Charge Kondo effects in a quadruple quantum dot in spinless and spinful regimes.

We theoretically study charge Kondo effects in a quadruple quantum dot, whose shape is such that three dots A,B,C are located at the three corners of a triangle respectively and the other dot D is at the center of the triangle. Here, the dots A and B are coupled to reservoirs. We consider a spinless regime under an external magnetic field and a spinful regime in the presence of electron tunneling between the dots A and B, when the system has two-fold degenerate ground-state charge configurations (n_A=1,n_B=1,n_C=1,n_D=0) and (0,0,0,1). In the spinless regime, a single-channel charge Kondo effect occurs. In this case, the two charge configurations act as the pseudospin states of the Kondo effect. In the spinful regime, electrons of the dots A and B in the charge configuration (1,1,1,0) form a spin singlet state, and the system is described by an anisotropic two-channel Kondo Hamiltonian. Because the channel anisotropy is large, the quadruple dot shows a single-channel charge Kondo effect. We compute electron transport through the quadruple dot for the two regimes.