YRLG Workshop: Correlation and Topology in magnetic materials, July 16th - 18th 2024
Kamal Das
I will discuss recent advancements in second and third-order nonlinear transport phenomena and their profound connection with quantum geometry, with a specific emphasis on crystalline symmetries. This aims to decipher the intricate relationship between the nonlinear response of materials and the underlying lattice structures, unraveling unique insights into quantum geometric properties of electronic wave-function.
Nonlinear transport phenomena manifest when transport responses exhibit a nonlinear dependency on the applied bias. These responses can be classified as reciprocal, where the sign changes with the applied bias (third order), or nonreciprocal, where the sign remains same (second order). They unveil unique properties such as the quantum geometry of electronic wave-functions and crystalline symmetries, inaccessible within linear response.
The transport coefficients linking nonlinear responses to the bias are predominantly extrinsic, where the information about the electronic state of the system is entangled with the effect of disorder. Conversely, intrinsic transport coefficients, which are independent of scattering and determined solely by material properties, are notably rare. While intrinsic coefficients are recognized in the context of Hall responses, their scarcity in longitudinal responses underscores their unique and elusive nature.
In my talk, I will be presenting two instances of intrinsic nonlinear longitudinal transport responses, one in the reciprocal and other in the nonreciprocal regime. In the nonreciprocal regime, a scattering time independent conductivity will be discussed which requires both time reversal and inversion symmetry breaking. In the reciprocal regime, I will discuss another intrinsic response which requires only time reversal breaking. As inversion symmetry breaking is not necessary, the reciprocal nonlinear response naturally becomes the lowest-order and dominant nonlinear response in centrosymmetric magnetic systems. I will elucidate the connection of these transport coefficients with quantum geometry examining their manifestations in different model Hamiltonian. Additionally, given that intrinsic responses are often overshadowed by other contributions, I will address methods to distinguish and extract these responses from the overall signal.