Sharp peaks in the conductance of a double quantum dot and a quantum-dot spin valve at high temperatures: A hierarchical quantum master equation approach

We study sharp peaks in the conductance-voltage characteristics of a double quantum dot and a quantum dot spin valve that are located around zero bias. The peaks share similarities with a Kondo peak but can be clearly distinguished, in particular as they occur at high temperatures. The underlying physical mechanism is a strong current suppression that is quenched in bias-voltage dependent ways by exchange interactions. Our theoretical results are based on the quantum master equation methodology, including the Born-Markov approximation and a numerically exact, hierarchical scheme, which we extend here to the spin-valve case. The comparison of exact and approximate results allows us to reveal the underlying physical mechanisms, the role of first-, second- and beyond-second-order processes and the robustness of the effect.

Figure 1

Left panel: Scheme of a typical conductance map, where the conductance is plotted as a function of both bias and gate voltage. The red diagonals are associated with tunneling through the single-particle levels ${\epsilon }_m$ and ${\epsilon }_m+U$. The blue line depicts a zero-bias peak. It occurs for gate voltages ${\mathrm{\Phi }}_{\text{gate}}$ where the impurity or quantum dot system is populated by an odd number of electrons on average. The dashed black line indicates the position of the conductance-voltage characteristics depicted in Fig. 3. Middle panel: Double quantum dot (DQD) where dot $a$ is coupled to the left (L) and dot $b$ to the right electrode (R). Right panel: Quantum dot spin valve (SV) with noncollinearly polarized electrodes. The angle between the polarization vectors is denoted by $\alpha$.

Figure 2

Conductance maps for symmetric coupling to electrodes, ${\mathrm{\Gamma }}_{\text{L}}={\mathrm{\Gamma }}_{\text{R}}=\mathrm{\Gamma }$. The left and right panels refer to the DQD and SV case, respectively. The upper panels are computed with $U=50\mathrm{\Gamma }$; the lower panels with $U=8\mathrm{\Gamma }$. For even lower $U$, the maps are similar to the one on the lower left side.

Figure 3

Conductance-voltage characteristics of the DQD with $U=50\mathrm{\Gamma }$ and ${\epsilon }_m=-0.3U$ (left panel) and the SV with $U=8\mathrm{\Gamma }$ and ${\epsilon }_m=-U/4$ (right panel).

Figure 4

Difference of the interaction-induced renormalizations ${\mathrm{\Delta }}_a-{\mathrm{\Delta }}_b$ [cf. Eq. (4)]. The red dashed lines mark the narrow range of voltages where $|{\mathrm{\Delta }}_a-{\mathrm{\Delta }}_b|<t_{\text{hopp}}$.

Figure 5

Zero-bias conductance of the DQD with $U=50\mathrm{\Gamma }$ and ${\epsilon }_m=-0.3U$ (left panel) and the SV with $U=8\mathrm{\Gamma }$ and ${\epsilon }_m=-U/4$ (right panel) as a function of temperature $T$.

Figure 6

Conductance-voltage characteristics of the DQD with $U=50\mathrm{\Gamma }$ and ${\epsilon }_m=-0.3U$ (left panel) and the SV with $U=8\mathrm{\Gamma }$ and ${\epsilon }_m=-U/4$ (right panel) for an asymmetric coupling to the electrodes, ${\mathrm{\Gamma }}_{\text{L}}=\mathrm{\Gamma }=4{\mathrm{\Gamma }}_{\text{R}}$.