Half-quantized helical hinge currents in axion insulators

Abstract

Fractional quantization can emerge in non-correlated systems due to the parity anomaly, while its condensed matter realization is a challenging problem. We propose that in axion insulators (AIs), parity anomaly manifests a unique fractional boundary excitation: the half-quantized helical hinge currents. These helical hinge currents microscopically originate from the lateral Goos-Hänchen (GH) shift of massless side-surface Dirac electrons that are totally reflected from the hinges. Meanwhile, due to the presence of the massive top and bottom surfaces of the AI, the helical current induced by the GH shift is half-quantized. The semiclassical wave packet analysis uncovers that the hinge current has a topological origin and its half quantization is robust to parameter variations. Lastly, we propose an experimentally feasible six-terminal device to identify the half-quantized hinge channels by measuring the nonreciprocal conductances. Our results advance the realization of the half quantization and topological magnetoelectric responses in AIs.

High spin axion insulator

“…The oppositely quantized surface Chern numbers in spin-3/2 HSAI thereby assure a quadruple axion field θ H S A I = 4 π . Moreover, since the Chern number difference between neighboring top (bottom) and side surfaces is an integer, HSAI supports a possible hinge state that is absent in spin-1/2 axion insulator 26 , 40 , which allows a subsequent QHHC owing to opposite chiralities on different surfaces. Nonetheless, we find that this QHHC survives counterintuitively without the existence of any hinge state.…”

“…We see that J x ( z ) is verily confined on the hinge, in agreement with 〈 z / L z 〉 and A ( k x , E ). Strikingly, this hinge current decays oscillatively into the side surface, exhibiting a beating mode (magenta line) in sharp contrast to that in spin-1/2 axion insulator 26 . This peculiar behavior can be quantitatively fitted by the superposition of two power-law decaying edge currents and 47 , where k F 1 and k F 2 are the Fermi momenta for the two distinct modes marked by the white stars in Fig.…”

“…This spectrum density can be verified experimentally by using the nano angle-resolved photoemission spectroscopy and microscopy 44 – 46 . Besides, the high spectrum density on the hinge indicates the presence of a hinge current, the current density of which can be quantitatively determined by 26 , 43 where E F is the Fermi energy labeled by the white line in Fig. 2 c, r = ( y , z ), H H S A I ( k x , r ) is the Hamiltonian for the HSAI and G r ( E F ; k x , r ) is the retarded Green’s function.…”

“…Owing to the chirality bonded to the quantized surface Chern number, this QHHC can be unveiled by the non-reciprocal conductance in a six-terminal device sketched in Fig. 2 e, where G i j is the differential conductance 26 , 48 . In this device, two longitudinal leads (terminals 5 and 6) are intimately connected to the two ends of the sample while four transverse leads (terminals 1, 2, 3, and 4) are attached to different hinges on the front surface.…”

Layer-dependent zero-line modes in antiferromagnetic topological insulators

“…Moreover, when the temperature is below the Néel ordering temperature, the antiferromagnetic domain walls have been experimentally observed in layered MnBi 2 Te 4 [32], which provides an ideal natural platform to investigate the effect of layer degree of freedom on ZLMs. Despite there are some studies on the magnetic domain walls recently [39][40][41][42][43][44], the exploration of the effect of layers on ZLMs in interlayer antiferromagnetic topological insulators remains scarce.…”