Excitonic correlations in the system of gated metallic wires with the applied Zeeman magnetic field

TL;DR

This work demonstrates excitonic correlations in a bi-wire system of coupled metallic wires described by a bi-wire Hubbard model under an external gate and Zeeman field. By applying a Hubbard-Stratonovich decoupling and a four-band Gorkov formalism, the authors derive self-consistent equations for the chemical potential, density imbalance, excitonic gaps, and AFM order, and they explicitly compute the energy spectrum with four bands. The results reveal a tunable excitonic landscape: the spin-up gap $\Delta_{\uparrow}$ can exhibit a two-peak structure as a function of inter-wire coupling, split by a critical field $B_C$, while the spin-down gap $\Delta_{\downarrow}$ remains smaller; large $U$ enhances AFM order and localization, and temperature damps excitonic features. The study underscores the interplay between excitonic pairing, AFM order, and external controls, with implications for exciton-based information transfer in low-dimensional quantum systems.

Abstract

We have studied the electron-electron interactions in the system composed of two metallic wires, placed in the external magnetic and electric fields. The interactions between the electrons in the wires have been taken into account within the usual Hubbard model. We have considered both half-filling and partial-filling limits for the occupation of the atomic lattice sites. We show the existence of the excitonic pairing in this low-dimensional system and calculate the excitonic order parameter in different electron-electron interaction regime, magnetic field and temperature. We demonstrate that the usual Hubbard-$U$ interaction leads to strong electron localization which enhance the local antiferromagnetic order in the system.

Figures (8)

• Figure 1: (Color online) The structure of the AB double-layer (DL) graphene in the external electric field potential $V$. The layers of the system have been indicated as $\ell=1$ (the bottom layer) and $\ell=2$ (the upper layer). In the picture, the $A$, $\tilde{A}$ atomic sites are represented by the black balls, and the $B$,$\tilde{B}$ atomic sites are represented by green balls.
• Figure 2: (Color online) The excitonic order parameters $\Delta_{\uparrow}$ (see panel (a)) and $\Delta_{\downarrow}$ (see panel (b)), calculated in Eq.(\ref{['Equation_32']}), as a function of the inter-wire Coulomb interaction potential $W$. The case of half-filling with $\kappa=1.0$ has been considered for different values of the external magnetic field parameter $\tilde{B}=\mu_{\rm B}B/t_{0}$. The external gate potential and local Hubbard-$U$ potential have been fixed at the values $V=t_{0}$ and $U=0.6t_{0}$. The calculations have been performed at the zero temperature limit $T=0.0$. The calculations have been performed at the zero temperature limit $T=0$.
• Figure 3: (Color online) (left picture) The excitonic order parameter $\Delta_{\uparrow}$ at $\tilde{B}<\tilde{B}_{\rm C}$. Two strong excitonic peaks arise when varying the inter-chain interaction potential $W$ or when changing the inter-chain separation distance. (right picture) The excitonic order parameter $\Delta_{\uparrow}$ at $\tilde{B}>\tilde{B}_{\rm C}$. The calculations have been performed at the zero temperature limit $T=0$.
• Figure 4: (Color online) The chemical potential (see panel (a)), average charge density imbalance between wires (see panel (b)) and antiferromagnetic order parameter $\Delta_{\rm AFM}$, calculated in Eq.(\ref{['Equation_32']}), as a function of the inter-wires Coulomb interaction potential $W$. The case of half-filling with $\kappa=1.0$ has been considered, for different values of the external magnetic field parameter $\tilde{B}=\mu_{\rm B}B/t_{0}$. The external gate potential and local Hubbard-$U$ potential have been fixed at the values $V=t_{0}$ and $U=0.6t_{0}$. The calculations have been performed at the zero temperature limit $T=0$.
• Figure 5: (Color online) The excitonic order parameter $\Delta_{\uparrow}$ (see panel (a)) and $\Delta_{\downarrow}$ (see panel (b)), as a function of the inter-wire Coulomb interaction potential. The case of half-filling has been considered with $\kappa=0.5$. The external gate potential $V$ and magnetic field parameter $\tilde{B}$ have been fixed at values $V=0.0$ and $\tilde{B}=0.0$. Two different values of the Hubbard-$U$ potential have been considered during the calculations. The calculations have been performed at the zero temperature limit $T=0$.