Electromagnetic responses of bilayer excitonic insulators: from exciton London equations to dipole and inverse dipole Hall effects

TL;DR

The paper develops a microscopic, TDHF-based framework for the linear electromagnetic response of bilayer excitonic insulators, resolving layer-symmetric and layer-antisymmetric channels. It identifies a gapped dipole-plasmon sector and a gapless Goldstone mode at zero field, enabling London-like equations for the exciton condensate and a layer-antisymmetric Meissner effect. In finite B, a magnetic roton signals a stripe EI instability, while charge–exciton coupling gives rise to dipole and inverse dipole Hall effects that remain finite in the DC limit, providing direct transport signatures of exciton superfluidity. The authors propose experimental routes—microwave waveguide transmission, microwave impedance microscopy, and Corbino-design DC measurements—to detect these phenomena and map the EI phase diagram in realistic bilayer systems. Overall, the work offers concrete targets for microwave and transport probes of bilayer exciton superfluidity and lays a foundation for exploring coupled charge–exciton electrodynamics in multilayer platforms.

Abstract

We develop a microscopic theory of the linear electromagnetic response of bilayer excitonic insulators relevant to electron-hole double-layer systems. Using a self-consistent Hartree-Fock description of the excitonic ground state and time-dependent Hartree-Fock for its dynamics, we compute the collective mode spectrum and the full first-order response to layer-symmetric (charge) and layer-antisymmetric (exciton) gauge fields. At zero magnetic field, we find that two gapped plasmon modes dominate the long-wavelength charge response, while the exciton channel is governed by a linearly dispersing phase (Goldstone) mode. From the Goldstone-dominated kernel we derive a London-like equation for the exciton condensate, demonstrating non-dissipative acceleration under a layer-antisymmetric electric field, which we identify as the direct evidence of exciton superfluid; in contrast, a normal exciton fluid shows a Drude-like, dissipative response. In a perpendicular magnetic field, the Goldstone mode develops a magnetic-roton minimum that signals an instability toward a finite-momentum stripe-ordered excitonic insulator. Besides, charge and exciton motions become coupled under the field, giving rise to dipole and inverse dipole Hall effects in which a charge (exciton) bias induces a transverse exciton (charge) current. As a manifestation of the exciton superfluidity, these mixed Hall responses remain finite even in the DC limit. Our findings provide concrete targets for microwave and transport probes of bilayer exciton superfluidity.

Figures (15)

• Figure 1: Setup of the bilayer EI. The electron and hole layers are encapsulated in a dielectric environment with dielectric constant $\epsilon$. A dielectric spacer is inserted between the two layers to suppress direct interlayer tunneling. The interlayer band gap can be tuned by the bias voltage $V_b$.
• Figure 2: (a) Mean-field phase diagram at zero temperature as a function of the exciton chemical potential $\mu_X$. As $\mu_{X}$ increases, the ground state turns from the normal insulator (NI) to the EI. (b) Collective mode spectrum at zero momentum as a function of $\mu_X$. The shading area represents the electron-hole continuum. A few lowest collective excitations are specially indicated by the color lines and labeled by their angular momentum in $z$ direction. For example, the modes labeled by $s,p,d$ have angular momentum $l_z=0,\pm1,\pm2$ respectively. (c)(d) Collective mode spectrum in momentum space along the $q_x$ axis ($q_x$ is the momentum in $x$ direction). Along this line, these modes can be distinguished by the mirror eigenvalue $M_y$. For clarity, the collective modes with $M_y=1$ are plotted in (c) and the modes with $M_y=-1$ are plotted in (d). In the inset of (c), we compare the spectrum near the level crossing point for different electron-hole asymmetry strength $\delta_m$.
• Figure 3: Typical wavefunctions of the collective modes at $\bm{q}=\bm{0}$ and $\mu_{X}=-0.2$. Here we only plot $\Phi_{n\bm{k}}^{cv}(\bm{q})$ in the two-component wavefunction $\Phi_{n\bm{k}}(\bm{q})=[\Phi_{n\bm{k}}^{cv}(\bm{q}),\Phi_{n\bm{k}}^{vc}(\bm{q})]$.
• Figure 4: (a1)(a2) Imaginary part of the correlation function $C_{\hat{\sigma}_y\hat{\sigma}_y}(\omega+i\eta)$, accounting for the phase fluctuations of the EI order parameter. The dominant pole is the $1s$ Goldstone mode represented by the dashed blue line. (b1)(b2) Imaginary part of the correlation function $C_{\hat{\sigma}_x\hat{\sigma}_x}(\omega+i\eta)$, accounting for the amplitude fluctuations of the EI order parameter. The dominant pole is the $2s$ mode represented by the dashed red line. In (a1)(b1), the momentum is taken as $\bm{q}=\bm{0}$ and the horizontal axis is the exciton chemical potential $\mu_X$. In (a2)(b2), we take $\mu_X=-0.2$, $q_y=0$ and the horizontal axis is the momentum in $x$ direction $q_x$.
• Figure 5: (a1) Imaginary part of the longitudinal response kernel to the layer symmetric gauge field $K^{+}_{L}(\omega+i\eta,\bm{q})$ along the $q_x$ axis. The dominant pole is the $1p_x$ mode, which represents a plasmon mode with both charge and longitudinal charge current density fluctuations as illustrated by (a2). (b1) Imaginary part of the transverse response kernel to the layer symmetric gauge field $K^{+}_{T}(\omega+i\eta,\bm{q})$ along the $q_x$ axis. The dominant pole is the $1p_y$ mode, which represents a plasmon mode with only transverse charge current density fluctuation as illustrated by (b2).