Extracting the ground-state spin of a quantum dot from the conductance peaks in a parallel magnetic field at a finite temperature

We derive a closed expression for the finite-temperature conductance of a Coulomb-blockade quantum dot in the presence of an exchange interaction and a parallel magnetic field. Parallel-field dependence of Coulomb-blockade peak position has been used to determine experimentally the ground-state spin of quantum dots. We find that for a realistic value of the exchange interaction, the peak motion can be significantly affected at temperatures as low as $kT\sim 0.1\Delta$, where $\Delta$ is the mean level spacing in the dot. This temperature effect can lead to misidentification of the ground-state spin when a level crossing occurs at low fields. We propose an improved method to determine unambiguously the ground-state spin. This method takes into account level crossings and temperature effects in the presence of interactions.

Figure 1

(a) CB peak position versus $g{\mu }_B{B}_{\Vert }∕\Delta$ for $J_S=0.3\Delta$ and four consecutive peaks at $kT=0.01\Delta$ (dashed lines) and $kT=0.1\Delta$ (solid lines). (b) CB peak spacing versus $g{\mu }_B{B}_{\Vert }∕\Delta$ for the peaks shown in (a). The dotted lines are the expected slopes of $\pm g{\mu }_B$ and $0$.

Figure 2

(a) CB peak position versus $g{\mu }_B{B}_{\Vert }∕\Delta$ for $J_S=0.3\Delta$ and for five consecutive peaks at temperatures of $kT=0.01\Delta$ (dashed lines), $kT=0.1\Delta$ (dash-dotted lines), and $kT=0.15\Delta$ (solid lines). (b) CB peak spacing versus $g{\mu }_B{B}_{\Vert }∕\Delta$ for the peaks shown in (a). The dotted lines describe slopes of $\pm g{\mu }_B$.

Figure 3

Results of the two-transition model [Eq. (4)] (symbols) are fitted to the full calculation data of Fig. 2 (solid lines) for both peak positions [panel (a)] and peak heights [panel (b)]. Simultaneous fitting of both peak positions and peak heights is needed to properly extract the values of the total spin from the data. The dashed circles indicate crossing positions. Also shown are the corresponding GS spin values.