Casimir interactions and drift currents

TL;DR

The paper investigates how steady-state drift currents in two parallel graphene sheets modify Casimir interactions, employing a shifted Fermi disk model to capture non-equilibrium optical response and the Maxwell stress tensor within a Rytov fluctuation framework. Drift induces a repulsive correction to the vertical Casimir force and a lateral friction-like force, both of which depend on drift velocity, temperature, and Fermi energy, and are enhanced when both layers drift (especially in opposite directions). The results demonstrate that drift provides a tunable knob to control fluctuation-induced forces in graphene-based nanosystems, with practical implications for non-equilibrium fluctuation phenomena in 2D materials and van der Waals heterostructures.

Abstract

We investigate the fluctuation-induced Casimir interactions between two parallel graphene sheets carrying steady-state drift currents. The graphene properties are modeled based on the shifted Fermi disk model to capture the non-equilibrium optical response of the system. We find that the drift current introduces a repulsive correction to the perpendicular to the layers Casimir interaction, thereby reducing the overall attractive force. Although the correction is repulsive, it does not overcome the underlying attraction between the layers. It also generates a lateral force that opposes the carrier flow direction. Both contributions are studied in terms of distance and drift velocity functionalities showing pathways for Casimir force control.

Figures (5)

• Figure 1: System setup: two parallel graphene sheets separated by a distance $d$ with drift currents $I_{d,1,2}$ corresponding to electrons moving with drift velocities $\boldsymbol{v}_{d,1,2}$ respectively.
• Figure 2: Color map of the optical conductivity components of graphene supporting a drift current in the $\hbar v_Fq$ vs $\hbar\omega$ space for (a) $\text{Re }(\sigma_{xx})/\sigma_u$; (b) $\text{Re }(\Delta \sigma_{xx})/\sigma_u$; (c) $\text{Im }(\sigma_{xx})/\sigma_u$; (d) $\text{Im }(\Delta \sigma_{xx})/\sigma_u$; (e) $\text{Re }(\sigma_{yy})/\sigma_u$; (f) $\text{Re }(\Delta \sigma_{yy})/\sigma_u$; (g) $\text{Im }(\sigma_{yy})/\sigma_u$; (h) $\text{Im }(\Delta \sigma_{yy})/\sigma_u$. Here we have used $\beta_d=0.1$, $E_F=0.01 {\rm eV}$ and $\theta_q=0$.
• Figure 3: Graphene-graphene Casimir interaction in the presence of a drift current in the top layer: (a) $\Delta F_z/F_z$ as a function of $\beta_d$ at $d=1$ nm; (b) $\Delta F_z/F_z$ as a function of $d$ for $\beta_d=0.1$; (c) $F_x/F_z$ as a function of $\beta_d$ for $d=1$ nm; (d) $F_x/F_z$ as a function of $d$ for $\beta_d=0.1$ Here $\Delta F_z= F_z- F_0$, where $F_z$ is the interaction along the $z$-axis when the drift current flows in the top graphene layer and $F_0=-\frac{3\hbar c\alpha}{32\pi d^4}$ is the equilibrium Casimir force. In all cases, the graphene Fermi level is taken as $E_F=0.1$ eV and $T=240$ K.
• Figure 4: Graphene-Graphene Casimir interaction in the presence of a drift current in the top layer: (a) $\Delta F_z/F_z$ as a function of temperature $T$; (b) $\Delta F_z/F_z$ as a function of $E_F$; (c) $F_x/F_z$ as a function of temperature $T$ ; (d) $F_x/F_z$ as a function of $E_F$. Here we used $d=10$ nm, and $\beta_d=0.5$. Also, $F_z$ is the interaction along the $z$-axis when the drift current flows in the top graphene layer and $F_0=-\frac{3\hbar c\alpha}{32\pi d^4}$ is the equilibrium Casimir force. In (a)(c), the graphene Fermi level is taken as $E_F=0.1$ eV and in (b)(d) the temperature is $T=300$ K.
• Figure 5: Graphene-Graphene Casimir interaction in the presence of drift currents in both layers in opposite directions with the same magnitude: (a) $\Delta F_z/F_z$ as a function of $\beta_d$ at $d=50$ nm; (b) $\Delta F_z/F_z$ as a function of $d$ for $\beta_d=0.5$; (c) $F_x/F_z$ as a function of $\beta_d$ for $d=50$ nm; (d) $F_x/F_z$ as a function of $d$ for $\beta_d=0.5$ Here $\Delta F_z= F_z- F_0$, where $F_z$ is the interaction along the $z$-axis when the drift current flows in the top graphene layer and $F_0=-\frac{3\hbar c\alpha}{32\pi d^4}$ is the equilibrium Casimir force. In all cases, the graphene Fermi level is taken as $E_F=0.1$ eV and $T=300$ K.