Quantum Many-Body Effects in a Single-Electron Transistor

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Science  28 May 2004:
Vol. 304, Issue 5675, pp. 1258-1259
DOI: 10.1126/science.1098302

One of the toughest challenges in physics is understanding how large groups of particles like electrons behave when their interactions are influenced by quantum mechanics. Meeting this challenge is key to the mastery of nanostructures, where tight confinement of electrons makes quantum effects dominant. On page 1293 of this issue, Kogan et al. (1) report the successful application of a novel spectroscopic technique to probe a quantum mechanical many-body phenomenon in a nanostructure. As with any new spectroscopy, this first application is likely to be far from the last. Impressively, the first spectral data already resolve a long-standing question about a quantum phenomenon known as the Kondo resonance. In the Kondo effect, a magnetic impurity in a material produces a resonant peak in electron scattering. Kogan et al. show that, with delicate tuning, spectroscopy can be performed on this resonance without the loss of quantum coherence.

In their experiments, Kogan et al. studied the properties of a single-electron transistor (SET): a two-dimensional island of electrons, about 100 nm in diameter, coupled to metallic electrodes in a specially fabricated semiconductor structure. Quantum mechanical screening of the spin of the confined electrons by those in the adjacent electrodes gives rise to a narrow many-body scattering resonance for electrons (named the Kondo resonance for its original explicator). Because this resonance is centered precisely at the Fermi energy (that is, the energy below which all free electron states are filled at absolute temperature T = 0) and because current is carried by states near the Fermi energy, the resonance is manifest as a strong enhancement of the conductance through the transistor. Because the resonance is narrow, the enhanced conductance is present only at very low temperatures (typically below 1 K in a SET) and at correspondingly low dc-bias voltages. Indeed, the low-temperature decrease in conductance with increasing dc bias was the first decisive signature of the Kondo effect in a SET—as reported in 1998 from the same MIT lab, headed by Kastner (2). Even before that time, theorists had predicted that an ac-bias voltage applied to an SET would, under the right circumstances, give rise to sidebands of the many-body Kondo resonance [see references in (1)], just as one might expect photon emission and absorption sidebands for an ordinary single-particle resonance. Why were the Kondo sidebands in Kogan et al. not seen in previous ac experiments (3)? Some differences in the present experiment include use of a smaller SET to increase the level spacing for confined electrons and use of a microwave cavity to reduce noise. The main difference, however, may be in the tuning of the many-body resonance width kBTK, where TK is the “Kondo temperature.” For Kondo sidebands to be visible and not quenched by decoherence, operation must occur in a narrow range kBTK < hf to separate the sidebands from the main resonance, with hf ∼ eVac to shift appreciable weight to the sidebands, and eVac < a few times kBTK to avoid decoherence. Kogan et al. were able to tune both the ac-bias voltage Vac and the Kondo temperature TK to be just right for their fixed ac frequency f.

The Kondo resonance studied by Kogan et al. is of the conventional type. A free spin, coming from an odd number of confined electrons, interacts with a Fermi sea, namely the electrons in the metallic electrodes. The free spin entangles with the spins in the electrodes to form a total-spin-zero ground state, as shown schematically in the figure. Put very simply, when faced with two degenerate states—spin up and spin down for the confined electrons—the system forms a lower energy quantum mechanical superposition of the two. One could imagine similar superpositions of other degenerate states, and indeed a number of such variant Kondo effects have been observed in recent years, including the superposition of local states of spin 0 and spin 1, brought into degeneracy by a magnetic field (4), and a related two-stage Kondo effect in which conductance first increases and then decreases again as the dc bias approaches zero (5). Why the recent renaissance in Kondo physics, 70 years after the effect was first observed in metals and 40 years after Jun Kondo's theoretical explanation? The use of SET structures has been the key: Each structure constitutes a single Kondo “spin” that can be studied in isolation, and the bias voltage can be scanned without inducing heating, thereby allowing dc-bias spectroscopy. Indeed, there are strong hints that ordinary semiconductor point contacts near pinch-off spontaneously organize themselves into SETs, giving rise to a Kondo effect (6). The advantages of SET structures are not unique to semiconductors; pronounced Kondo resonances have recently been seen in carbon nanotubes (7) and single molecules (8) arranged in SET geometries.

Kondo effect examined with ac spectroscopy.

Schematic energy-level diagram of Kondo sidebands in the single-electron transistor studied by Kogan et al. An odd number of electrons is confined in the central region, leaving a net spin. At low temperatures, this spin entangles with spins from the metallic electrodes (shaded region), creating a total-spin-zero ground state and a quantum many-body resonance (the Kondo resonance) at the Fermi energy of each electrode. Application of an ac-bias voltage at frequency f creates sidebands of the Kondo resonance spaced by hf, as shown schematically with respect to the left electrode. Simultaneous application of a dc-bias voltage Vdc reveals the sidebands of the Kondo resonance in the differential conductance when Vdc = hf.


The development of an ac-bias spectroscopy to complement dc-bias spectroscopy promises a new window onto all of these Kondo systems. Moreover, ac-bias spectroscopy offers unique opportunities in three directions. First, ac measurements are critical to study the formation time of the Kondo spin-screening cloud. Second, ac-bias spectroscopy is particularly well suited to study the decoherence of the Kondo ground state by excitations. Third, the success of ac-bias spectroscopy points toward the regime of strong photon-matter coupling—in principle, an ac bias can create a strong coupling of Kondo resonances in the same way that two atomic states can be coupled by a laser to create coherent Rabi oscillations. We will have to stay tuned.


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