Gate-Tunable Giant Negative Magnetoresistance in Tellurene Driven by Quantum Geometry

Negative magnetoresistance in conventional two-dimensional electron gases is a well-known phenomenon, but its origin in complex and topological materials, especially those endowed with quantum geometry, remains largely elusive. Here, we report the discovery of a giant negative magnetoresistance, reaching a remarkable $- 90\%$ of the resistance at zero magnetic field, $R_0$, in $n$-type tellurene films. This record-breaking effect persists over a wide magnetic field range (measured up to $35$ T) at cryogenic temperatures and is suppressed when the chemical potential shifts away from the Weyl node in the conduction band, strongly suggesting a quantum geometric origin. We propose two novel mechanisms for this phenomenon: a quantum geometric enhancement of diffusion and a magnetoelectric spin interaction that locks the spin of a Weyl fermion, in cyclotron motion under crossed electric $\boldsymbol{\cal E}$ and magnetic ${\bf B}$ fields, to its guiding-center drift, $(\boldsymbol{\cal E}\times{\bf B})\cdot\sigma$. We show that the time integral of the velocity auto-correlations promoted by the quantum metric between the spin-split conduction bands enhance diffusion, thereby reducing the resistance. This mechanism is experimentally confirmed by its unique magnetoelectric dependence, $\Delta R_{zz}(\boldsymbol{\cal E},{\bf B})/R_0=-\beta_{g}(\boldsymbol{\cal E}\times{\bf B})^2$, with $\beta_{g}$ determined by the quantum metric. Our findings establish a new, quantum geometric and non-Markovian memory effect in magnetotransport, paving the way for controlling electronic transport in complex and topological matter.