Transport of electrons at low temperatures in nano-devices such as semiconductor quantum dots has led to many fascinating phenomena in recent years. In these devices electrons are confined in a very small region at the nano-scale with strong electron-electron repulsion, leading to strong suppression of charge fluctuations, so called "Coulomg Blockade." However, if the quantum dot contains odd number of electrons, the spins of conduction electrons tend to couple antiferromagnetically to those in the quantum dots, so called the "Kondo effect." This leads to enhancement of zero-bias conductance at low temperatures. In this talk, I will present a few interesting examples of my recent works on quantum transport in quantum dots associated with Kondo effect.
In this talk, I will focus on the systems where Kondo effect competes with additional interactions in the systems which couple to the quantum dot. Examples are the antiferromagnetically coupled double-quantum-dot-system and a dissipative quantum dot coupled to a noisy environment induced by quantum charge fluctuations in the setup. When there is more than one competing quantum ground states, interesting "quantum phase transitions" often occur. These are the continuous phase transitions at zero temperature between one quantum ground state to another, which give rise to many unconventional transport properties at low temperatures near the "quantum critical point." Moreover, there is a growing interest in nonequilibrium transport through a Kondo dot near the quantum phase transition when an external bias voltage is imposed on the dot. I will discuss some of the new results on both equilibrium and nonequilibrium charge transports near the quantum phase transition of the Kondo dot systems. Due to high tenability of these nano-devices, one can address fundamentally important issues in both Condensed Matter and Mesoscopic physics.