A sharp signal at the hole line
A simulation suggests that a 400-attosecond light pulse could read how carriers are divided between the K and K′ valleys in monolayer MoS2. Under a resonant σ+ pump, the model reported a normalized valley population imbalance of VP = 0.92. The study defined VP as the population difference between the K and K′ valleys divided by their combined population. With a circularly polarized probe, the hole line that co-rotated with the pump appeared at 35.0 eV, while the counter-rotating line was nearly dark. At a pump-probe delay of 12.9 fs, the co-rotating signal was 17 times stronger.
The proposal depends on keeping different carrier responses apart in energy. The electron channel appeared as a bleach near 38.5 eV. Both probe helicities shared a common d0 bleach between 36.7 and 37.5 eV. Taken with the 35.0 eV hole line, those features gave the calculation separate hole, electron and reference channels.
The calculation behind the proposal
This was a modeling study, not a measurement from an empirical sample. Monolayer MoS2 was represented by a 16-Wannier-function tight-binding model derived from a PBE-DFT calculation. The model was propagated with semiconductor Bloch equations using a global T2 of 10 fs and no population relaxation. The simulated pump was circularly or elliptically polarized, with a photon energy of 1.69 eV, a duration of 7.2 fs and an intensity of 100 GW/cm2. A weak circularly polarized XUV probe lasted 400 attoseconds and was centered at 37.5 eV. Circular dichroism, or CD, was defined as the difference between the absorption changes for the two probe helicities, Δμ+ − Δμ−.
Timing, sign and calibration
Delay-resolved calculations compared the hole-line CD with the simulated K-valley hole population. Using a 10% to 90% rise-time measure, the readout rose in 4.0 fs and the population in 4.2 fs. The probe duration was 0.4 fs. In the modeled system, that close match linked the spectral readout to the buildup of the simulated hole population.
The sign of the signal carried information too. Reversing the pump helicity reversed the simulated CD exactly, and the sign of the hole-line CD identified the written valley. At K, the d±2 hole channel and the strongest electron channel were fully helicity selective, with asymmetry values η = +1.00 and η = −1.00, respectively.
The calculation also tested whether signal size could track the amount of polarization. Across a modeled ellipticity scan covering VP from −0.92 to +0.92, hole-line contrast followed C = 0.96 × VP, with a Pearson correlation greater than 0.9999. Raw CD supplied a second linear calibration: across the modeled ellipticity and pump-intensity conditions, it followed CD = κ (NK − NK′), with r = 0.998. Reducing the pump intensity by an order of magnitude changed the contrast calibration by only 1%.
Linear pumping provided an important control. It retained 93% of the maximum single-helicity hole-line amplitude, but CD collapsed by four orders of magnitude. A separate three-pulse σ+ σ− σ− sequence represented writing, cancellation and reversal of net valley polarization, and delayed probing tracked the reversal of the hole-line CD.
What remains to be tested
The paper also estimated the size of the signal in experimental units. The pump-induced hole line reached 3.6% of static edge absorption, corresponding to an optical-density change of about 10^-4 at the percent-level absorbance of a monolayer. The estimate comes from the model, not an experimental measurement.
A real sample could change the result. The analysis flags core-hole attraction and carrier scattering as effects that may reshape the lines, redistribute populations within tens of femtoseconds and shift the numerical calibration. The supplied calculation therefore does not establish that the same contrast or timing will survive outside its modeled conditions.
The manuscript is an arXiv version 1 preprint, arXiv:2608.25121v1, dated 25 Aug 2026.
Paper data and sources
Original title: Carrier-Resolved Attosecond Valley Polarimetry of Monolayer MoS$_2$
Authors: Navdeep Rana, Lun Yue, Mette B. Gaarde
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text