Intrinsic Nonlinear Planar Thermal Hall Effect Demonstrates Dissipationless Heat Current Proportional to Temperature Gradient

The flow of heat can exhibit surprising behaviours, and recent work by Chanchal K. Barman from the University of Cagliari, and colleagues, reveals a previously unknown phenomenon called the intrinsic nonlinear planar thermal Hall effect. This dissipationless response to heat arises when a temperature gradient and magnetic field align within the same plane, and originates from a correction to the fundamental properties of electron behaviour within a material. The team demonstrates that this effect, driven by the material’s band geometry, offers a new way to control heat flow and provides a sensitive probe of a material’s internal structure, potentially paving the way for novel thermal technologies. This discovery establishes a new class of geometry-driven thermal transport, offering both a sensitive probe of band geometry and a pathway toward nonlinear thermal functionalities in certain materials.

The research focuses on understanding how electrons move in response to applied fields, revealing fundamental principles governing charge transport. The core concept involves a nonlinear Hall effect occurring within a plane, unlike traditional effects requiring perpendicular fields. This nonlinearity means the effect isn’t directly proportional to the applied field, demanding a more complex understanding of electron behavior. Importantly, the study concentrates on the intrinsic origin, meaning the effect arises from the material’s fundamental band structure, not from imperfections or impurities.

The team identifies the Berry connection polarizability tensor as the key driver of this effect. This tensor describes how an electron’s wave function responds to an electric field, a property directly linked to the material’s band structure. The research demonstrates that materials lacking inversion symmetry are essential for a non-zero polarizability tensor and, consequently, for observing this effect. This work highlights the relevance of this effect in topological materials, where the Berry connection plays a crucial role. The understanding of symmetry requirements and the connection to topological materials can guide the discovery of new materials with enhanced nonlinear planar Hall effects. Nonlinear Hall effects have potential applications in novel sensors for detecting weak magnetic fields, logic devices for non-volatile memory, thermoelectric devices for improved efficiency, and spintronics for manipulating spin currents.

Noncentrosymmetric Crystals Exhibit Nonlinear Thermal Hall Effect

Scientists have established a new understanding of thermal transport with the discovery of the intrinsic nonlinear planar thermal Hall effect, a dissipationless phenomenon proportional to the square of the temperature gradient. This effect arises from a correction to the Berry curvature induced by a thermal gradient, characterized by the thermal Berry connection polarizability tensor, and results in a heat current independent of scattering events. The research team demonstrated that this intrinsic nonlinear thermal Hall effect is only permitted in noncentrosymmetric crystal structures lacking horizontal mirror symmetry, establishing a fundamental link between material symmetry and thermal response. To explore this phenomenon, the study involved a detailed symmetry analysis of the intrinsic conductivity tensor, considering various point groups.

Researchers systematically enumerated allowed and forbidden tensor components to predict material behavior. The team further investigated the underlying physics using a tilted Dirac model, a minimal Hamiltonian capturing the low-energy behavior of two-dimensional Dirac materials. Through analytical and numerical calculations, they assessed the thermal Berry connection polarizability tensor, finding it directly proportional to the valley-dependent tilt parameter in the Dirac model. This contrasts with previously studied electric field induced effects, highlighting a unique mechanism for generating nonlinear thermal responses.

Dissipationless Thermal Hall Effect from Band Geometry

Scientists have discovered a new phenomenon, the intrinsic nonlinear planar thermal Hall effect, which generates a heat current transverse to both a temperature gradient and an in-plane magnetic field. This effect arises from a correction to the Berry curvature induced by the temperature gradient, characterized by the thermal Berry connection polarizability tensor, and is fundamentally dissipationless. The research establishes a new class of quantum geometry driven thermal transport, offering a sensitive probe of band geometry within materials. Experiments reveal that the effect is uniquely permitted in noncentrosymmetric crystal structures lacking horizontal mirror symmetry, defining specific material requirements for observation. Theoretical work demonstrates that the effect’s angular dependence provides a means to control the nonlinear thermal response, opening possibilities for tunable thermal devices. The team’s analysis shows the effect originates from the interplay between the in-plane magnetic field and the band geometry, mediated by the thermal Berry connection polarizability tensor, and is independent of scattering processes within the material.

Geometric Origin of Nonlinear Thermal Hall Effect

This research establishes a new understanding of thermal transport through the discovery of the intrinsic nonlinear planar thermal Hall effect, a dissipationless phenomenon arising from a correction to the Berry curvature induced by a temperature gradient. The team demonstrates that this effect is characterised by the thermal Berry connection polarizability tensor and is independent of scattering time, offering a fundamentally new pathway for controlling heat flow. Through a tilted Dirac model, they show that the strength of this effect can be tuned by manipulating material properties such as tilt strength, chemical potential, and anisotropy. The significance of this work lies in identifying a geometric origin for nonlinear thermal transport, distinct from conventional mechanisms. Crucially, the researchers derived symmetry rules indicating that this effect is only possible in materials lacking certain symmetries, providing a clear criterion for experimental verification. This intrinsic nature and characteristic angular dependence distinguish it from other nonlinear Hall effects, offering a sensitive probe of band geometry and potential for novel thermal functionalities.