# Helicoidal excitonic phase in an electron-hole double layer system

## TL;DR

This paper predicts a novel helicoidal excitonic phase in electron-hole double layers with spin-orbit interaction, revealing controllable magnetic order and low-energy excitations, and discusses experimental detection methods.

## Contribution

It introduces the helicoidal excitonic phase induced by Rashba spin-orbit coupling in EHDL systems, highlighting its controllability and unique magnetic order.

## Key findings

- Helicoidal structure of excitonic field due to Rashba interaction.
- Helicoidal magnetic order in the electron layer induced by excitonic phase.
- Calculated dispersion relations of Goldstone modes in the phase.

## Abstract

We propose helicoidal excitonic phase in a Coulomb-coupled two-dimensional electron-hole double layer (EHDL) system with relativistic spin-orbit interaction. Previously, it was demonstrated that layered InAs/AlSb/GaInSb heterostructure is an ideal experimental platform for searching excitonic condensate phases, while its electron layer has non-negligible Rashba interaction. We clarify that due to the Rashba term, the spin-triplet (spin-1) exciton field in the EHDL system forms a helicoidal structure and the helicoid plane can be controlled by an in-plane Zeeman field. We show that due to small but finite Dirac term in the heavy hole layer the helicoidal structure of the excitonic field under the in-plane field results in a helicoidal {\it magnetic} order in the electron layer. Based on linearization analyses, we further calculate momentum-energy dispersions of low-energy Goldstone modes in the helicoidal excitonic phase. We discuss possible experimental probes of the excitonic phase in the EHDL system.