Double quantum dots provide an ideal model system for studying interactions between localized impurity spins. We report on the transport properties of a series-coupled double quantum dot as electrons are added one by one onto the dots. When the many-body molecular states are formed, we observe a splitting of the Kondo resonance peak in the differential conductance. This splitting reflects the energy difference between the bonding and antibonding states formed by the coherent superposition of the Kondo states of each dot. The occurrence of the Kondo resonance and its magnetic field dependence agree with a simple interpretation of the spin status of a double quantum dot.

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Strong electron and spin correlations in a double-quantum-dot (DQD) can give rise to different quantum states. We observe a continuous transition from a Kondo state exhibiting a singlepeak Kondo resonance to another exhibiting a double peak by increasing the inter-dot-coupling (t) in a parallel-coupled DQD. The transition into the double-peak state provides evidence for spinentanglement between the excess-electron on each dot. Toward the transition, the peak splitting merges and becomes substantially smaller than t because of strong Coulomb effects. Our device tunability bodes well for future quantum computation applications. The double-quantum-dot (DQD) is emerging as a versatile system for studying a variety of strongly correlated behaviors [1,2,3,4,5,6,7]. Following the experimental demonstration of the Kondo impurity-spin screening effect in single quantum dots [8,9,10,11,12,13], recent theoretical investigations of the coupled-DQD system is uncovering new correlated behaviors [1,2,3,4,5,6,7]. These works suggest that the DQD enables a realization of the two-impurity Kondo problem first discussed in the context of metallic systems [1,14,15,16] in which a competition between Kondo correlations and antiferromagnetic (AF) impurity-spin correlation leads to a quantum critical phenomenon. In a different regime of parameters, a related quantum critical phenomenon can occur driven by a competition between intra-dot Kondo coupling to leads and the inter-dot-coupling [2,3]. In each scenario, a transition is predicted to occur between a quantum state characterized by a single-peaked Kondo resonance, and a different state with a double-peaked resonance. Depending on model and DQD geometry-whether series or parallel coupled-both a continuous or discontinuous [6] behavior in the Kondo peak characteristics have been predicted. The quantum transition in the two-impurity Kondo problem has received wide attention in the theoretical literature in the past two decades, to a large extent because the Kondo to antiferromagnetic transition involves an unusual non-Fermi liquid fixed point. Experimental investigation of this problem thus far has not been reported.Here we describe transport properties of an artificial molecule formed by two-path, parallel-coupled doublequantum-dots, where the inter-dot-tunnel-coupling, t, can be tuned. In the Kondo regime the differentialconductance, dI/dV, exhibits a single peak centered at zero-bias for t comparable to the lead-coupling induced * Electronic address: yingshe@physics.purdue.edu level broadening. Increasing t by less than 10% resulted in a continuous evolution into a split Kondo resonance. At the same time the conductance at zero-bias exhibits a maximum in the vicinity of the transition. This peak splitting behavior in conjunction with distinct temperature dependences in the different regimes demonstrates a direct observation of an inter-dot-coupling-induced quantum transition. Moreover, on the double peak side the zero-bias conductance becomes suppressed; this suppression represents ...

The definition of GL should read GL =8@=k B T c ÿ T. An inadvertent error in fitting to the magneto resistance of the Al wires led to an underestimate of the wire widths and cross sections [1]. The revised width/cross section for the Al wires s1 (10 m long) and s2 (100 m long) are 11:4 nm=130 nm 2 and 7:5 nm=58 nm 2 , respectively, roughly an increase of 40% in width and factor of 2 in cross section from the previous values. The wire widths have an error of 10%, and the cross section error is 20%. The resultant revised sample parameters are listed in the revised Table I. Note that the wire length L and normal state resistance R N remain unchanged.The dependence of the free-energy barrier F on the cross sectional area A is contained in the quantity L=R N [3], removing any explicit dependence on A. Thus, the revised quantities, including A, are not used in the main analysis and do not affect the main conclusion of the Letter. The only notable effect is that the agreement between the fitted coherence length c and the calculated now occurs at the boundary of the error bars. Note that the error on c is 15%. The fitted values for FH 0; T 0 and c H 0; T 0 (135 nm), combined with the revised A, yield a thermodynamic critical field H th H 0; T 0 0:0096 T (96 Oersted), close to the known value of 0.0105 T (105 Oersted) for bulk aluminum.

The unusual properties of two-dimensional electron systems that give rise to the quantum Hall effect have prompted the development of new microscopic models for electrical conduction. The bulk properties of the quantum Hall effect have also been studied experimentally using a variety of probes including transport, photoluminescence, magnetization, and capacitance measurements. However, the fact that two-dimensional electron systems typically exist some distance (about 100 nm) beneath the surface of the host semiconductor has presented an important obstacle to more direct measurements of microscopic electronic structure in the quantum Hall regime. Here we introduce a cryogenic scanning-probe technique-- subsurface charge accumulation imaging-- that permits very high resolution examination of systems of mobile electrons inside materials. We use it to image directly the nanometer-scale electronic structures that exist in the quantum Hall regime.Comment: 6 pages, 4 figure