Circular dichroism and radial Hall effects in topological materials

Abstract

Under symmetry breaking, a three-dimensional nodal-line semimetal can turn into a topological insulator or Weyl semimetal, accompanied by the generation of momentum-space Berry curvature. We develop a theory that unifies their circular dichroism and highlights the roles of Berry curvature distribution and light incident direction. Nontrivially, these phases exhibit distinct dichroic optical absorption and radial Hall effects, with characteristic scalings with photon energy and electric field. Our findings offer a new diagnosis tool for examining topological phases of matter.Topological phases of matter have been attracting significant attention in the past decade [1][2][3][4]. A variety of topological insulators (TI) and semimetals have been discovered successively, which often feature protected band crossing points. For instance, TI's possess protected Kramers degeneracies on their surfaces [1][2][3], whereas Dirac and Weyl semimetals have discrete point singularities in their bulk [4][5][6][7][8][9][10][11][12][13][14][15][16]. Intriguingly, the band-crossing can also form a symmetry-protected 1D loop [16][17][18][19][20][21][22][23][24][25][26][27][28]. Upon symmetry breaking, the loop can be reduced to Weyl points or a full gap [19]. Hence such a nodal-line semimetal (NLSM) may be regarded as a parent phase for Weyl semimetals and TI's. Indeed, such transformations have been observed in concrete materials [18][19][20][21][28][29][30][31][32].Characterizing and distinguishing topological phases have been a critical topic in the field. Currently, most studies of 3D topological materials strongly rely on angleresolved photoemission spectroscopy (ARPES) that images the bulk and surface band structures [33][34][35]. However, ARPES results in some materials may not be sufficiently clear to resolve possible avoided band crossings, due to the narrow gaps and complex bands. Magnetotransport could in principle offer useful information [36][37][38][39][40][41][42][43], yet its indirect inference is often complicated by alternative mechanisms, charge impurities, conventional bands etc [44,45]. This is in sharp contrast to the 2D case in which topological materials can enjoy gatetunable doping, ultra-high mobilities, and quantized Hall conductances. Therefore, it is desirable to develop new methods for studying topological phases of 3D matter.In this Letter, we propose new schemes for probing 3D topological materials via circular dichroism by taking its advantages of unparalleled precision and versatile controllability [46][47][48][49][50][51]. We first develop a general theory for optical transitions in 3D materials induced by circularly polarized lights, which manifests Berry curvature effects. Applying the theory to the NLSM, where the curvature vanishes apart from the nodal ring, and to its derived topological phases, where the curvature spreads under symmetry breaking, we reveal their characteristic scalings of optical absorption with photon energy. Moreover, in optoelectronic transport, we discover a novel radial H...

Probing topology by “heating”: Quantized circular dichroism in ultracold atoms

“…20 . We note that similar Berry curvature effects have been recently investigated in the context of circular dichroism in nodal-line semimetals ( 80 ).…”

Light-induced anomalous Hall effect in massless Dirac fermion systems and topological insulators with dissipation

“…The anomalous Hall effect induced by circularly polarized light has been heavily discussed in various theoretical works [18,[29][30][31][32][33][34] from the point of view of intrinsic and light-induced Berry curverture contributions in order to explore a possibility of diagnosing and steering topological properties by light. However, despite the great interest in the subject, population effects with dissipation have only recently been discussed more seriously in the context of Floquet and topological engineering in open [35,36] and closed [37][38][39] nonequilibrium many-body systems.…”

Measuring quantized circular dichroism in ultracold topological matter

“…in the circular photogalvanic effect in Weyl semimetals [16]. While circular dichroism was previously studied in solid-state systems via the irradiation of circularly-polarized light [17][18][19][20], the quantization law predicted in Eq. (1) has never been observed so far.…”