Anomalous Coulomb-Enhanced Charge Transport in Triangular Triple Quantum Dots Systems

Abstract: Electron correlation and quantum interference are pivotal in mesoscopic transport. We theoretically study the nonequilibrium transport dynamics of a triangular triple quantum dot (TTQD) molecule connected to fermionic reservoirs using the exact hierarchical equations of motion (HEOM) formalism. We demonstrate a counter-intuitive transport signature where the stationary current is significantly enhanced by increasing the $U$, a behavior distinct from the suppression typically observed in linear quantum dot arrays. By analyzing the evolution of spectral functions, we attribute this enhancement to the interplay between Coulomb interaction-induced energy shifts and quantum interference effects unique to the triangular topology. We also explore how the circulation of chiral currents and electrode coupling strength modulates these interaction effects. Finally, we present a three-dimensional map of the transport current as a function of inter-dot tunneling ($t$) and Coulomb interaction ($U$), illustrating their combined effect on the current magnitude and its applications.

• The paper demonstrates with numerically exact HEOM simulations that stationary current in triangular triple quantum dots rises and then falls with increasing Coulomb repulsion, peaking near intermediate U/t.
• Coulomb interactions shift an antibonding many-body resonance toward the Fermi level and into the narrow bias window, while triangular-loop interference enables the enhancement absent in linear triple dots.
• The non-monotonic current persists across lead couplings and hopping strengths, identifying closed-loop topology and tunable U/t as practical design principles for nanoscale conductors, while large-bias and finite-flux effects remain open questions.

Overview and central result

This paper reports a nonequilibrium transport study of a triangular triple quantum dot (TTQD) molecule coupled to two fermionic reservoirs, performed with the numerically exact hierarchical equations of motion (HEOM) formalism (2603.11488). The central, counterintuitive finding is that the stationary current through the TTQD is enhanced by increasing the on-site Coulomb repulsion $U$ over an intermediate range of interaction strength, in direct contrast to the monotonic suppression observed in linear triple quantum dots (LTQDs) under otherwise identical conditions. The authors attribute this anomalous behavior to Coulomb-induced energy shifts of many-body spectral resonances combined with the quantum interference inherent to the closed-loop triangular topology.

The system is modeled as a three-impurity Anderson model: dots 1 and 3 couple to the left and right leads respectively, while dot 2 is connected only via interdot hopping $t$. Electron-hole symmetry is maintained at $\varepsilon_d = -U/2$, and transport is driven by a small bias $V = 0.1$ meV with $k_B T = 0.1$ meV, $\Gamma = 0.025$ meV, and $t = 0.25$ meV in the reference calculation. The HEOM treatment, built on the Feynman–Vernon influence functional with Grassmann algebra for fermionic dissipation and Padé spectral decomposition of the Fermi function, is truncated at tier level $L = 4$, which the authors state suffices for numerically exact results.

Mechanism: Coulomb-driven spectral migration

The key diagnostic is the frequency-resolved spectral function $A(\omega)$ evaluated along the current curve. At small $U$ both spectral peaks lie below the Fermi level. As $t$0 increases, the right (antibonding) peak migrates toward $t$1 while its weight decreases; at $t$2 it sits near $t$3, and at $t$4 it aligns optimally with the bias window, where the current reaches its maximum. For larger $t$5 the peak crosses the Fermi level and exits the window on the opposite side while continuing to lose weight, producing the falling branch of the non-monotonic $t$6–$t$7 curve. The left peak approaches the Fermi level only slowly and never enters the narrow conducting window, so its growing weight cannot compensate.

Physically, the enhancement arises because increasing $t$8 differentially renormalizes the energies of correlated many-body states in the triangular geometry—states that minimize mutual repulsion while retaining lead connectivity shift toward the Fermi level relative to other states. This tuning is enabled by interference between the direct tunneling path between dots 1 and 3 and the indirect path via dot 2; Coulomb interactions introduce energy-dependent phase shifts that reposition transmission resonances. Linear geometries lack alternative pathways and therefore cannot support interference-based resonances manipulable by interactions, which explains why the LTQD shows only monotonic suppression from $t$9 to $\varepsilon_d = -U/2$0.

Robustness checks

Two consistency tests support the interpretation. First, sweeping the lead-dot hybridization $\varepsilon_d = -U/2$1 changes the current magnitude systematically but preserves the qualitative non-monotonic $\varepsilon_d = -U/2$2–$\varepsilon_d = -U/2$3 structure, with the position of the maximum shifting only weakly. Since the peak migration is controlled by the many-body self-energy, it depends primarily on $\varepsilon_d = -U/2$4 rather than on $\varepsilon_d = -U/2$5, confirming that the effect is not an artifact of a particular coupling regime. Second, a three-dimensional map of the current over the full $\varepsilon_d = -U/2$6 plane shows that the rise-and-fall behavior at fixed $\varepsilon_d = -U/2$7 persists across all hopping amplitudes explored. Notably, the value of $\varepsilon_d = -U/2$8 at which the current peaks increases with $\varepsilon_d = -U/2$9: the phenomenon is governed by the dimensionless ratio $V = 0.1$0 and occurs in an intermediate-coupling regime where kinetic and interaction scales are comparable—not as a perturbative correction at small $V = 0.1$1 nor a strong-coupling effect at $V = 0.1$2.

The paper also derives an effective low-energy Hamiltonian in perturbation theory in $V = 0.1$3, containing a Heisenberg exchange term $V = 0.1$4 and a chiral term $V = 0.1$5 with $V = 0.1$6, connecting the transport anomaly to the chiral spin physics and flux-dependent loop structure of the TTQD.

Limitations and open questions

Several caveats should be noted. The analysis is confined to the small-bias regime, where the current is governed by spectral weight inside a narrow window around the Fermi level; the behavior at large bias, where nonequilibrium occupation effects could modify the resonance alignment, is not addressed. The effective spin-exchange description assumes $V = 0.1$7, whereas the enhancement itself occurs at intermediate coupling, so the perturbative Hamiltonian is illustrative rather than quantitatively valid in the relevant parameter range. The calculations are purely theoretical, with no comparison to experimental transport data on fabricated TTQD devices, and the role of magnetic flux and chiral currents is discussed formally (via $V = 0.1$8) but not systematically mapped against the transport results. Finally, the claim that analogous interaction-driven renormalization extends to tetrahedral clusters, ladders, and two-dimensional loop-containing arrays remains an expectation; whether the sign and magnitude of the current correction generalize across network topologies is explicitly left as an open question for systematic study.

Conclusion

Using numerically exact HEOM dynamics, this work establishes that strong on-site Coulomb repulsion can enhance, rather than suppress, stationary transport in a triangular triple quantum dot, with the current peaking at intermediate $V = 0.1$9 when a Coulomb-shifted antibonding resonance sweeps through the bias window. The effect is absent in linear geometries, robust against variations in lead coupling, and controlled by the ratio $k_B T = 0.1$0 across a wide parameter plane. The results identify closed-loop topology plus geometric frustration as a design principle for interaction-tunable nanoscale conductors, while leaving open the large-bias, finite-flux, and extended-network regimes for future investigation.