Non-Abelian tensor Berry connections in multi-band topological systems

Abstract

Here, we introduce and apply non-Abelian tensor Berry connections to topological phases in multi-band systems. These gauge connections behave as non-Abelian antisymmetric tensor gauge fields in momentum space and naturally generalize Abelian tensor Berry connections and ordinary non-Abelian (vector) Berry connections. We build these novel gauge fields from momentum-space Higgs fields, which emerge from the degenerate band structure of degenerate-band models. Firstly, we show that the conventional topological invariants of two-dimensional topological insulators and three-dimensional Dirac semimetals can be derived from the winding number associated to the Higgs field. Secondly, through the non-Abelian tensor Berry connections we construct higher-dimensional Berry-Zak phases and show their role in the topological characterization of several gapped and gapless systems, ranging from two-dimensional Euler insulators to four-dimensional Dirac semimetals. Importantly, through our new theoretical formalism, we identify and characterize a novel class of models that support space-time inversion and chiral symmetries. Our work provides an unifying framework for different multi-band topological systems and sheds new light on the emergence of non-Abelian gauge fields in condensed matter physics, with direct implications on the search for novel topological phases in solid-state and synthetic systems.

4 pages, 2 figures, accepted version on Physical Review Letters

References in corpus (16)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Field Theory of Time-Reversal Invariant Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological Euler class as a dynamical observable in optical lattices
• $PT$ Symmetric Real Dirac Fermions and Semimetals
• Geometric approach to fragile topology beyond symmetry indicators
• Boundary criticality of $PT$-invariant topology and second-order nodal-line semimetals
• Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy
• Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop
• Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric
• Topological Euler insulators
• Four-dimensional semimetals with tensor monopoles: From surface states to topological responses
• Non-Abelian Berry Phases and BPS Monopoles
• Type I D-branes in an H-flux and twisted KO-theory
• Models for the BPS Berry Connection
• Topology of three-dimensional Dirac semimetals and generalized quantum spin Hall systems without gapless edge modes

Cited by in corpus (15)

• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps
• Topological Insulators with Hybrid-order Boundary States
• Higher Gauge Theory
• Coexisting Euler and Stiefel-Whitney Topological Phases in Elastic Metamaterials
• Second Euler number in four dimensional synthetic matter
• Geometric semimetals and their simulation in synthetic matter
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Singular connection approach to topological phases and resonant optical responses
• Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction