Fig. 1

Magneto-optical spectroscopy of monolayer WS\({}_{2}\). a Image of a sample/fiber assembly: An exfoliated TMD monolayer, sandwiched between hBN slabs, is constructed over the \(3-4\ \mu\)m diameter core of a single-mode optical fiber (white circle). The assembly is mounted in helium exchange gas at 4 K in the bore of a pulsed magnet. The diagram depicts the optical selection rules in the \(K\) and \(K^{\prime}\) valleys. b Normalized transmission spectra (\(T/{T}_{0}\)) of monolayer WS\({}_{2}\) at selected magnetic fields \(B\)=0, 20, 40, and 60 T. Blue/red curves indicate \({\sigma }^{+}\)/\({\sigma }^{-}\) circular polarization (optical transitions in the \(K/K^{\prime}\) valleys, respectively). c Intensity map of all the transmission spectra, from \(-65\) to \(+65\) T. Excellent sample quality allows observation of the \(2s\), \(3s\), \(4s\), and \(5s\) excited Rydberg states of the neutral A exciton. d Energies of the \(1s-5s\) excitons for both \({\sigma }^{\pm }\) polarizations. e Average energy of the \({\sigma }^{\pm }\) transitions for each \(ns\) state, \(\frac{1}{2}({E}_{\sigma +}+{E}_{\sigma -})\), reveals distinct diamagnetic shifts. Solid lines show calculated energies using the Rytova–Keldysh model described in the text. Parameters: \({m}_{\mathrm{r}}=0.175\ {m}_{0}\), \({r}_{0}=3.4\ {\rm{nm}}\), \(\kappa =4.35\), and \({E}_{{\rm{gap}}}=2.238\) eV. Inset: Expanded plot of the \(1s\) exciton energy, showing its small quadratic diamagnetic shift. f The Zeeman splitting of the \(1s\), \(2s\), and \(3s\) exciton states (\({E}_{\sigma +}-{E}_{\sigma -}\)); dashed lines depict linear fits