Photonic topological Lifshitz interfaces

Xianji Piao,Jonghwa Shin,Namkyoo Park

doi:10.1515/nanoph-2021-0807

Abstract

Abstract The intrinsic geometry of wavevector diagrams describes electronic or photonic transport at a given energy level. Lifshitz transition is an intriguing example of the topological transition in wavevector diagrams, which plays a critical role in abnormal transport with enhanced magnetoresistance or superconductivity. Here, we develop the spatial analogy of the Lifshitz transition, which provides a comprehensive topological perspective on transverse-spin interface states. We establish the excitation conditions of transverse-spin interface states, which require the “Lifshitz interface” – the interface between different topologies of wavevector diagrams – along with the gap in wavevector diagrams. Based on the detailed analysis of this topological phenomenon with respect to the dimensionality and gaps of wavevector diagrams across the Lifshitz interface, we show distinct parity of transverse spins and power flows in transverse-spin modes. The unique symmetry of interface states realizing Abraham-spin-momentum locking represents the gauge induced by the Lifshitz interface, which provides a novel insight into the Abraham–Minkowski controversy.

Highlights

Transport properties of electrons or photons at a given energy level are described by wavevector diagrams: an electronic Fermi surface or a photonic isofrequency surface (IFS), both of which represent the density of states in reciprocal spaces
As an analogy of topologically-protected interface states in topological bandgap materials [24, 25, 30], we show that the Lifshitz interface with overlapped gaps between wavevector diagrams leads to a transverse spin (T-spin) interface mode
As widely studied in quantum-optical analogy [33], we develop the spatial analogy of the dynamical Lifshitz transition, by constructing the abrupt topological transition of the isofrequency contours (IFCs): “Lifshitz interface”

Summary

Introduction

Transport properties of electrons or photons at a given energy level are described by wavevector diagrams: an. At the same time, when considering the universal definition of topology – geometric properties preserved under continuous deformation – the analogy of topological wave phenomena in terms of the Lifshitz transition will stimulate the extension of topological photonics into various classes of topologies, not restricted to the topology of the IFS [5, 27]. We establish the notion of “Lifshitz interfaces” – a class of spatial boundaries between different IFS topologies – which covers the environments for surfaceplasmon [29], Dyakonov [21, 22], and pure T-spin waves [23]. As an analogy of topologically-protected interface states in topological bandgap materials [24, 25, 30], we show that the Lifshitz interface with overlapped gaps between wavevector diagrams leads to a T-spin interface mode. Our result provides an intuition on the role of the IFS topologies in elucidating the discrepancy between the Abraham and Minkowski interpretations of optical momenta

Topology and gap of wavevector diagrams

Lifshitz interface at the same IFC dimensionality

Lifshitz interface at different dimensionalities

Abraham–Minkowski controversy in T-spin modes

Conclusions