A strong Kondo effect is observed for a vertical quantum dot holding an odd number of electrons and spin 1=2 when an orbital degeneracy is induced by magnetic field. The estimated Kondo temperature for this ''doublet-doublet'' degeneracy is similar to that for the singlet-triplet degeneracy with an even electron number, indicating that a total of fourfold spin and orbital degeneracy accounts for the enhancement of the Kondo temperature. The experimental observation is qualitatively reproduced by scaling calculations using an SU(4) model at the orbital degeneracy.A quantum dot offers unprecedented opportunities of realizing and manipulating a single magnetic impurity interacting with a Fermi sea of conduction electrons. Rich aspects of the Kondo physics [1] have been explored owing to the tunability of relevant parameters in quantum dots. Pioneering works on the Kondo effect in quantum dots [2 -6] proceed within the framework of the conventional spin 1=2 Anderson impurity model for a spindegenerate single level. The Kondo effect is observed only when the number of electrons, N, is odd with a spin S 1=2. However, exceptions to this odd-even parity behavior have been noted in a lateral quantum dot [7] where the Kondo effect is observed for both odd and even N. This has been followed by a more detailed report of the Kondo effect for even N in a ''vertical'' quantum dot having well-defined N and S [8]. This novel Kondo effect occurs when a magnetic field induces a spin singlet (S 0)-triplet (S 1) degeneracy in the multiorbital ground state [9][10][11][12][13][14][15].In this Letter, we present a new multilevel mechanism which enhances the Kondo temperature, T K , using a vertical quantum dot. We observe a strong Kondo effect when a magnetic field induces an orbital degeneracy for odd N and S 1=2. The estimated T K is similar to that for the singlet-triplet (S-T) Kondo effect for even N, indicating that a total of fourfold spin and orbital degeneracy for both cases contributes to enhance T K .It is known that the orbital degeneracy plays an important role in the Kondo effect of magnetic impurities with f electrons. When the total degeneracy factor is N d for spin and orbital degrees of freedom, the Kondo effect is described by the Coqblin-Schrieffer model of SUN d symmetry [16]. The factor N d increases T K as D 0 e ÿ1=N d J with exchange coupling J, where D 0 and are the bandwidth and density of states of conduction electrons. We examine a model which has the SU(4) symmetry at the orbital degeneracy, yielding a larger T K than in a single-orbital case of SU(2) symmetry, explaining the experimental results [17].

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