Anomalous geometric transport signatures of topological Euler class
arXiv:2412.01810 · doi:10.1103/5gmg-q1z5
Abstract
We investigate Riemannian quantum-geometric structures in semiclassical transport features of two-dimensional multigap topological phases. In particular, we study nonlinear Hall-like bulk electric current responses and, accordingly, semiclassical equations of motion induced by the presence of a topological Euler invariant. We provide analytic understanding of these quantities by phrasing them in terms of momentum-space geodesics and geodesic deviation equations and further corroborate these insights with numerical solutions. Within this framework, we moreover uncover anomalous bulk dynamics associated with the second- and third-order nonlinear Hall conductivities induced by a patch Euler invariant. As a main finding, our results show how one can reconstruct the Euler invariant by coupling to electric fields at nonlinear order and from the gradients of the electric fields. Furthermore, we comment on the possibility of deducing the nontrivial non-Abelian Euler class invariant specifically in second-order nonlinear ballistic conductance measurements within a triple-contact setup, which was recently proposed to probe the Euler characteristics of more general Fermi surfaces. Generally, our results provide a route for deducing the topology in real materials that exhibit the Euler invariant by analyzing bulk electrical currents.
9+10 pages, 4+3 figures
References in corpus (33)
- Topological Field Theory of Time-Reversal Invariant Insulators
- Nearly-flat bands with nontrivial topology
- The space group classification of topological band insulators
- Topology of crystalline insulators and superconductors
- Helical Metal Inside a Topological Band Insulator
- Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure
- Quantum metric-induced nonlinear transport in a topological antiferromagnet
- Optical conductivity of bilayer graphene with and without an asymmetry gap
- Topological Euler class as a dynamical observable in optical lattices
- Observation of non-Abelian topological semimetals and their phase transitions
- Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry
- Geometric approach to fragile topology beyond symmetry indicators
- Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
- Berry connection polarizability tensor and third-order Hall effect
- Torsion, Parity-odd Response and Anomalies in Topological States
- Measurements of the quantum geometric tensor in solids
- Fluctuations, uncertainty relations, and the geometry of quantum state manifolds
- Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase
- Multi-gap topology and non-Abelian braiding of phonons from first principles
- Observation of topological Euler insulators with a trapped-ion quantum simulator
- Quantized Integrated Shift Effect in Multigap Topological Phases
- Third-order intrinsic anomalous Hall effect with generalized semiclassical theory
- Quantum Field Theory Anomalies in Condensed Matter Physics
- Optical manifestations and bounds of topological Euler class
- Quantum geometry quadrupole-induced third-order nonlinear transport in antiferromagnetic topological insulator MnBi2Te4
- Multipole theory of optical spatial dispersion in crystals
- Non-Abelian Hopf-Euler insulators
- Chirality flip of Weyl nodes and its manifestation in strained MoTe
- Interferometry of non-Abelian band singularities and Euler class topology
- Three-dimensional -symmetric topological phases with Pontryagin index
- Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
- Andreev reflection in Euler materials
- Exact projected entangled pair ground states with topological Euler invariant