We investigate the second-order nonlinear electronic thermal  transport induced by temperature gradient. We develop the quantum kinetic theory framework to describe thermal transport in the presence of a temperature gradient. Using this, we predict an intrinsic scattering time-independent nonlinear thermal current in addition to the known extrinsic nonlinear Drude and Berry curvature dipole contributions. We show that the intrinsic thermal current is determined by the band geometric quantities and is non-zero only in systems where both the space inversion and time-reversal symmetries are broken. We employ the developed theory to study the thermal response in tilted massive Dirac systems. We show that besides the different scattering time dependents, the various current contributions have distinct temperature dependencies in the low-temperature limit. Our systematic and comprehensive theory for nonlinear thermal transport paves the way for future theoretical and experimental studies on intrinsic thermal responses.

We present a systematic study of the nonlinear thermal Hall responses in bosonic systems using the quantum kinetic theory framework. We demonstrate the existence of an intrinsic nonlinear boson thermal current, arising from the quantum metric which is a wavefunction dependent band geometric quantity. In contrast to the nonlinear Drude and nonlinear anomalous Hall contributions, the intrinsic nonlinear thermal conductivity is independent of the scattering timescale. We demonstrate the dominance of this intrinsic thermal Hall response in topological magnons in a two-dimensional ferromagnetic honeycomb lattice without Dzyaloshinskii-Moriya interaction. Our findings highlight the significance of band geometry induced nonlinear thermal transport and motivate experimental probe of the intrinsic nonlinear thermal Hall response with implications for quantum magnonics.

The planar Hall effect in 3D systems is an effective probe for their Berry curvature, topology, and electronic properties. However, the Berry curvature-induced conventional planar Hall effect is forbidden in 2D systems as the out-of-plane Berry curvature cannot couple to the band velocity of the electrons moving in the 2D plane. Here, we demonstrate a unique 2D planar Hall effect (2DPHE) originating from the hidden planar components of the Berry curvature and orbital magnetic moment in quasi-2D materials. We identify all planar band geometric contributions to 2DPHE and classify their crystalline symmetry restrictions. Using gated bilayer graphene as an example, we show that in addition to capturing the hidden band geometric effects, 2DPHE is also sensitive to the Lifshitz transitions. Our work motivates further exploration of hidden planar band geometry-induced 2DPHE and related transport phenomena for innovative applications.

Van Hove singularities enhance many-body interactions and induce collective states of matter ranging from superconductivity to magnetism. In magic-angle twisted bilayer graphene, van Hove singularities appear at low energies and are malleable with density, leading to a sequence of Lifshitz transitions and resets observable in Hall measurements. However, without a magnetic field, linear transport measurements have limited sensitivity to the band’s topology. Here, we utilize nonlinear longitudinal and transverse transport measurements to probe these unique features in twisted bilayer graphene at zero magnetic field. We demonstrate that the nonlinear responses, induced by the Berry curvature dipole and extrinsic scattering processes, intricately map the Fermi surface reconstructions at various fillings. Importantly, our experiments highlight the intrinsic connection of these features with the moiré bands. Beyond corroborating the insights from linear Hall measurements, our findings establish nonlinear transport as a pivotal tool for probing band topology and correlated phenomena.

The second-order nonlinear electrical response (NLER) is an intrinsic property of inversion symmetry-broken systems that can provide deep insights into the electronic band structures of atomically thin quantum materials. However, the impact of Fermi surface reconstructions, also known as Lifshitz transitions, on the NLER has remained elusive. NLER is investigated in bilayer graphene (BLG), where the low-energy bands undergo Lifshitz transitions. Here, NLER undergoes a sign change near the Lifshitz transitions even at elevated temperatures T ≥ 10 K. At the band edge, NLER in BLG is modulated by both extrinsic scattering and interfacial-strain-induced intrinsic Berry curvature dipole, both of which can be finely tuned externally by varying doping and interlayer potential. Away from the band edge, BLG exhibits second-order conductivity exceeding 30 µm V−1 Ω−1 at 3 K, higher than any previous report. This work establishes NLER as a reliable tool to probe Lifshitz transitions in quantum materials.

The Nernst and Seebeck effects are crucial for thermoelectric energy harvesting. However, the

linear anomalous Nernst effect requires magnetic materials with intrinsically broken time-reversal

symmetry. In non-magnetic systems, the dominant transverse thermoelectric response is the non-

linear Nernst current. Here, we investigate nonlinear Nernst and Seebeck effects to reveal intrinsic

scattering-free Seebeck and Nernst currents arising from band geometric effects in bipartite antiferro-

magnets (parity-time-reversal symmetric systems). We show that these contributions, independent

of scattering time, originate from the Berry connection polarizability tensor which depends on the

quantum metric. Using CuMnAs as a model system, we demonstrate the dominance of intrinsic

nonlinear Seebeck and Nernst currents over other scattering-dependent contributions. Our find-

ings deepen the fundamental understanding of nonlinear thermoelectric phenomena and provide the

foundation for using them to develop more efficient, next-generation energy harvesting devices

The Nernst effect is a versatile phenomenon relevant for energy harvesting, magnetic sensing, probing band topology and charge-neutral excitations. The planar Nernst effect (PNE) generates an in-plane voltage transverse to an applied temperature gradient under an in-plane magnetic field. Conventional Berry curvature-induced PNE is absent in two-dimensional (2D) systems, as the out-of-plane Berry curvature does not couple to the in-plane electron velocity. We challenge this notion by demonstrating a distinct planar Nernst effect in quasi-2D materials (2DPNE). We show that the 2DPNE originates from previously overlooked planar components of Berry curvature and orbital magnetic moment, arising from inter-layer tunneling in multilayered 2D systems. We comprehensively analyze the band-geometric origin and crystalline symmetry constraints on 2DPNE responses. We illustrate its experimental feasibility in strained bilayer graphene. Our findings significantly expand the theoretical understanding of planar Nernst effects, providing a clear pathway for next-generation magnetic sensing and energy-harvesting applications.