Abstract How localized electrons interact with delocalized electrons is a question central to many of the problems at the forefront of solid state physics. The simplest example, the Kondo effect, occurs when an impurity atom with an unpaired electron is placed in a metal, and the energy of the unpaired electron is far below the Fermi energy. At low temperatures a spin singlet state is formed between the unpaired localized electron and delocalized electrons at the Fermi energy. The consequences of this singlet formation were first observed over 60 years ago in metals with magnetic impurities, but full theoretical understanding was slow to come. Today, the situation is reversed: scaling theories and recent renormalization group calculations (T.A. Costi, A.C. Hewson (1994) J. Phys.: Cond. Mat. 6, 2519) can predict quantitatively the bonding strength of the singlet state, and the singlet's effect on the conduction electrons at all temperatures. The detailed dependence of these properties on parameters such as the energy of the localized electron cannot be tested experimentally in the classic Kondo systems, since the relevant parameters cannot easily be tuned for impurities in a metal. Recently it has become possible to test these predictions with a new experimental approach — creating an artificial Kondo system by nanofabrication (D. Goldhaber-Gordon et al. (1998), Nature 391, 156). The confined droplet of electrons interacting with the leads of a single electron transistor (SET) is closely analogous to an impurity atom interacting with the delocalized electrons in a metal, as described in the Anderson model (Y. Meir, N.S. Wingreen, P.A. Lee, Phys. Rev. Lett. (1993) 70 2601–2604). We review here measurements on a new generation of SETs that display all the aspects of the Kondo effect: the spin singlet forms and causes an enhancement of the zero-bias conductance when the number of electrons on the artificial atom is odd but not when it is even. The singlet is altered by applying a voltage or magnetic field or by increasing the temperature, all in ways that agree with predictions (N.S. Wingreen, Y. Meir (1994), Phys. Rev. B 49, 11040; T.A. Costi, A.C. Hewson (1994), J. Phys.: Cond. Mat. 6, 2519; W. Izumida, O. Sakai, Y. Shimizu (1998), J. Phys. Soc. Jpn. 67; D. Goldhaber-Gordon et al. (1998), Nature 391, 156; D. Goldhaber-Gordon, J. Gores, M.A. Kastner, H. Shtrikman, D. Mahalu, U. Meirav (1998), Phys. Rev. Lett. 81, 5225).

Kondo Effect in a Single Electron Transistor

We study the effect of Coulomb interactions on the conductance of a single-mode quantum wire connecting two bulk leads. When the density of electrons in the wire is very low, they arrange in a finite-length Wigner crystal. In this regime the electron spins form an antiferromagnetic Heisenberg chain with an exponentially small coupling J. An electric current in the wire perturbs the spin chain and gives rise to a temperature-dependent contribution of the spin subsystem to the resistance. At low temperature T >J the spin effect reduces the conductance to e2/h.

Conductance of a quantum wire in the Wigner crystal regime

We report conductance measurements of ballistic one-dimensional (1D) wires defined in GaAs/AlGaAs heterostructures in an in-plane magnetic field, B. When the Zeeman energy is equal to the 1D subband energy spacing, the spin-split subband N(up-spin) intersects (N+1)(down-spin), where N is the index of the spin-degenerate 1D subband. At the crossing of N=1(up-spin) and N=2(down-spin) subbands, there is a spontaneous splitting giving rise to an additional conductance structure evolving from the 1.5(2e^2/h) plateau. With further increase in B, the structure develops into a plateau and lowers to 2e^2/h. With increasing temperature and magnetic field the structure shows characteristics of the 0.7 structure. Our results suggest that at low densities a spontaneous spin splitting occurs whenever two 1D subbands of opposite spins cross.

Interaction Effects at Crossings of Spin-Polarised One-Dimensional Subbands

Conductance measurements of quantum point contacts (QPCs) reveal an anomalous plateau in the conductance at roughly 0.7 x ^ , just before a fully transmitting ID channel is available. Past experiments have built a consensus that this so-called "0.7 structure" is related to electron spin and electron-electron interaction, but the detailed description remains controversial. We have performed measurements on two new kinds of devices which give new insight into the interactions of electrons in these clean quasi-lD systems. One new device allows us to measure the compressibility of the electrons in a QPC for different conduction modes. Comparison with density functional calculations give new information about the relative importance of interactions (including exchange) as the density in the QPC is depleted. The other device allows us to measure the local density of states (dos) in the QPC as we tunnel directly into the constriction. Deviations from the ID dos would help to develop a more complete picture of the transport through a QPC.

Lindsay Shannon Moore

Papers

Novel devices for measuring interactions in quantum point contacts