We study non-equilibrium magneto-transport through a single electron transistor or an impurity. We find that due to spin-flip transitions, generated by the spin-orbit interaction, the spectral density of the tunneling current fluctuations develops a distinct peak at the frequency of Zeeman splitting. This mechanism explains modulation in the tunneling current at the Larmor frequency observed in scanning tunneling microscope (STM) experiments and can be utilized as a detector for single spin measurement. In the present work we demonstrate that the spectral density of current fluctuations of a single electron transistor in the external magnetic field develops a peak at the electron Zeeman frequency generated by spin-orbit interactions. We attribute such effect to the interference between the spin up and spin down components of the transmitted current resulting from the spin flips in the tunneling process.
PACSAs a model system we consider a heterostructure (for example Si/Ge) schematically shown in Fig. 1. The two regions, to the right and to the left from the dotted line denoting the interface, have different g-factors, g 1 ≈ 2 for the left region and g 2 = 2 for the right region. There are two contacts/Fermi reservoirs in each of the regions. The left region also contains a quantum dot, so that when a potential difference V is applied between the two reservoirs, electrons can tunnel from left to the right reservoirs via the dot. The energy levels of the dot are spin-split by an external magnetic field. In this case the spin-orbit coupling causes the spin-flip transitions resulting in coherent effects in the tunneling current [4]. We describe our system by the Hamiltonian H = H L + H R + H S + H C + H T where the first two terms represent the unperturbed states of two contacts, H L = l,s ǫ ls a † ls a ls and H R = r,s ǫ rs a † rs a rs , where a † ls (a † rs ) creates a fermion/electron at the energy level ǫ l (ǫ r ) and with spin s in the left (right) reservoir. We assume that there is a single discrete level in the dot due to spatial quantization. The level is spin-split by the magnetic field B, so that the states in the dot are described by H S = s ǫ sns , wheren s = a † s a s , and a † s creates an electron in the dot at the level ǫ s with spin s. We denote ǫ −1/2 − ǫ 1/2 = gβB ≡ E, Fig. 1, where g is the electronic g-factor in the dot and β is Bohr's magneton. The term H C = s U 2n sn−s corresponds to the Coulomb charging energy for the electron in the well. In what follows we will assume the case of complete Coulomb blockade, i.e., U → ∞, thus allowing for only one electron to occupy the two spin states in the dot. The tunneling transitions between the left reservoir, the dot and the right reservoir are represented by the Hamiltonian:Here we use gauge in which tunneling amplitudes Ω l and Ω rss ′ are real. As we noted above the key point of our work is that we consider the tunneling transitions accompanied by spin flips . These are generated by the second term in Eq. (1) due to g-factor difference between th...