Spin-orbit effects in carbon-nanotube double quantum dots

Abstract

We study the energy spectrum of symmetric double quantum dots in narrow-gap carbon nanotubes with one and two electrostatically confined electrons in the presence of spin-orbit and Coulomb interactions. Compared to GaAs quantum dots, the spectrum exhibits a much richer structure because of the spin-orbit interaction that couples the electron's isospin to its real spin through two independent coupling constants. In a single dot, both constants combine to split the spectrum into two Kramers doublets while the antisymmetric constant solely controls the difference in the tunneling rates of the Kramers doublets between the dots. For the two-electron regime, the detailed structure of the spin-orbit split energy spectrum is investigated as a function of detuning between the quantum dots in a 22-dimensional Hilbert space within the framework of a single-longitudinalmode model. We find a competing effect of the tunneling and Coulomb interaction. The former favors a left-right symmetric two-particle ground state while in the regime where the Coulomb interaction dominates over tunneling, a left-right antisymmetric ground state is found. As a result, ground states on both sides of the ͑11͒-͑02͒ degeneracy point may possess opposite left-right symmetry, and the electron dynamics when tuning the system from one side of the ͑11͒-͑02͒ degeneracy point to the other is controlled by three selection rules ͑in spin, isospin, and left-right symmetry͒. We discuss implications for the spin-dephasing and Pauli blockade experiments.

Temperature-dependent dynamical nuclear polarization bistabilities in double quantum dots in the spin-blockade regime

“…The additional inelastic rates can e.g. be provided by co-tunneling [12][13][14][15][16] or spin-orbit mediated [19][20][21][22][23] spin relaxation processes. Importantly, the inelastic processes contained in Γ ine f,i give an additional escape path from the triplets without a nuclear spin-flip.…”

“…Next, we find the leakage current close to the crossing of the triplets using the simplified rate equations (20)(21).…”

“…Analyzing the leakage current is therefore an excellent tool to obtain information about the spin relaxation processes from a transport experiment. 6,10,11 There are several ways to escape from the blocking states: via co-tunneling processes, 5,[12][13][14][15][16] spin-orbit meditated spin relaxation [17][18][19][20][21][22][23][24][25] and/or by hyperfine interaction 26 (HFI) between the electronic spins and the nuclear spins of the host material. 6,10,11, The relative importance of these mechanisms depends on the material and the external parameters.…”

“…To find the stationary DNP, we solve the system of rate equations (20)(21), i.e.Ṗ = 0 andṅ ν = 0 for all ν.…”

Signatures of spin-orbit interaction in transport properties of finite carbon nanotubes in a parallel magnetic field

“…The SOI-modified band structure and its implications on the electronic properties of CNT's in a magnetic field have been in the focus of extensive theoretical work. 15,[30][31][32][33][34][35][36] However, at present only a few theoretical works exist 16,37 that investigate quantum transport through CNT's including magnetic field, curvature, and SOI effects.…”