Effects of correlated hopping on thermoelectric response of a quantum dot strongly coupled to ferromagnetic leads

We theoretically investigate the impact of correlated hopping on thermoelectric transport through a quantum dot coupled to ferromagnetic leads. Using the accurate numerical renormalization group method, we analyze the transport characteristics, focusing on the interplay between electronic correlations, spin-dependent transport processes, and thermoelectric response. We calculate the electrical conductance and thermopower as functions of the dot energy level, lead polarization, and the amplitude of correlated hopping. Moreover, we analyze the effect of competing correlations on the Kondo resonance and discuss the asymmetry of conductance peaks under the influence of the exchange field. We demonstrate that the presence of correlated hopping is responsible for asymmetric spin-dependent transport characteristics. Our results provide valuable insight into how correlated hopping affects spin-dependent transport and thermoelectric efficiency in quantum dot systems with ferromagnetic contacts.

💡 Research Summary

In this work the authors theoretically investigate how correlated hopping—also known as assisted tunneling—affects thermoelectric transport through a single‑level quantum dot (QD) that is strongly coupled to ferromagnetic leads. The system is modeled by an Anderson impurity Hamiltonian augmented with a hopping‑dependent term
(H_T=\sum_{\alpha k\sigma}V_{\alpha k}(1-x,n_{\bar\sigma})c^{\dagger}{\alpha k\sigma}d{\sigma}+{\rm H.c.})
where the dimensionless parameter (x) controls the strength of the correlated hopping. Ferromagnetic electrodes are characterized by a spin polarization (p_{\alpha}) that leads to spin‑dependent hybridizations (\Gamma_{\sigma\alpha}=(1\pm p_{\alpha})\Gamma_{\alpha}). After a left‑right orthogonal transformation the dot couples to a single effective conduction channel with total hybridization (\Gamma=\Gamma_L+\Gamma_R) and effective polarization (p=(p_L+p_R)/2).

The authors employ the full‑density‑matrix numerical renormalization group (fDM‑NRG) method, as implemented in the Budapest Flexible NRG code, to compute the dot’s retarded Green’s function and the spin‑resolved transmission function (T_{\sigma}(\omega)). Linear‑response transport coefficients are obtained from the Onsager integrals
(L_{n\sigma}=-(1/h)\int d\omega,\omega^{n},\partial f/\partial\omega,T_{\sigma}(\omega)).
From these they derive the spin‑resolved conductance (G_{\sigma}=e^{2}L_{0\sigma}), the total conductance (G=G_{\uparrow}+G_{\downarrow}), the charge Seebeck coefficient (S=-(1/eT)(L_{1}/L_{0})) and the spin Seebeck coefficient (S_{S}=-(2/\hbar T)(M_{1}/L_{0})) with (M_{1}=L_{1\uparrow}-L_{1\downarrow}).

The numerical analysis focuses on several key aspects:

1. Kondo physics without correlated hopping ((x=0)).
   At particle‑hole symmetry ((\varepsilon=-U/2)) a pronounced Kondo resonance appears, yielding a conductance close to the unitary limit (G=2e^{2}/h). Ferromagnetic leads generate an effective exchange field (\Delta\varepsilon_{\rm exch}=2p\Gamma\pi\ln