weak antilocalization and phase coherence

Since LaCuSb 2 is an inversion-symmetric material and time-reversal symmetry is not broken, all bands in the bulk band structure are at least twofold spin degenerate. 2(d) only shows the k z = 0 plane since it provides the best agreement with the ARPES data (for a comparison with the k z = π plane, see Fig. To ensure an accurate comparison with the data, one must consider the effect of SOC on the band structure, since the linearly dispersing bands arise from Sb p bands, which can show large avoided crossings due to the large atomic mass of Sb. Both show several bands along Γ ¯– X ¯⁠, dispersing linearly over a large energy range and crossing the Fermi level (two bands with comparably low intensity are marked with two arrows). Figures 2(c) and 2(d) show the experimental and theoretical dispersion plots along the path shown in Fig. Since intensity modulations due to matrix element effects resulting from multiple atoms in the basis affect successive BZs differently, it is also clearly resolved with a higher intensity in neighboring BZs. 2(b), display similar structural behavior but also reveal a cylindrical internal structure inside the diamond centered around Γ ¯⁠, which is weakly visible in the first experimental BZ. 33 DFT calculations of the Fermi surface, shown in Fig. 30–32 The literature theoretical value of 0.719 Å −1 for the Γ ¯– X ¯ distance is in accordance with the experimental data. This kind of diamond-shaped Fermi surface is common for square-net based nodal line materials. It consists of a diamondlike feature centered around the Γ ¯ point connected to the next BZ at the X ¯ points and contains no bands around the M ¯ point. Figure 2(a) shows a constant energy cut at the Fermi level (E i = 0 eV) of the first BZ and its vicinity, elucidating the nature of the LaCuSb 2 Fermi surface. To further understand the electronic structure of materials, ARPES measurements were performed and compared to DFT calculations. Given that Cu is d 10 in this system, no magnetism or strong electron correlations are expected.

In LaCuSb 2, however, there are also several parabolic bands crossing the Fermi level that are primarily Cu- d bands, which may result in some conventional multiband effects. Dirac fermion behavior may arise as a result of the linearly dispersive bands that cross at certain points in the Brillouin zone, which has also been observed in some of the aforementioned square-net materials. The two-dimensionality of the structure is reflected in the band structure as the bands become flat and minimally dispersive in reciprocal space directions along k z, such as Γ–Z and M–A. 1(b), the calculated DFT band structures for LaCuSb 2 excluding and including spin-orbit coupling (SOC) are shown in Figs. 16–27 Using a path indicated by the primitive tetragonal Brillouin zone shown in Fig. This distance is shorter than in some of the other aforementioned 112 Dirac materials and thus results in linearly dispersive bands with relatively large bandwidths. 10,29,30 The bandwidth of these linearly dispersing bands is determined by the Sb-Sb interatomic distance, which is 3.08 Å in LaCuSb 2. The presence of a spin-orbit interaction manifested as weak antilocalization in the p-type epilayer suggests that these structures could be developed for use in spintronic devices such as the spin-FET, where significant spin lifetimes would be important for efficient device operation.It is the bonding of the Sb atoms in the square net layers that can lead to the formation of linearly dispersing Dirac or Weyl crossings in the electronic band structure due to the symmetry of the Sb p band overlap. In the p-type device, the measured spin diffusion length does not change over the range of temperatures for which weak antilocalization can be observed. The decay of the phase coherence length with temperature is found to obey the same power law of lϕ ∝ Tc, where c = −0.68 ± 0.03, for each device, in spite of the clear differences in the nature of the conduction. We obtain phase coherence lengths as large as 325 nm in the highly doped n-type device, presenting possible applications in quantum technologies. From fits to these data using the Hikami-Larkin-Nagaoka model, the phase coherence length of each device is extracted, as well as the spin diffusion length of the p-type device. Both n- and p-type devices show quantum corrections to the conductivity in an applied magnetic field, with n-type devices displaying weak localization and p-type devices showing weak antilocalization. The magnetoresistance of 50 nm thick epilayers of doped germanium is measured at a range of temperatures down to 1.6 K.

Weak antilocalization and phase coherence