Tensor monopoles and negative magnetoresistance effect in optical lattices

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.

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Cited by in corpus (6)

• Non-Abelian tensor Berry connections in multi-band topological systems
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Higher Gauge Theory
• Second Euler number in four dimensional synthetic matter
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Quantum geometric tensors from sub-bundle geometry