A robust and tuneable mid-infrared optical switch enabled by bulk Dirac fermions

Pulsed lasers operating in the mid-infrared (3–20 μm) are important for a wide range of applications in sensing, spectroscopy, imaging and communications. Despite recent advances with mid-infrared gain platforms, the lack of a capable pulse generation mechanism remains a significant technological challenge. Here we show that bulk Dirac fermions in molecular beam epitaxy grown crystalline Cd3As2, a three-dimensional topological Dirac semimetal, constitutes an exceptional ultrafast optical switching mechanism for the mid-infrared. Significantly, we show robust and effective tuning of the scattering channels of Dirac fermions via an element doping approach, where photocarrier relaxation times are found flexibly controlled over an order of magnitude (from 8 ps to 800 fs at 4.5 μm). Our findings reveal the strong impact of Cr doping on ultrafast optical properties in Cd3As2 and open up the long sought parameter space crucial for the development of compact and high-performance mid-infrared ultrafast sources.

Calculations based on density-functional theory for the given substitution configuration (one Cr atom at f1 position). (b) Experimental X-ray diffraction spectra. The intensity is normalized by the intensity of (224) peak. Meanwhile the pulse energy increases nonlinearly from 77.9 nJ to 178.6 nJ.

Supplementary Table 1 Atom ratio of Cr-doped Cd3As2 samples with different Cr concentrations.
The doping concentration is obtained by energy-dispersion X-ray spectroscopy inside a scanning electron microscope.

Cr
Cd As  Fig. 5b). Then we substitute one Cr for one Cd atom in a primitive unit cell, which approximates the case for ~2% concentration (Supplementary Fig. 5a). Configurations with the Cr atom in the same position type is equivalent, so it has only 6 nonequivalent configurations here. We calculate the total energy of doped Cd3As2 with the Cr atom in non-equivalent position a1-f1 (see Supplementary Table 2), respectively. The most stable configuration corresponds to the scenario where a Cr atom occupies the f1 position, and the calculated energy difference among these possible configurations is quite large (Supplementary Table 2). From the table, one expects that the Cr atoms should occupy specific (low energy) positions instead of distributing randomly.
Thus, the substitution of Cd atoms will automatically break the C4 rotational symmetry around kz axis. Without the rotational symmetry protection, the Dirac nature and band topology are significantly altered. The calculated C4 rotation symmetry breaking and the site substitution can be experimentally verified by examining the fine structure though X-ray diffraction (XRD) spectroscopy.
Based on the most likely geometry (substitution at f1 position), a doping induced peak around seven degrees is predicted. The peak intensity is also predicted to be 2000 times smaller than the main (224) peak. This prediction is realized by the XRD experiments. As shown in Supplementary Fig. 6, the measured peak shows almost identical position but the intensity is 2 times smaller although still on the same order of magnitude. The lower intensity indicates that the doping induced substitution is neither ideal nor perfectly repeated in each unit cell. However, the observed fine structure at the right diffraction angle can clearly verify the site substitution and the resultant C4 rotation symmetry breaking. If the Cr atoms are randomly distributed, no peak should appear on the XRD spectrum in the doped sample.
Supplementary Fig. 5c displays the electronic structure of Cr-doped Cd3As2 with one of the Cd atoms in unit cell substituted by a Cr atom. Due to the broken rotation symmetry, the original Dirac cone is eliminated by the generation of a finite quasi-particle gap which directly supports the existence of massive fermions. Therefore, combining the DFT calculations and high-resolution XRD results, it can be concluded that the Cr doping leads to a symmetry breaking and band structure modification.

Supplementary Note 2. Optical conductivity in Cr-doped Cd3As2
Models and eigenstates. The general form of the low-energy Hamiltonian for a Weyl semimetal is described as 4,5 , Here denotes the Pauli spin matrices, is the field operators, 0 is the mass term which can be regarded as arising from the internode coupling, or the bare gap. From this general Hamiltonian, we made two modifications: b=0 for Dirac semimetals, and the dispersion along the z direction is different to that along the film surface. Furthermore, the z-component of the electron momentum is quantized. The bare gap term can be written as 4 0 0 , where the 0 matrix is given as The interaction term int is the electron-phonon coupling which governs the relaxation of photo-excited hot carriers.