb blockade effects, such as Middleton-Wingreen's collective pinning, should be expected. For example, Coulomb blockade oscillations were observed in mesoscopic In 2 O 3Ϫx samples, confirming the importance of charge effects near the MIT. 4 Another consequence of a strong on-site Coulomb repulsion 5 is the activated behavior ͑␥ϭ1͒ of the resistance, even if some disorder is present-at least in an intermediate range of temperatures. This is indeed the case in our Y x Si 1Ϫx samples in the immediate vicinity of the MIT ͑xӍ0.2͒, for T in the range 20-500 mK, where VRH holds at high temperatures and becomes simply activated for lower temperatures. ͑Such a behavior was also reported in Ref. 6.͒ It is thus our ...

Non-Ohmic hopping transport ina−YSi: From isotropic to directed percolation

“…Previous studies of electrical transport in such Y x Si 1−x samples [54]- [59], have shown that a small variation of x allows to cross the metal-insulator transition : above x ≃ 0.22 the samples are metallic; while for lower values of x, the samples exhibit an insulating behavior, i.e. a divergence of the resistance for T → 0, in agreement with the VRH predictions [55]- [58], except for the very weakly insulating samples at the lowest temperatures [59]. In the present work x ≃ 0.19 and the samples are strongly insulating, exhibiting VRH below T ≃ 2 K. Since the two samples we used behaved similarly, we report only the data of one of them.…”

Sequential tunneling and inelastic cotunneling in nanoparticle arrays

“…This modifies the zero-temperature I-V characteristics by an experimentally determined crossover function with a power-law temperature dependence. 27 A different approach was proposed in Ref. 13.…”

Effects of disorder on the blockade voltage of two-dimensional quantum dot arrays

“…5 The current dependence Iϰ(VϪV b ) resulting from the effect of background charges was suggested 6 using ϭ1 in case of one-dimensional arrays, and ϭ5/3 in case of two-dimensional networks. That work has spawned a number of experiments [7][8][9][10][11] with in part different values of .…”