Theory for electric dipole superconductivity with an application for bilayer excitons

Abstract

Exciton superfluid is a macroscopic quantum phenomenon in which large quantities of excitons undergo the Bose-Einstein condensation. Recently, exciton superfluid has been widely studied in various bilayer systems. However, experimental measurements only provide indirect evidence for the existence of exciton superfluid. In this article, by viewing the exciton in a bilayer system as an electric dipole, we derive the London-type and Ginzburg-Landau-type equations for the electric dipole superconductors. By using these equations, we discover the Meissner-type effect and the electric dipole current Josephson effect. These effects can provide direct evidence for the formation of the exciton superfluid state in bilayer systems and pave new ways to drive an electric dipole current.

Figure 1. A side view of the exciton in bilayer system and the induced supercurrent by magnetic field gradient.

(a) The top and bottom layers host holes and electrons respectively, and the middle blue block stands for the interlayer barrier which prevents tunneling between the two layers. (b) The left (right) panel shows the induced super electric dipole current for magnetic field gradient ∂B_z/∂z < 0 (∂B_z/∂z > 0). The arrows on the blue lines denote the direction of positive charge flow in each layer.

Figure 2. Meissner-type effect of the electric dipole superconductor.

(a) The schematic diagram of the device consisting of a cylindrical hollow conductor and a circular bilayer exciton system (the electric dipole superconductor), and (b) the cross section of the device. R_in (R_out) is the inner (outer) radius of the hollow conductor, and r_out is the radius of the dipole superconductor. m is the middle plane of the bilayer exciton, and l is distance between dipole superconductor and the point Q where magnetic field can be measured. h and d are, respectively, the thickness of the conductor and the dipole superconductor and t is the distance between them. (c,d) The induced super dipole current J_p and the gradient of the induced magnetic field in the middle plane m versus radius r. (e) The induced magnetic field versus the distance l. The parameters are R_in = 1 mm, R_out = 1 cm, h = 1.5 cm, t = 0.1 mm, and r_out = 1 mm, and the thickness d = 13 nm and d = 10 nm, respectively.

Figure 3. The proposed device for detection of a zero dipole resistance.

(a,b) The schematic diagram of the proposed device and its cross section. The electric dipole superconductor is in annular shape with an inner radius r_in and a outer radius r_out. Other symbols appeared in these figures have the same meanings as those in Fig. 2a,b. (c,d) The super electric dipole current and its induced magnetic field with the sizes of the dipole superconductor r_in = 7 mm and r_out = 9 mm. The other parameters are the same as in Fig. 2.

Figure 4. The electric dipole current Josephson junction.

(a) The schematic diagram for the device of dipole current Josephson junction, the bilayer exciton system-insulator-bilayer exciton system junction. The left sides of the two layers are connected by a wire, and the right sides of the two layers are connected with voltages V₂ and −V₂, respectively. V₁ and −V₁ are the voltages of the left sides of the two layers. The red arrows denote the direction of the electric fields in the top layer and bottom layer, respectively, while the blue arrows represent the flowing direction of holes (electrons) in the top (bottom) layer. (b) The top figure and the bottom figure show the Cooper pairs (electron-electron pairs) in a ordinary superconductor under a voltage V₂ − V₁ and the electric dipoles (electron-hole pairs) in an electric dipole superconductor under a bilayer counter voltage, respectively. Here the Cooper pairs and the electric dipoles feel the same electric forces.