Prediction of superconductivity in mass-asymmetric electron-hole bilayers

TL;DR

The work addresses superconductivity in mass-asymmetric electron-hole bilayers, proposing an acoustic-plasmon mechanism for pairing in the EL-HC phase. It employs multi-species Hartree-Fock and Hartree-Fock-Bogoliubov analyses to map phase diagrams that include exciton condensates, Wigner crystals, and the EL-HC state, with EL-HC arising for mass ratios $m_h/m_e \gtrsim 2$. By deriving an effective attractive electron–electron interaction mediated by acoustic plasmons and estimating $T_c$ from first principles via $T_c \approx 1.13\,T_D \exp\left(1/(g_0 V)\right)$, the study shows $T_c$ is optimized at intermediate densities and small interlayer separation $d$, with the strength governed by the plasmon velocity ratio $α$ and the electron density parameter $r_s^e$. The predictions point to experimental realizations in van der Waals heterostructures (e.g., TMD bilayers with graphene), where moiré potentials could stabilize the EL-HC phase and enable observation of plasmon-mediated superconductivity in two dimensions.

Abstract

We study density-balanced, mass-asymmetric electron-hole bilayers as a tunable platform for correlated quantum phases. With independent control of carrier density and interlayer separation, the system exhibits a rich phase diagram, including exciton condensates, Wigner crystals, and for large hole-to-electron mass ratios, an electron-liquid hole-crystal phase. This mixed phase is an analog of two-dimensional metallic hydrogen, featuring an electron liquid immersed in and coupled to a lattice of heavy holes. We show that acoustic plasmons mediate an attractive interaction between electrons, leading to BCS-type superconductivity at experimentally accessible parameters. The superconducting transition temperature is calculated from first principles, and experimental realization in van der Waals heterostructures is discussed.

Figures (11)

• Figure 1: When $m_h/m_e>1$, the additional EL-HC phase emerges as compared to the symmetric bilayer. At sufficiently low interlayer distances, no crystallization occurs, and a Mott transition directly connects the exciton condensate and Fermi liquid phases. At larger interlayer distances, crystal phases become accessible, first in the hole and then in both layers.
• Figure 2: Left: The combined Hartree-Fock and Hartree-Fock-Bogoliubov phase diagram for $N_h=36$ spin-polarized holes (of fixed mass $m_h = m_0$ the bare mass) and equal electron populations of each spin. $n^*_h$ is the critical density for hole crystallization in an isolated monolayer. Note in particular the Mott transition for $d=1\, a_h$, with a transition directly from the Fermi liquid to exciton condensate phase as density decreases. Right: The pure Hartree-Fock phase diagram for the same scenario. This parameter range also includes the electron-crystal hole-liquid (EC-HL) phase.
• Figure 3: The restricted Hartree-Fock EL-HC phase for $d=a_h$ and $m_h/m_e = 10$ with 36 holes ($m_h = m_0$) at $r_s^h = 7$. $\epsilon_F$ is the free electron Fermi energy. The charge density shows the crystallized holes and liquid electrons. The Hartree-Fock electron band structure---referenced to the Fermi level---is well described by a free-particle model with $m_e^* \approx 0.93\, m_e$. The hole band structure has a gap $\Delta \approx 0.74\, \epsilon_F$ at the Fermi level.
• Figure 4: a) The Hartree-Fock calculation of $\alpha^2$ in the EL-HC phase at $m_h/m_e = 10$, fixing $m_h = m_0$. Across different interlayer spacings, there is an approximately linear relationship between $\alpha^2$ and $r_s^e$. Also shown is the analytic relation for the Hartree-Fock uniform electron gas. b) The calculated BCS critical temperature for $m_h/m_e = 10$ in units of the electron Hartree temperature. $n^*_e$ is the monolayer electron crystallization density. Intermediate densities and low interlayer distances give the highest $T_c$. For very high densities, superconductivity does not occur at any interlayer spacing.
• Figure 5: Left: Calculation of the average effective Cooper pair potential and the onset of superconductivity for fixed values of $\alpha$. Because of the finite interlayer spacing, electron-plasmon interactions are strongly suppressed for high densities. Right: The calculated BCS critical temperature for $m_h/m_e = 10$---the same scenario as in the main text---but with $r_s^* = 2$ as predicted by Hartree-Fock. The qualitative features are maintained, though superconductivity occurs in a much narrower region and at much higher temperatures.