[Paper Review] A monolayer transition metal dichalcogenide as a topological excitonic insulator

Daniele Varsano, Maurizia Palummo+2 more|arXiv (Cornell University)|Jun 19, 2019

2D Materials and Applications54 references105 citations

TL;DR

This paper proposes that monolayer MoS2 in the T′ phase is a topological excitonic insulator, where strong electron-hole interactions lead to exciton condensation that cooperatively enhances the spin-orbit gap, resulting in a chiral, gapped ground state with broken inversion symmetry. First-principles many-body calculations via GW and Bethe-Salpeter equation reveal an exciton binding energy of 32 meV exceeding the GW band gap, driving a self-consistent transition to a topological excitonic insulator phase with circular dichroism and ferroelectricity under strain.

ABSTRACT

Monolayer transition metal dichalcogenides in the T' phase promise to realize the quantum spin Hall (QSH) effect at room temperature, because they exhibit a prominent spin-orbit gap between inverted bands in the bulk. Here we show that the binding energy of electron-hole pairs excited through this gap is larger than the gap itself in MoS2, a paradigmatic material that we investigate from first principles by many-body perturbation theory (MBPT). This paradoxical result hints at the instability of the T' phase against the spontaneous generation of excitons, and indeed we find that it gives rise to a recostructed `excitonic insulator' ground state. Importantly, we show that in this system topological and excitonic order cooperatively enhance the bulk gap by breaking the crystal inversion symmetry, in contrast to the case of bilayers where the frustration between the two orders is relieved by breaking time reversal symmetry. The excitonic topological insulator departs distinctively from the bare topological phase as it lifts the band spin degeneracy, which results in circular dichroism. A moderate biaxial strain applied to the system leads to two additional excitonic phases, different in their topological character but both ferroelectric as an effect of electron-electron interactions.

Motivation & Objective

• . The research aims to determine whether monolayer T′-MoS2 exhibits a spontaneous excitonic instability due to strong electron-hole interactions.
• The problem is that despite a large spin-orbit gap, the system may be unstable to exciton formation if e-h binding exceeds the band gap.
• The objective is to investigate the coexistence of topological order (from spin-orbit coupling) and excitonic order (from electron-hole attraction) in a monolayer T′-MoS2 system.
• The study aims to characterize the resulting ground state as a topological excitonic insulator with unique fingerprints such as circular dichroism and permanent electric dipole.

Proposed method

• . The study uses first-principles many-body perturbation theory (GW approximation) to compute quasiparticle band structures with spin-orbit coupling.
• The Bethe-Salpeter equation (GW-BSE) is solved to calculate the electron-hole binding energy and excitonic wave functions.
• A self-consistent mean-field approach is employed to solve for the excitonic hybridization gap ∆X(k), coupled with the spin-orbit gap ∆SO(k), using a screened Coulomb interaction W(q) fitted to first-principles results.
• The two-dimensional dielectric screening is modeled via a long-range Coulomb interaction W(q) = V0(q)/(1 + 2πα2D|q|), with α2D adjusted to match experimental and ab initio exciton binding energies.
• The topological invariant Z2 is computed using the Kane-Mele method via the overlap function P(k) between time-reversed valence states.
• Optical circular dichroism and permanent electric dipole are calculated using Fermi’s golden rule and the dipole matrix elements extracted from first-principles.

Experimental results

Research questions

• RQ1 . Does the electron-hole binding energy in monolayer T′-MoS2 exceed the quasiparticle band gap, indicating a spontaneous excitonic instability?
• RQ2 Can topological order (Z2 = 1) and excitonic order coexist in a monolayer system without time-reversal symmetry breaking?
• RQ3 How does the interplay between spin-orbit coupling and electron-hole attraction modify the bulk gap and electronic structure?
• RQ4 What are the optical and electric response signatures of the resulting topological excitonic insulator phase?
• RQ5 How does moderate biaxial strain tune the topological and ferroelectric properties of the system?

Key findings

• . The exciton binding energy in monolayer T′-MoS2 is 32 meV, exceeding the GW band gap, indicating a strong instability toward exciton condensation.
• The system undergoes a self-consistent transition to a topological excitonic insulator ground state, where both spin-orbit and excitonic gaps coherently enhance the total bulk gap.
• The ground state breaks inversion symmetry and lifts spin degeneracy, resulting in circular dichroism in optical absorption.
• The system exhibits a permanent electric dipole moment due to the chiral nature of the excitonic order, with a dipole strength of 1.94 Å in the x-direction and 0.308 Å in the z-direction.
• Under moderate biaxial strain, two additional excitonic phases emerge, both ferroelectric and topologically distinct.
• The topological invariant Z2 is preserved in the excitonic phase, confirming the robustness of the topological order despite strong electron-electron correlations.