Distribution of conduction channels in nanoscale contacts: Evolution towards the diffusive limit

Abstract

We present an experimental determination of the conduction channel distribution in lead nanoscale contacts with total conductances ranging from 1 to 15 G 0 , where G 0 = 2e 2 /h. It is found that even for contacts having a cross section much smaller than the mean free path the distribution tends to be remarkably close to the universal diffusive limit. With the help of theoretical calculations we show that this behavior can be associated with the specific band structure of lead which produces a significant contribution of partially open channels even in the absence of atomic disorder. Published in Europhysics Letters, Electron transport properties in a quantum coherent conductor are fully characterized by the set of transmission coefficients {τ n } corresponding to the conductance eigenchannels of the system [1,2]. Clearly, the whole set {τ n } cannot be extracted from the total conductance which only yields information on ∑ n τ n . The possibility of an accurate determination of the individual {τ n } was demonstrated by Scheer et al. [3] for the case of one-atom contacts, by analyzing electron transport in the superconducting state [4]. This technique allowed to prove that the number of channels for one-atom contacts is basically determined by the valence orbital structure while the particular values in the set {τ n } depend also on the contact geometry at the atomic scale [5].A natural question that arises is how the set {τ n } evolves as the size of the contact is increased. One would expect that for sufficiently large contacts (where the size is larger than the mean free path) the transmission coefficients would be distributed according to P(T ) = ∑ n δ (T − τ n ) = G / 2G 0 T √ 1 − T , i.e. the universal distribution function predicted for a quantum conductor in the diffusive regime [6,7]. Although indirect evidence of this distribution has been obtained through shot-noise measurements [8] a direct determination of P(T ) in this regime is still an open experimental challenge.In the present work we combine experimental and theoretical efforts in order to analyze the evolution of the channel distribution in nanocontacts as the size of the contact is increased from the atomic-size limit. We obtain the set {τ n } from transport measurements in lead nanocontacts with conductances ranging from 1 to 15 G 0 . These results are compared with model calculations in which the effects of geometry, atomic disorder, and band structure can be included. We find that even for small contacts (G ∼3-4 G 0 ) the channels distribution for Pb is unexpectedly close to the diffusive limit. We show that this behavior can be attributed to the particular band structure of Pb.Highly stable atomic scale contacts are formed using a mechanically controlled break-junction (MCBJ) [9]. A notched lead wire 99.99% pure is glued on top of a flexible substrate.

Statistical analysis of the transmission based on the DMPK equation: an application to Pb nano-contacts

“…[10] by analyzing several samples of Pb nano-contacts. To be specific, the functions ρ norm (τ ) and q(τ ) defined as…”

“…We find convenient and motivating to reproduce here some of the results of Refs. [10] and [11]. In figure 2, we show ρ norm (τ ) and ρ(τ ) for Pb contacts with conductances ranging from 4 to 15 (in units of the conductance quantum 2e 2 /h ) [20].…”

“…(8) We next present the results for ρ norm (τ ) and q(t) [Eqs. (10) and (11)] obtained from the above expression for ρ(τ ) [Eq. (14)], where the integrals were performed numerically.…”

“…For example, statistical properties of the transport like the density of the transmission eigenvalues have been estimated for Pb nano-contacts [10,11]; in these experiments, it has been pointed out that the transmission density for contacts with a few open channels is unexpectedly similar to the known bimodal density distribution in the diffusive metallic regime. We recall that in the metallic limit a large number of channels are assumed to contribute to the transport.…”

“…Motivated by recent break-junctions experiments where some statistical properties of the transmission eigenvalues have been estimated for Pb nano-contacts [10,11], in this paper we calculate the density of the transmission eigenvalues within the framework of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation [12,13]. In order to apply DMPK ideas to those break-junctions experiments, we assume that the constriction, or neck, formed during the elongation processes of the MBCJ device is smaller or of the order of the mean free path.…”