Spin-related effects in transport properties of open quantum dots

We study the interaction corrections to the transport coefficients in open quantum dots (i.e., dots connected to leads of large conductance $G⪢e^2∕\pi \hslash$), via a quantum kinetic equation approach. The effects of all the channels of the universal (in the random matrix theory sense) interaction Hamiltonian are accounted for at one-loop approximation. For the electrical conductance we find that even though the magnitude of the triplet channel interaction is smaller than the charging energy, the differential conductance at small bias is greatly affected by this interaction. Furthermore, the application of a magnetic field can significantly change the conductance due to the Zeeman splitting, producing finite bias anomalies. For the thermal conductance we find that the Wiedemann-Franz law is violated by the interaction corrections, and we investigated the effect of magnetic field on the Lorentz ratio for contacts of finite reflection. The charge and triplet channel corrections to the electrical and thermal conductance vanish for reflectionless contacts. In the latter case the temperature and magnetic-field dependence of the conductance is determined by the Maki-Thompson correction in the Cooper channel.

Figure 1

Quantum dot connected to two leads, and the corresponding Hamiltonians.

Figure 2

Interaction correction to the dimensionless differential conductance for varying strength of the triplet interaction in the absence of Zeeman splitting. Here $T=0.1{\delta }_1$, ${\Gamma }_0=5{\delta }_1$, and $E_c=100{\delta }_1$ where ${\delta }_1$ is the mean level spacing, and we have taken $N_L=N_R$ and $T_n=1∕2$ for all channels. The value of $J_s$ is shown above each graph. For clarity, graphs are shifted upwards by 0.05 at each step.

Figure 3

The magnetoconductance of the starred curve of Fig. 2 vs bias voltage, for different values of Zeeman splitting energy (shown above each graph). The graphs are shifted upwards by 0.03 at each step.

Figure 4

The magnetoconductance of the starred curve of Fig. 2 vs Zeeman splitting energy, at various bias voltages (shown above each graph). The graphs are not shifted here.

Figure 5

Correction to dimensionless differential conductance for reflectionless contacts and symmetric leads at zero temperature and ${\Gamma }_{*}=5{\delta }_1$. Here we have plotted ${\epsilon }^2\Delta G_{\mathit{MT}}$, so that the actual magnitude of the correction is further suppressed by $1∕{\epsilon }^2$. The values of the effective Zeeman splitting $E_Z^{*}$ are shown below each graph, and the graphs are shifted upwards by 0.25 at each step.

Figure 6

The relative change in the Lorentz number vs temperature for different values of Zeeman splitting energy (shown above each graph). Here, $E_c=100{\delta }_1$, $J_s=-0.45{\delta }_1$, and ${\Gamma }_0=5{\delta }_1$, and we have taken $N_L=N_R=1$ and $T_n=1∕2$ for all channels. The graphs are shifted upwards by 0.03 at each step.

Figure 7

Dyson equation for the ensemble averaged dot Green function (a)–(c), and the expression for the lead Green function (d). The crossing diagrams in (c) are smaller than the noncrossing one by powers of $1∕M$ and can be ignored. The disordered matrix elements in (e) are given by Eq. (1.1).

Figure 8

Leading singular contribution to the thermodynamic potential. The shaded box corresponds to $2E_c$, defined through the two particle vertex (see, e.g., Ref. 24); the solid lines are coherent parts of the electron Green functions.