Unconventional superconductivity mediated by exciton density wave fluctuations

TL;DR

This work investigates electrically tunable unconventional superconductivity mediated by exciton density wave fluctuations in type-II bilayer semiconductors. Using a self-consistent Hartree-Fock framework, the authors identify an exciton density-wave (X-DW) instability at finite momentum $oldsymbol{Q}$ and analyze the coupling of X-DW fluctuations to fermions, uncovering two Goldstone modes whose static interactions split into a repulsive, even-parity superfluid channel and an attractive, odd-parity phonon channel that can realize anisotropic $p$-wave superconductivity in the collinear X-DW phase. Near the quantum critical line, critical fluctuations give rise to a pair-density-wave (PDW) state with pairing momentum $oldsymbol{Q}$, characterized by an anisotropic nodal PDW gap and enhanced interlayer pairing, while zero-momentum pairing is not realized in the studied window. The paper also discusses non-Fermi-liquid behavior with $z=3$ and experimental signatures such as drag transport and STM/kinetic-inductance probes to validate the proposed phases, providing a roadmap for tunable, unconventional superconductivity in synthetic bilayer platforms.

Abstract

Synthetic platforms afford an unparalleled degree of controllability in realizing strongly-correlated phases of matter. In this work, we study the possibility of electrically tunable exciton-mediated superconductivity arising in charge-imbalanced bilayer semiconductors. Focusing on the case of a bilayer semiconductor heterostructure, we identify the gating conditions required to achieve exciton density wave order within a self-consistent Hartree-Fock approximation. We analyze the role of the coupling of excitonic fluctuations to the fermionic charge carriers to find that the Goldstone mode of the density wave order can mediate attractive interactions leading to superconductivity. Furthermore, when the system is close to the density wave ordering, the interactions mediated by low-energy exciton modes can support an interlayer pair-density wave superconductor of anisotropic character. We discuss experimental signatures associated with these phenomena.

Figures (11)

• Figure 1: Left: Schematic of semiconductor $-$ hBN spacer $-$ semiconductor sandwich. The densities on the individual layer are controlled independently with an external bias potential $V_b$ applied staggerdly on each layer. Right top: Schematic of the unequally occupied conduction and valence bands in the electron-hole plasma state. Right bottom: Schematic of the Fermi surfaces, where the red (blue) is an electron (hole)-like Fermi surface. The exciton density wave order is triggered by the condensation of electron-hole pairs connected by the wave-vector $|\mathbf{Q}|$.
• Figure 2: Self-consistent Hartree-Fock exciton order parameter at total density $n$ and bias voltage $V_b$. Left: Inversion symmetric exciton order parameter $\chi = (\chi_+ + \chi_-)$, where $\chi_{\pm}$ is the exciton order parameter for $\pm \textbf{Q}$ momentum. Right: Ratio of $+\textbf{Q}$ and $-\textbf{Q}$ exciton ordering. Momentum mesh of 15$\times$15, and up-to 7$\times$2 (including both conduction and valence) folded bands was used.
• Figure 3: Development of collinear exciton density wave for $n=-0.7\times 10^{12}$ cm$^{-2}$ and $V_b = 12$ meV within a three-band Hubbard approximation (valence band for ${\mathbf{k} \pm \mathbf{Q}}$ and conduction band for ${\mathbf{k}}$). Left: Electronic Fermi surface Fermi surface in the collinear X-DW phase (yellow denotes the filled Fermi sea). Right: Electronic Bandstructure for $k_x = 0$ in the presence/absence of the collinear X-DW in red/black.
• Figure 4: Goldstone mode ($\delta \chi_p$)-mediated superconductivity inside the collinear X-DW phase. Top: Superconducting order parameter as a function of $V_b$ for $n=-0.7\times 10^{12}$ cm$^{-2}$. Bottom: BCS gap function as a function of momentum for $V_b=12$ meV. Momentum mesh of $59 \times 59$, $\epsilon = 10$, and momentum space cutoff along the $x$-direction $k_{c,x} = 0.2$.
• Figure 5: Critical fluctuation-mediated pair-density wave superconductivity. Top: Order parameter of the pair-density wave (PDW) superconductor plotted on the electron-hole plasma side of the phase diagram (lower triangle). Bottom: The PDW gap function for pairing momentum $\mathbf{Q}$ plotted in the first Brillouin zone. Parameters: $n=-0.36\times 10^{12}$ cm$^{-2}$ and $V_b = 4.2$ meV. Dashed lines are Fermi surfaces of $f_{c,\mathbf{k}}$, $f_{v,\mathbf{k} + \mathbf{Q}}$ and $f_{c,\mathbf{k} - \mathbf{Q}}$. Momentum mesh of $79 \times 79$.