Fermiology of Chiral Cadmium Diarsenide CdAs2, a Candidate for Hosting Kramers–Weyl Fermions

Nonmagnetic chiral crystals are a new class of systems hosting Kramers–Weyl Fermions, arising from the combination of structural chirality, spin–orbit coupling (SOC), and time-reversal symmetry. These materials exhibit nontrivial Fermi surfaces with SOC-induced Chern gaps over a wide energy range, leading to exotic transport and optical properties. In this study, we investigate the electronic structure and transport properties of CdAs2, a newly reported chiral material. We use synchrotron-based angle-resolved photoelectron spectroscopy (ARPES) and density functional theory (DFT) to determine the Fermiology of the (110)-terminated CdAs2 crystal. Our results, together with complementary magnetotransport measurements, suggest that CdAs2 is a promising candidate for novel topological properties protected by the structural chirality of the system. Our work sheds light on the details of the Fermi surface and topology for this chiral quantum material, providing useful information for engineering novel spintronic and optical devices based on quantized chiral charges, negative longitudinal magnetoresistance, and nontrivial Chern numbers.

C rystal symmetries play a pivotal role in determining the electronic properties of various quantum systems, and their study has garnered substantial interest for both fundamental research and technological applications. 1−9 Crystals exhibiting well-defined handedness, due to the breaking of inversion, mirror, or any other roto-inversion symmetries, are referred to as chiral crystals. 10−12 Even in their nonmagnetic state, these chiral crystals show universal topological electronic properties due to their spin−orbit coupling and crystalline chirality, resulting in the presence of Kramers−Weyl Fermions in their spectrum. 13,14 These Fermions are pinned to Kramers degenerate points, leading to the appearance of topological gaps, which are significantly larger than those observed in Weyl semimetals. 13 Within such gaps, ubiquitous topological properties, such as quantized chiral charges, 15 negative longitudinal magnetoresistance, 16 and nontrivial Chern numbers 17 can arise, opening up exciting avenues for engineering exotic transport phenomena and applications. Furthermore, Kramers−Weyl Fermions differ from conventional Weyl Fermions as they occur at timereversal invariant points in momentum space. SOC, structural chirality, and time-reversal symmetry combine to produce these unique properties, which can also enable additional exotic phenomena such as magneto-chiral dichroism, 18,19 large optical activity, 20,21 and even the emergence of skyrmions with the lifting of time-reversal symmetry. 22,23 As such, understanding the electronic structure of these compounds is of paramount importance, especially given the evident potential for technological applications in spintronics and optics. 11 In this study, we investigate the electronic structure of the newly reported 24,25 chiral material CdAs 2 using synchrotronbased angle-resolved photoelectron spectroscopy (ARPES), density functional theory (DFT), and transport experiments, shedding light on the details of the Fermi surface and topology for this chiral quantum material. Our findings suggest that CdAs 2 is a promising candidate for enabling novel topological properties protected by its structural chirality, offering useful information for the development of disruptive spintronic and optical devices based on quantized chiral charges, negative longitudinal magnetoresistance, and nontrivial Chern numbers. CdAs 2 exhibits trigonal symmetry belonging to the space group n. 98, I4 1 22(see Figure 1). The lattice parameters a = b = 8.152 Å and c = 4.771 Å were determined from our X-ray diffraction (XRD) measurements (Figure 2c). The crystal structure reflects the chirality of the system, with atoms forming spiral chains of covalent As−As and Cd−As bonds ( Figure 1a), which influence both the optical and electronic properties.
The electronic structure of the bulk, along the highsymmetry directions (for Brillouin zone, BZ, see Figure 1b), shows a small indirect energy gap (∼0.13 eV) as displayed in Figure 1c, indicating the semiconducting nature of the bulk crystal. The inclusion of SOC reduces the gap by approximately 20 meV, as shown in Figure 1d, but the semiconducting character is retained. With the inclusion of SOC, the band structure of CdAs 2 displays a 2-fold splitting, whereas in its absence, it exhibits a 2-fold spin degeneracy. However, at time-reversal-invariant-momenta, 2-fold spin degeneracy is retained even in the presence of SOC, which is crucial for the emergence of Kramers−Weyl Fermions. 11,12 We calculated the Wannier charge centers for six time reversal invariant planes: k 1 = (0.0, 0.5), k 2 = (0.0, 0.5), k 3 = (0.0, 0.5) of primitive CdAs 2 , as shown in Figure S4 in the Supporting Information. The results indicate that the k 2 −k 3 plane and the k 1 −k 3 plane have a reverse topological number 2 , i.e., 2 (k 1 = 0) = 2 (k 2 = 0.5) = 0, 2 (k 1 = 0.5) = 2 (k 2 = 0.0) = 1. We hypothesized that this may be attributed to the structural chirality of CdAs 2 . It is worth noting that the surface electronic structure may differ significantly from the bulk. In this study, we examine four possible surface terminations along the (110) plane: As−S1, As−S2, Cd−S1, and Cd−S2 (refer to Figure S1 in the Supporting Information). Using DFT calculations, we found that the As−S1 and Cd−S1 surfaces are notably more stable than the others, without any observed distortions. Conversely, the As−S2 and Cd−S2 surfaces exhibit reconstruction, where the topmost Cd atoms in Cd−S2 sink into the As-sublayer. This behavior is comparable to a selfpassivation mechanism reported in three-dimensional Dirac semimetal Cd 3 As 2 . 26 To determine the most realistic configuration for comparison to the experiment, we relaxed the (2 × 1) and (3 × 1) supercells of As−S1, As−S2, Cd−S1, and Cd−S2 terminated (110) surface to simulate their electronic structure ( Figure 3). The surface formation energy as a function of the chemical potential of As atoms (μ As ) for the four types of surfaces (with a thickness of 17 Å) is illustrated in Figure S2a. The Cd−S1 termination exhibits the lowest surface energy for lower μ As (blue line in Figure S2a in the Supporting Information), following a linear trend. Conversely, the As−S1 termination  Therefore, we focus on the As−S1 and Cd−S1 surfaces, which exhibit the lowest and most favorable surface energy configurations, in our further analysis of (110)-oriented crystals. CdAs 2 single crystals with (110) orientation were analyzed using high-resolution transmission electron microscopy (HR-TEM, Figure 2a,b). The unit cell parameters, determined to be a = b = 0.795 nm and c = 0.467 nm, were found to be consistent with previous reports 27 and XRD results ( Figure  2c). Temperature-dependent magnetoresistance measurements were carried out on the same crystals, revealing a semiconductor-metal transition that is quenched with increasing magnetic field. The data in Figure 2d demonstrate that the semiconducting behavior persists below 150 K and becomes metallic above this threshold. 28 The experimental results support the conclusion that CdAs 2 undergoes a transition from semiconductor to metal with increasing temperature.
The electronic structure of CdAs 2 was probed using synchrotron-based ARPES. Consistent with the bulk semiconducting nature of the material, the ARPES spectra showed an energy gap separating the valence and conduction bands (Figure 4 and 5). The constant energy maps (Figure 4a−c) revealed a complex Fermiology, particularly for the valence band manifold, with small metallic conduction band pockets comprising the Fermi surface (Figure 4a). The energymomentum dispersion along high-symmetry directions ( Figure  5) indicated the presence of strongly dispersing bands with broad features, suggestive of the three-dimensional nature of the material, which introduces a significant k z contribution in ARPES measurements.
DFT calculations predicted the presence of metallic in-gap surface states that cross the Fermi level for the most stable Asterminated surface, where the presence of dangling bonds is expected to generate these states. Band structures were calculated for As−S1 (110) and Cd−S1 (110) surfaces with thicknesses of 17−35 Å ( Figure S3 in the Supporting Information), revealing that the surface states of As−S1 (110) and Cd−S1 (110) surfaces are metallic and cross the Fermi energy level ( Figure S5 in the Supporting Information). The As−S1 (110) surface showed decreasing conduction bands at the Γ point as thickness increased from 17 to 35 Å, while the conduction band at Γ from the topmost As atoms of As−S1 (110) surface decreased from 0.43 to 0.34 eV. The Cd−S1 (110) surface, on the other hand, showed surface states that crossed the Fermi energy level regardless of the slab thickness, indicating that the Cd−S1 surface is more active and less stable than the As−S1 surface. To further investigate the surface state of As−S1 and Cd−S1 (110) surfaces, Wannier90 code 29 and Wannier Tools 30 package were used ( Figure S4 in the Supporting Information). A tight-binding model generated by Wannier90 code confirmed that the surface state of As−S1 (110) surface slightly crosses the Fermi energy level in the direction of Γ to X, while the Cd−S1 (110) surface has several surface states crossing the Fermi energy level.
Although the identification of surface states in ARPES spectra was challenging due to their broad and intense spectral features, derivative plots of the bands ( Figure 5) facilitated a more detailed comparison between theory and experiment, revealing additional dispersing features in the gap region, potentially attributed to the surface states. The comparison of   Figure 1d with the experimental results in Figure 5 showed a maximum of the valence band at the M point, where Kramers−Weyl Fermions are imposed by the T symmetry. The chirality and lack of mirror (inversion) symmetry in CdAs 2 are of great significance, as they give rise to topological gaps that are much larger than those found in conventional Weyl semimetals. These gaps are clearly evident in our ARPES experiment and make CdAs 2 an ideal platform for studying a range of unique phenomena. Notably, the topological properties of this material enable the existence of Kramers−Weyl Fermions, which have been suggested as promising candidates for developing novel spin-torque devices and quantum solenoids. 31 In summary, our study has provided a comprehensive investigation of the electronic properties of CdAs 2 . Our results demonstrate that CdAs 2 is a semiconducting chiral material with a small gap that can be overcome by thermal activation, leading to a semiconducting-metal transition. We found that the topological properties of this material are mediated by SOC, although it has a minor effect in reducing the gap size. Furthermore, we showed that the presence of metallic states on the material's surface is crucial in enabling additional metallic states. Although identifying these surface states by ARPES is complicated due to the broadening of the spectra, our experimental results are consistent with our theoretical model.
Our findings have significant implications for the development of optical and spintronic devices based on quantized chiral charges, negative longitudinal magnetoresistance, and nontrivial Chern numbers associated with this chiral quantum material and its Kramers−Weyl Fermions.

■ METHODS
Theory. First-principles calculations were performed by using the Vienna ab initio simulation package (VASP). 32 The exchange-correlation interaction was described using the Perdew−Burke−Ernzerhof (PBE) functional 33 in the generalized gradient approximation (GGA), with core electrons described by the Projector-augmented wave (PAW) technology. 34 A plane-wave basis kinetic energy cutoff of 500 eV and a convergence criterion of 10 −5 eV were used in the calculations. All configurations were fully relaxed until the force was lower than 0.02 eV/Å, with a k-point sampling of 0.02 1/Å used for structural relaxation.
Crystal Growth. CdAs 2 single crystals were grown by the Chemical Vapor Transport (CVT) method, using Cd metal chunks (purity 99.99%), As chunks (purity 99.999%), and I 2 transport agent (purity 99.999% analytical grade) purchased from Alfa Aesar Chemical in a weight ratio of 43:57. The growth process was carried out in a carbon-coated quartz tube, sealed under an Ar gas atmosphere using a glovebox. A horizontal two-zone furnace with programmable temperature and time was used to maintain the furnace hot and cold zones at 600 and 550°C, respectively, for 2 weeks. The grown crystals were collected, washed in a glovebox to protect them from surface oxidation, and further washed with ethanol to remove any surface contamination from I 2 .
TEM. HR-TEM investigation of the grain surface was performed on crystal grains hanging freely in carbon membrane holes with no support underneath. We selected grains tilted to the nearest available zone axis orientation, as shown in the selected area electron diffraction (SAED) patterns in Figure 2b. HR-TEM micrographs were acquired from the thinnest regions at the grain border. ARPES measurements were carried out at the National Synchrotron Radiation Centre SOLARIS in Cracow, Poland, using the variable polarization and high-resolution URANOS beamline depicted in Figure S6 in the Supporting Information. Samples were glued with epoxy resin to a sample holder and cleaved in an ultrahigh vacuum by a metal post. The experiment was conducted using a quasiperiodic elliptically polarizing undulator APPLE II type as a photon source. Experimental data were collected by a VGScienta DA30L electron spectrometer, with an energy and angle resolution better than 3 meV and 0.1°, respectively. Data measurements were performed at T = 40 K and for an energy range from 20 to 140 eV. The spot size on the sample was 250 × 250 μm.
Transport Experiments. The temperature-dependent transport properties were investigated using a 4-probe measurement with the magnetic field varying from 0 to 2 T in a Quantum Design (QD) based Physical Property Measurement System (PPMS).
Further information on the theoretical model and geometry of ARPES experiments (PDF)