Tensor monopoles and negative magnetoresistance effect in optical lattices

TL;DR

This paper introduces a method to simulate 4D tensor monopoles using ultracold atoms in optical lattices, revealing their topological properties and a negative magnetoresistance effect, with potential experimental realizations.

Contribution

It proposes a novel simulation of 4D tensor monopoles in optical lattices and explores their topological features and magnetoresistance effects.

Findings

Tensor monopoles relate to quantum metric tensor in 4D.

Negative magnetoresistance of approximately -B^2 observed.

Experimental scheme for realizing 4D Hamiltonians proposed.

Abstract

We propose that a kind of four-dimensional (4D) Hamiltonians, which host tensor monopoles related to quantum metric tensor in even dimensions, can be simulated by ultracold atoms in the optical lattices. The topological properties and bulk-boundary correspondence of tensor monopoles are investigated in detail. By fixing the momentum along one of the dimensions, it can be reduced to an effective three-dimensional model manifesting with a nontrivial chiral insulator phase. Using the semiclassical Boltzmann equation, we calculate the longitudinal resistance against the magnetic field $B$ and find the negative relative magnetoresistance effect of approximately $ -B^{2} $ dependence when a hyperplane cuts through the tensor monopoles in the parameter space. We also propose an experimental scheme to realize this 4D Hamiltonian by introducing an external cyclical parameter in a 3D optical lattice. Moreover, we show that the quantum metric tensor and Berry curvature can be detected by applying an external drive in the optical lattices.