Scientists have observed complex electronic behaviour, known as topology, in a lossy system within a semiconductor.

Despite the losses, such topological systems could be used to create dissipationless pathways – pathways without the scattering that causes dissipation of energy and heat in conventional materials. This would enable electrical current to flow with almost zero wasted energy.

“Typically, one needs exotic materials or sophisticated material engineering to induce topological behaviour," said Dr Eli Estrecho, from ANU Research School of Physics and FLEET ARC Centre of Excellence, one of the lead authors of the study, which is published in Science Advances.

"However, in this work, we discovered that the mere presence of loss in an exciton-polariton system based on lead-halide perovskite causes it to exhibit a nontrivial topology”.

Losses, such as friction or electrical resistance, are ubiquitous in nature, but are seen as detrimental to devices. In electronics, for example, resistance leads to heating and limits computing efficiency, and in photonic systems, loss allows photons to escape confinement, limiting transmission efficiency. 

These losses can be incorporated into quantum mechanics, an approach known as Non-Hermitian physics.

“Advances in non-Hermitian physics, have significantly changed this negative view about loss,” says Prof Elena Ostrovskaya from the Australian National University.

“It has shown that losses can lead to striking effects not possible in a perfect lossless world.”

In the parallel field of photonics, recent results have shown that judicious control of losses can lead to counter-intuitive effects, such as lasers that turn on despite increasing loss, robust switching between lasing modes, and irreversible propagation of light.

Studies of non-Hermitian effects in quantum condensed matter systems, such as electronic materials, are less common.

In particular, this work, led by Singapore’s Nanyang Technological University (NTU) and ANU, is the first experimental observation of a non-Hermitian topological invariant in a semiconductor in the strong light-matter coupling regime supporting formation of exciton-polaritons.

It introduces a new avenue in designing topological materials, complementing conventional topology. Instead of avoiding loss, losses can be re-engineered or introduced intentionally to induce topological effects in an inherently non-topological system.

The key is that losses can induce nontrivial topology, turning a conventional material into a topological one.

Topological electronic materials are classified using topological invariants, for example, the Chern number, which quantifies how the electron wavefunctions effectively wind or rotate in momentum space.

If two materials with contrasting topology are merged, robust effects, such as dissipationless one-way transport, occur at their interface.

In this study, the team mixed excitons (electronic excitations) in a lead-halide perovskite semiconductor with photons to create exciton-polaritons.

The team carefully measured the energy and linewidths at different momenta and polarisations of polaritons in the system.

The energy and linewidths correspond to the real and imaginary parts of the complex energy of the lossy system in the language of non-Hermitian physics. And the two polarisation states give rise to two distinct energy bands in momentum space.

From this analysis, the team found the points where both real and imaginary parts of the two complex energy bands coincide. These are called exceptional points, and in this system they occur in pairs.

This would not have been possible if the linewidths were neglected, as was typically done in previous works.

Furthermore, the team found that the complex energies rotate with a defined handedness and phase around the exceptional points. In fact, the phase winds exactly as predicted by theory – this quantity is the new topological invariant that arises only in non-Hermitian systems.

“This is the first direct measurement of a non-Hermitian topological invariant associated with an exceptional point in momentum space of a condensed matter system,” said Dr Rui Su from Nanyang Technological University, one of the lead authors from study.

Furthermore, the team found that the winding of the wavefunctions and the energy bands are distinct from each other, confirming that they indeed observe a novel topology.

This could be instrumental in exploiting robust effects due to topology towards realizing a topological transistor in a lossy system.

Furthermore, because exciton-polaritons in perovskites can exhibit collective quantum behaviour – a Bose-Einstein condensate, this work paves the way for studying non-Hermitian topological effects on the quantum behaviour of condensates and superfluids.

The ANU group has previously used polaritons to observe non-Hermitian degeneracies called exceptional points and have shown chiral flow of polaritons due to these points. However, these points were observed in parameter space.

In this work, the exceptional points are demonstrated in momentum space, which can directly affect the propagation of the particles, including polariton superfluids.

“Creating these exceptional points in momentum space paves the way towards studies of combined effects of topology and non-Hermitian physics in exciton-polariton systems,” said Dr Estrecho.

Direct Measurement of Non-Hermitian Topological Invariant in a Hybrid Light-Matter System was published in Science Advances in November 2021. (DOI 10.1126/sciadv.abj8905)