Beyond Hubbard: the role of correlated hopping interaction in superconductors and quantum dot devices

TL;DR

The paper investigates correlated hopping (CH) beyond the Hubbard model in two settings: superconductivity near the Mott metal–insulator transition and transport in normal metal–quantum dot–normal metal (N–QD–N) devices. Using the Spałek-Hatsugai-Kohmoto (SHK) model with a CH term, the authors derive Green's function descriptions (including a momentum-dependent gap $\Delta_k=\Delta_0+\Delta_1\gamma(k)$) that reveal CH can drive a superconducting instability across the Mott transition and reshape the spectral function. In nanoscale devices, CH is encoded by $x=-K/V$ and analyzed with the Keldysh formalism to show that CH mainly perturbs the lower Hubbard band, breaking particle–hole symmetry and producing distinctive nonlinear conductance and Seebeck signatures that depend on the sign of $x$. Together, the results provide experimentally accessible fingerprints of CH in both bulk superconductors and dot-based devices, highlighting its potential role in shaping correlated electron phenomena.

Abstract

We investigate the role of strong Coulomb interactions beyond the standard Hubbard model in two distinct physical contexts. First, we analyze the superconducting phase transition occurring near the Mott metal-insulator transition. Second, we study transport properties of artificial nano-scale structures containing quantum dots coupled to external electrodes. In both cases, we focus on the impact of the correlated (assisted) hopping (CH) interaction. For superconductors, CH acts as a driving mechanism for the phase transition and modifies the spectral properties of the system. We present the evolution of the spectral function as the system approaches the Mott-type transition under varying model parameters. In quantum-dot-based devices, CH influences the tunneling amplitude between the dot and metallic leads. We demonstrate that the characteristic changes in the conductance of a normal metal-quantum dot-normal metal structure provide a clear signature of the presence and sign of CH interaction.

Figures (4)

• Figure 1: Spectral functions of (a) normal metal calculated for $U=2$, (b) s-wave superconductor with constant order parameter $\Delta_0=0.8$ and (c) correlated hopping superconductor with $\Delta(k)=\Delta_0+\Delta_1 \gamma(k)$ with $\Delta_1=0.5$. Comparison of the middle and right figures illustrates the changes of the spectral function induced by the particle-hole symmetry breaking term $\Delta_1\gamma(k)$.
• Figure 2: Evolution of the spectral function calculated for $U=3$ and $\Delta_0=0.8$, $\Delta_1=0.0$ (a), $\Delta_0=0.8$, $\Delta_1=0.3$ (b) and $\Delta_0=0.8$, $\Delta_1=0.5$ (c).
• Figure 3: Spectral function calculated for s-wave superconductor in doped Mott insulator: $U=6$ and $\Delta_0=0.8$, $\Delta_1=0.0$ (a), $\Delta_0=0.8$, $\Delta_1=0.3$ (b) and $\Delta_0=0.8$, $\Delta_1=0.5$ (c). The magnitude of the superconducting gap at the Fermi level crossing the lower Hubbard band is nearly independent of $\Delta_1$.
• Figure 4: The differential conductance $G_d$ (left panel) and the differential Seebeck coefficient are plotted as functions of the back-gate voltage characterised by $\delta^\prime$ chosen in such a way as to show particle-hole symmetry for $x=0$. The other parameters are: Hubbard interaction $U=16$, temperature $T=0.3$, and bias voltage $V=4$ distributed symmetrically. All the parameters are expressed in units of the effective couplings to the electrodes $\Gamma_L=\Gamma_R=1$. Correlated hopping- characterised by $x$ - modifies mainly the lower Hubbard band, leaving the upper one nearly intact.