Nonlinear Odd Viscoelastic Effect

Abstract

We uncover a class of nonlinear odd viscoelastic effects in three spatial dimensions. We show that these dissipationless effects arise upon combining strains in two orthogonal directions, yielding momentum flow in the third direction. We demonstrate that the effect arises from nontrivial geometric tensors in quantum states, and can be scaled up with integer topological invariants. We further demonstrate that the effect fingerprints the multiband Hilbert-space geometry of underlying quantum states, as encoded in three-state geometric tensors. Our findings unravel the role of multistate geometry in viscoelastic phenomena, paving a path for experimental observation of uncharted nonlinear odd viscoelastic responses in quantum systems.

Figures (3)

• Figure 1: Nonlinear odd viscoelastic effects. The effects are encoded in the stress tensor correlators $\langle [T_{mn},[T_{kl},T_{ij}]] \rangle$ of the electron fluid. (a) Nonlinear elastic response to normal stresses manifested as $\langle [T_{yy}, [T_{xx}, T_{zz}]] \rangle$. (b) Nonlinear viscous response to shear-stress deformations, captured by nontrivial $\langle [T_{zy}, [T_{xz}, T_{yx}]] \rangle$ correlators.
• Figure 2: Two- and three-band contributions to the nonlinear odd viscosity. (a) Two-band $\eta_{xx;yy,zz}$ and (b) Two-band $\eta_{yy;zz,xx}$ for the perturbed MRW model with mass $m$, showcasing an increasing response strength with the increasing Hopf invariant magnitude $|\chi|$. Here, $p \in \mathbb{Z}$ denotes the momentum scaling factor $k_z \rightarrow p k_z$ which leads to scaling of the invariant. (c) Three-band $\eta_{xx;yy,zz}$ and $\eta_{yy;zz,xx}$ realized in a flattened three-dimensional chiral model with chiral invariant $|\nu_i|$ which trivializes upon adding a symmetry-breaking perturbation. The $\eta_{zz;xx,yy}$ response component follows from the sum rule $\eta_{xx;yy,zz}+\eta_{yy;zz,xx}+\eta_{zz;xx,yy}=0$.
• Figure 3: Real-space representation of the NOVE in the perturbed MRW model for $\chi = 1$ and $\delta = 1/2$, see End Matter. Rate of change of Wannier center $x$-coordinate $x_c$ with equal normal-stresses $w_{yy},w_{zz}$ (red) and equal shear-stresses $w_{xz},w_{zy}$ (blue), depicted as a function of mass parameter $m$. The plots show the net current in the $x$ direction, which admits gradients in the $y$ direction for the shear-stress response. The viscoelastic response of the Wannier functions changes across TPTs, displaying correspondence to the hydrodynamics derived in the momentum-space formalism.