The role of discrete orbital symmetry in mesoscopic physics is manifested in a system consisting of three identical quantum dots forming an equilateral triangle. Under a perpendicular magnetic field, this system demonstrates a unique combination of Kondo and Aharonov-Bohm features due to an interplay between continuous [spin-rotation SU(2)] and discrete (permutation C3v) symmetries, as well as U(1) gauge invariance. The conductance as a function of magnetic flux displays sharp enhancement or complete suppression depending on contact setups.
Kondo tunneling reveals hidden SO(n) dynamical symmetries of evenly occupied quantum dots. As is exemplified for an experimentally realizable triple quantum dot in parallel geometry, the possible values n=3,4,5,7 can be easily tuned by gate voltages. Following construction of the corresponding o(n) algebras, scaling equations are derived and Kondo temperatures are calculated. The symmetry group for a magnetic field induced anisotropic Kondo tunneling is SU(2) or SO(4).
Indirect exchange interaction between itinerant electrons and nano-structures with non-trivial geometrical configurations manifests a plethora of unexpected results. These configurations can be realized either in quantum dots with several potential valleys or in real complex molecules with strong correlations. Here we demonstrate that the Kondo effect may be suppressed under certain conditions in triple quantum dots with mirror symmetry at odd electron occupation. First, we show that the indirect exchange has ferromagnetic sign in the ground state of triple quantum dot in a two-terminal cross geometry for electron occupation N=3. Second, we show that for electron occupation N=1 in three-terminal fork geometry the zero-bias anomaly in the tunnel conductance is absent (despite the presence of Kondo screening) due to special symmetry of the dot wave function.Comment: 8 two-column page
The effective spin Hamiltonian of a triple quantum dot with odd electron occupation weakly connected in series with left (l) and right (r) metal leads is composed of two-channel exchange and co-tunneling terms. Renormalization group equations for the corresponding three exchange constants J l , Jr and J lr are solved (to third order). Since J lr is relevant, the system is mapped on an anisotropic two-channel Kondo problem. The structure of the conductance as function of temperature and gate voltage implies that in the weak and intermediate coupling regimes, twochannel Kondo physics persists at temperatures as low as several TK. At even electron occupation, the number of channels equals twice the spin of the triple dot (hence it is a fully screened impurity).PACS numbers: 72.10. -d, 72.15.-v, 73.63.-b Motivation: In the present work, a simple configuration of localized moment in nanostructures is studied, where the two-channel Kondo Hamiltonian appears in resonance tunneling. Concrete experiment is proposed in order to elucidate the pertinent physics at T > T K (the Kondo temperature). In the strong coupling regime, a multichannel Kondo system is known to be a non-Fermi liquid [1], but construction of simple theoretical models pertaining to experimentally feasible setups is notoriously elusive. Examples are magnetic impurity scattering, physics of two-level systems and Kondo lattices (see [2,3] for review). Recent attempts to realize twochannel Kondo effect in tunneling through quantum dots [4] using peculiar setups still await experimental manifestation. The problem is exemplified in tunneling through a simple quantum dot sandwiched between two metallic "left" (l) and "right" (r) leads. Starting from the single impurity Anderson model, it is tempting to think of the two leads as a source of two tunneling channels. However, if the two fermion lead operators c kσa (k = momentum, σ = spin projection and a = l, r the lead index) are coupled to a single dot electron operator d σ , one channel can always be eliminated by an appropriate rotation in l − r space [5]:
In a cold atom gas subject to a 2D spin-dependent optical lattice potential with hexagonal symmetry, trapped atoms execute circular motion around the potential minima. Such atoms are elementary quantum rotors. The theory of such quantum rotors is developed. Wave functions, energies, and degeneracies are determined for both bosonic and fermionic atoms, and magnetic dipole transitions between quantum rotor states are elucidated. Quantum rotors in optical lattices with precisely one atom per unit cell can be used as extremely high sensitivity rotation sensors, accelerometers, and magnetometers.
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