Influence of leads on signatures of strongly-correlated zero-bias anomaly in double quantum dot measurements

TL;DR

The work addresses how disorder and strong interactions produce a strongly-correlated zero-bias anomaly (SZBA) in ensembles of two-site systems and tests its visibility in parallel double quantum dot (DQD) measurements when lead coupling is included. The authors model a DQD with onsite repulsion $U$, inter-dot hopping $t_h$, and inter-dot Coulomb term $V$, connected to source and drain leads, and solve a Pauli master equation in the weak-coupling (sequential tunneling) regime to obtain steady-state occupations and current. They compare stability diagrams and the integrated current to prior DOS-based predictions, showing SZBA signatures persist despite lead effects; the signature's prominence depends on the lead-coupling ratio $t_d/t_s$ and on temperature $T$, weakening with increasing $T$ and vanishing at sufficiently high $T$. The work provides a practical framework for observing SZBA in experiments on two-site ensembles and clarifies how lead coupling and temperature shape the measurable transport signatures.

Abstract

The combination of disorder and interactions is known in many systems to produce a feature in the single-particle density of states, the shape and parameter dependence of which act as signatures of the underlying electronic state. Strong Coulomb repulsion gives rise to a host of novel phenomena, among these is a unique zero-bias anomaly. While understanding of the anomaly in bulk materials remains incomplete, a version of this anomaly can be found in an ensemble of two-site systems and hence has been predicted to be observable in parallel-coupled double quantum dots. However, prior work did not include the influence of the leads. Here we show that the presence of the leads results in changes to the projected stability diagrams but that the signature of the strongly-correlated zero-bias anomaly nonetheless remains clearly visible.

Figures (4)

• Figure 1: Stability diagrams for a parallel-coupled double quantum dot calculated using the DOS approachWortis2022 (a) and the Pauli equation approach described in the text with (b) $t_d/t_s=100$ and (c) $t_d/t_s=1$. Horizontal and vertical axes are the potential energy on the two dots, and the colour scale indicates the magnitude of the current. All panels are at zero temperature with dot parameters $U=8,\ V=0.6,\ t_h=0.6$ and lead parameters $\mu_d=V+U/2,\ \mu_s=\mu_d+V_{sd},\ V_{sd}=0.6,\ t_s=0.0001$. Panel (d) labels regions in the stability diagram for reference in the text. Each region without current is labeled gs$n$ indicating that the ground state has $n$ particles in the region. Each region in which current flows is labeled i$\alpha\beta$ where $\alpha$ and $\beta$ indicate the transitions involved as detailed further in the text.
• Figure 2: Integrated current (a) at $T=0$ comparing results from the DOS approach with $t_d/t_s=100$, the Pauli approach with $t_d/t_s=100$, and the Pauli approach with $t_d/t_s=1$ (multiplied by a factor of 2.25); and (b) Pauli calculations with $t_d/t_s=0$ comparing four temperatures. The DOS calculation gives the true single-particle density of states as a function of frequency, while the Pauli calculations more accurately reflect what would be observed in an experiment and still show the kinetic-energy-driven zero-bias anomaly unique to the strongly correlated system. Both panels use dot parameters $U=8,\ V=0.6,\ t_h=0.6$ and lead parameters $\mu_d=V+U/2,\ \mu_s=\mu_d+V_{sd},\ V_{sd}=0.6,\ t_s=0.0001$.
• Figure 3: Stability diagrams for a parallel-coupled double quantum dot calculated using the Pauli equation approach described in the text at temperatures (a) $T=0$, (b) $T=0.01$, (c) $T=0.05$, and (d) $T=0.5$. Horizontal and vertical axes are the potential energy on the two dots, and the colour scale indicates the magnitude of the current. All panels use dot parameters $U=8,\ V=0.6,\ t_h=0.6$ and lead parameters $\mu_d=V+U/2,\ \mu_s=\mu_d+V_{sd},\ V_{sd}=0.6,\ t_s=0.0001$ and $t_d/t_s=100$.
• Figure 4: Energy differences $\Delta_{\alpha \to \beta}=E_{\beta}-E_{\alpha}$ corresponding to all single particle transitions plotted as a function of the dot potential along the diagonal in the stability diagram, $V_1=V_2$. Also shown are the chemical potentials of the source and drain.