Spin Textures Mimic Gravity, Enabling Electron Lensing in Materials.

Materials exhibiting long-wavelength spin textures generate an effective gravitational field for itinerant electrons. Strong coupling between electron spin and the background texture causes electrons to behave as spinless particles in curved space, resulting in an electron lensing effect analogous to gravitational lensing, and revealing novel emergent phenomena.

The behaviour of electrons within certain materials can mimic the effects of gravity, according to new research published in Physical Review Letters. Researchers demonstrate that collective spin arrangements within a material create an effective curved spacetime for electrons, causing them to behave as if influenced by a gravitational field. This results in an ‘electron lensing’ effect, analogous to the bending of light around massive objects. Yugo Onishi, Nisarga Paul, and Liang Fu, all from the Department of Physics at the Massachusetts Institute of Technology, detail this phenomenon in their article, “Emergent gravity and gravitational lensing in quantum materials”, revealing a potential pathway to explore gravitational physics using condensed matter systems and opening avenues for investigation into non-adiabatic effects.

Emergent Gravity Demonstrated in Solid-State Materials

Researchers have demonstrated the emergence of an effective gravitational field within certain materials, establishing a direct connection between material properties and the behaviour of electrons in curved spacetime. The findings, published recently, reveal that strongly correlated electrons within materials exhibiting long-wavelength spin textures behave as if propagating within a gravitational field.

Spin textures refer to the arrangement of electron spins within a material. Long-wavelength textures imply that the spin orientation changes gradually over relatively large distances within the material. In these materials, corrections to the electrons’ spin orientation induce curvature in the effective spacetime they experience. This curvature manifests as electron lensing – the bending of electron trajectories – directly analogous to gravitational lensing observed in astrophysics, where light bends around massive objects.

The research team employed Riemannian geometry – a branch of differential geometry concerned with curved spaces – to mathematically describe the curved spacetime experienced by the electrons. This framework establishes a link between the material’s quantum geometry and the emergent curved spacetime. Crucially, the quantum metric – a measure of distances within the underlying quantum system – defines the geometry of the Hilbert space (the mathematical space containing all possible states of the quantum system) and dictates the curvature experienced by the electrons.

The observed effect arises from non-adiabatic effects. These occur when a quantum system changes rapidly, preventing it from remaining in its lowest energy state. The researchers demonstrate that these non-adiabatic effects generically produce phenomena resembling gravity, suggesting that emergent gravity is not solely confined to the realm of general relativity, but can emerge as a consequence of material properties and quantum interactions.

The study confirms that the curvature of the emergent spacetime is determined by the underlying spin texture, offering a pathway to engineer materials with specific ‘gravitational’ properties. This control allows for precise manipulation of electron trajectories and potentially the creation of novel electronic devices. Furthermore, the findings suggest that similar emergent gravitational effects may be present in other physical systems exhibiting rapid or significant changes in their underlying structure.

Future research will focus on exploring the limits of this analogy and identifying materials where the emergent gravitational effects are sufficiently strong for practical applications.