Chirality-Driven Orbital Angular Momentum and Circular Dichroism in CoSi

Chiral crystals and molecules were recently predicted to form an intriguing platform for unconventional orbital physics. Here, we report the observation of chirality-driven orbital textures in the bulk electronic structure of CoSi, a prototype member of the cubic B20 family of chiral crystals. Using circular dichroism in soft x-ray angle-resolved photoemission, we demonstrate the formation of a bulk orbital-angular-momentum texture and monopolelike orbital-momentum locking that depends on crystal handedness. We introduce the intrinsic chiral circular dichroism, $ic\mathrm{CD}$, as a differential photoemission observable and a natural probe of chiral electron states. Our findings render chiral crystals promising for spin-orbitronics applications.

Figure 1

(a) The atomic configuration of enantiomers $A$ and $B$ of CoSi in a unit cell with Co in blue and Si in white. (b) The high-symmetry points in a simple cubic Brillouin zone. ARPES datasets for CoSi(001) along the high-symmetry lines (c) $\mathrm{\Gamma }\text{−}M$ and (d) $\mathrm{\Gamma }\text{−}X$, obtained for enantiomer $A$ at a photon energy of $h\nu =593\mathrm{eV}$. (e) Constant-energy momentum distribution in the $\mathrm{\Gamma }\text{−}X\text{−}M$ plane. Labels (1) and (2) indicate two branches of the multifold band crossing at the $\mathrm{\Gamma }$ point [3, 32].

Figure 2

(a) Geometry of the ARPES experiment using incoming left ($I_L$) and right ($I_R$) circularly polarized light, in the gray $xz$ plane. (b)–(c), (f)–(g) Isoenergy momentum distributions in the $\mathrm{\Gamma }\text{−}X\text{−}M$ plane for enantiomer $A$ (left panels) and enantiomer $B$ (right panels), obtained using $h\nu =593\mathrm{eV}$ and $E-E_F=-0.25\mathrm{eV}$. The $\mathrm{\Gamma }\text{−}X$ direction is aligned along the plane of light incidence. The momentum distributions were taken with (b),(f) left and (c),(g) right circularly polarized light. (d),(h) The corresponding circular dichroism, $I_{\mathrm{CD}}=I_L-I_R$, for enantiomer $A$ and $B$, respectively. (e),(i) Circular dichroism $I_{\mathrm{CD}}$ in the plane of light incidence ($k_y=0$) extracted from (d) and (h), respectively.

Figure 3

Constant-energy momentum distributions of the circular dichroism in the $\mathrm{\Gamma }\text{−}X\text{−}M$ plane for (a)–(c) enantiomer $A$ and (d)–(f) enantiomer $B$. The datasets were obtained at a photon energy of $h\nu =350\mathrm{eV}$ and at different binding energies as indicated. (g),(h) Circular dichroism in band-structure maps in the plane of light incidence ($k_y=0$), obtained with $h\nu =350$ and 593 eV.

Figure 4

(a) Schematic of the OAM monopole (gray arrows) in the $\mathrm{\Gamma }\text{−}X\text{−}M$ plane according to Ref. [14], and the corresponding dichroic signal. (b) Momentum distribution of the intrinsic chiral circular dichroism, $ic\mathrm{CD}=\frac{1}{2}(I_{\mathrm{CD}}^A-I_{\mathrm{CD}}^B)$, at $h\nu =593\mathrm{eV}$ and $E-E_F=-0.25\mathrm{eV}$.