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In topological materials, shielding of bulk and surface states by crystalline symmetries has provided hitherto unknown access to electronic states in condensed matter physics. Interestingly, photo-excited carriers relax on an ultrafast timescale, demonstrating large transient mobility that could be harnessed for the development of ultrafast optoelectronic devices. In addition, these devices are much more effective than topologically trivial systems because topological states are resilient to the corresponding symmetry-invariant perturbations. By using optical pump probe measurements, we systematically describe the relaxation dynamics of a topologically nontrivial chiral single crystal, PtAl. Based on the experimental data on transient reflectivity and electronic structures, it has been found that the carrier relaxation process involves both acoustic and optical phonons with oscillation frequencies of 0.06 and 2.94 THz, respectively, in picosecond time scale. PtAl with a space group of $P$$2_{1}$3 allows only one non-zero susceptibility element i.e. $d_{14}$, in second harmonic generation (SHG) with a large value of 468(1) pm/V, which is significantly higher than that observed in standard GaAs(111) and ZnTe(110) crystals. The intensity dependence of the SHG signal in PtAl reveals a non-perturbative origin. The present study on PtAl provides deeper insight into topological states which will be useful for ultrafast optoelectronic devices., Comment: 10 pages, 5 figures

Chalcopyrite compounds are extensively explored for their exotic topological phases and associated phenomena in a variety of experiments. Here, we discuss the electrical transport properties of a direct energy gap semiconductor CdGeAs$_{2}$. The observed transverse magnetoresistance (MR) is found to be around 136% at a temperature of 1.8 K and a magnetic field of 14 T, following the semiclassical exponent MR $\sim$ $B^{2.18}$. The MR analysis exhibits a violation of the Kohler rule, suggesting the involvement of multiple carriers in the system. Below 15 K, with decreasing magnetic field, the MR increases, leading to the well known quantum interference phenomenon weak localization (WL). The analysis of the magnetoconductivity data based on the Hikami-Larkin-Nagaoka (HLN) model unveils three dimensional nature of the WL and the weak spin-orbit coupling in CdGeAs$_{2}$. The phase coherence length follows the $L_{\phi}$ $\sim$ $T^{-0.66}$ power law, which exhibits the 3D nature of the observed WL feature., Comment: 5 pages, 4 figures

Realization of topologically protected quantum states leads to unprecedented opportunities for fundamental science and device applications. Here, we demonstrate the coexistence of multiple topological phononic states and calculate the associated thermoelectric properties of a chalcopyrite material CdGeAs$_2$ using first-principles theoretical modeling. CdGeAs$_{2}$ is a direct bandgap semiconductor with a bandgap of $0.65$ eV. By analysing the phonon spectrum and associated symmetries, we show the presence of nearly isolated Weyl, nodal line, and threefold band crossings in CdGeAs$_2$. Specifically, the two triply degenerate points (TDPs) identified on the $k_{z}$ axis are formed by the optical phonons bands 7, 8, and 9 with type-II energy dispersion. These TDPs form a time reversal pair and are connected by a straight nodal line with zero Berry phase. The TDPs formed between bands 14, 15, and 16 exhibit type-I crossings and are connected through the open straight nodal line. Our transport calculations show a large thermopower exceeding $\sim$500 and $200$ $\rm \mu V/K$ for the hole and electron carriers, respectively, above 500 K with a carrier doping of 10$^{18}$ cm$^{-3}$. The large thermopower in $p$-type CdGeAs$_{2}$ is a consequence of the sharp density of states appear from the presence of a heavy hole band at the $\Gamma$ point. We argue that the presence of topological states in the phonon bands could lead to low lattice thermal conductivity and drive a high figure-of-merit in CdGeAs$_{2}$.

Symmetry-protected non-trivial states in chiral topological materials hold immense potential for fundamental science and technological advances. Here, we report electrical transport, quantum oscillations, and electronic structure results of a single crystal of chiral quantum material $\rm PtAl$. Based on the de Haas-van Alphen (dHvA) oscillations, we show that the smallest Fermi pocket ($\alpha$) possesses a non-trivial Berry phase $1.16$$\pi$. The band associated with this Fermi pocket carries a linear energy dispersion over a substantial energy window of $\sim$700 meV that is further consistent with the calculated optical conductivity. First-principles calculations unfold that $\rm PtAl$ is a higher-fold chiral fermion semimetal where structural chirality drives the chiral fermions to lie at the high-symmetry $\Gamma$ and $R$ points of the cubic Brillouin zone. In the absence of spin-orbit coupling, the band crossings at $\Gamma$ and $\rm R$ points are three- and four-fold degenerate with a chiral charge of $-2$ and $+2$, respectively. The inclusion of spin-orbit coupling transforms these crossing points into four- and six-fold degenerate points with a chiral charge of $-4$ and $+4$. Nontrivial surface states on the $(001)$ plane connect the bulk projected chiral points through the long helical Fermi arcs that spread over the entire Brillouin zone.

Anisotropic transport, Shubnikov-de Haas (SdH), and de Haas-van Alphen (dHvA) quantum oscillations studies are reported on a high-quality CoSi single crystal grown by the Czochralski method. Temperature-dependent resistivities indicate the dominating electron-electron scattering. Magnetoresistance (MR) at 2 K reaches 610% for I||[111] and B||[01-1], whereas it is 500% for I||[01-1] and B||[111]. A negative slope in field-dependent Hall resistivity suggests electrons are the majority carriers. The carrier concentration extracted from Hall conductivity indicates no electron-hole compensation. In 3D CoSi, the electron transport lifetime is found to be approximately in the same order as quantum lifetime, whereas in 2D electron gas the long-range scattering drives the transport life much larger than the quantum lifetime. From linear and Hall SdH oscillations the effective masses and Dingle temperatures have been calculated. The dHvA oscillation reveals three frequencies at 18 ($\gamma$), 558 ($\alpha$) and 663 T ($\beta$)), whereas, SdH oscillation results in only two frequencies $\alpha$ and $\beta$. The $\gamma$ frequency observed in dHvA oscillation is a tiny hole pocket at the $\Gamma$ point.

Single crystal of the binary equi-atomic compound GdBi crystallizing in the rock salt type cubic crystal structure with the space group $Fm\bar{3}m$ has been grown by flux method. The electrical and magnetic measurements have been performed on well oriented single crystals. The antiferromagnetic ordering of the Gd moments is confirmed at $T_{\rm N} = 27.5$~K. The magnetization measurement performed at $2$~K along the principal crystallographic direction [100] did not show any metamagnetic transition and no sign of saturation up to $7$~T. Zero field electrical resistivity reveals a sharp drop at $27.5$~K suggesting a reduction in the spin disorder scattering due to the antiferromagnetic alignment of the Gd moments. The residual resistivity at $2$~K is 390~n$\Omega$cm suggesting a good quality of the grown crystal. The magneto resistance attains a value of $1.0~\times~10^{4}\%$ with no sign of saturation, in a field of $14$~T, at $T = 2$~K. Shubnikov de Hass (SdH) oscillations have been observed in the high field range of the magnetoresistance with five different frequencies corresponding to the extremal areas of the Fermi surface. Analysis of the Hall data revealed a near compensation of the charge carriers accounting for the extremely large magnetoresistance., Comment: 6 figures, 1 Table and 8pages

Single crystals of ${\rm Ce_2Re_3Si_5}$ and ${\rm Pr_2Re_3Si_5}$ have been grown by Czochralski method in a tetra-arc furnace. Powder x-ray diffraction confirmed that these compounds crystallize in the ${\rm U_2Mn_3Si_5}$-type tetragonal crystal structure with space group $P4/mnc$ (No. 128). The anisotropic physical properties have been studied comprehensively by measuring the magnetic susceptibility, isothermal magnetization, electrical transport and specific heat. The low value of magnetic susceptibility together with no magnetic transition down to $2$~K gives evidence that the Ce-ions are in the intermediate valence state in ${\rm Ce_2Re_3Si_5}$. On the other hand ${\rm Pr_2Re_3Si_5}$ revealed a magnetic ordering at $9$~K. The sharp drop in the magnetic susceptibility and a spin flip like metamagnetic transition, for $H~\parallel~[001]$ in the magnetization plot of ${\rm Pr_2Re_3Si_5}$ suggest an Ising-type antiferromagnetic ordering. Based on magnetic susceptibility and isothermal magnetization data, a detailed crystal electric field (CEF) analysis shows that degenerate ${J} = 4$ Hund's rule derived ground state of ${\rm Pr^{3+}}$ ion splits into nine singlets with an overall splitting of $1179$~K. The magnetic ordering in ${\rm Pr_2Re_3Si_5}$ is due to the exchange-generated admixture of the lowest lying CEF energy levels. Heat capacity data reveal a sharp peak at $9$~K, that confirms the bulk nature of the magnetic ordering in ${\rm Pr_2Re_3Si_5}$., Comment: Article was already published

Quantum oscillations in both linear and Hall resistivities and weak antilocalization (WAL) are barely observed in bulk single crystals. Here we report the transport properties of a CaCuSb single crystal that crystallizes in the hexagonal crystal structure. The magnetotransport studies reveal WAL and Shubnikov-de Haas (SdH) quantum oscillations with a unique frequency at 314 T. A cusp-like behavior in the low field regime of magnetotransport for J // (ab)-plane and B // [0001] confirms the WAL in CaCuSb. Angular-dependent normalized magnetoconductance and SdH oscillations studies reveal that the observed phenomena originate from the 2D transport channels. The high magnetic field (up to 45 T) experiments demonstrate plateau-like features in the Hall measurements. The first-principles calculations unfold that CaCuSb is a non-topological semimetal with dominant hole carries at the Fermi level. Our study reveals that CaCuSb is a promising candidate to explore the quasi-2D quantum transport phenomenon in the transition metal pnictide materials.

Linear magnetoresistance is a phenomenon that has been observed in a few topological compounds that originate from classical and quantum phenomena. Here, we performed electrical transport measurements, in zero and applied magnetic fields, on the YSi single crystal along all three principal crystallographic directions of the orthorhombic crystal structure. For $I~\parallel~[001]$ and $H~\parallel~[100]$ direction above $\approx 10$~T, mobility fluctuation driven linear magnetoresistance is observed without any sign of saturation up to $14$~T magnetic field. Anisotropy in the Fermi surface is immanent from the angular dependence of the magnetoresistance. Kohler rule violation is observed in this system and Hall data signifies multiple charge carriers in YSi., Comment: 4 pages, 4 figures

The Fermi surface properties of a nontrivial system YSi is investigated by de Haas-van Alphen (dHvA) oscillation measurements combined with the first-principle calculations. Three main frequencies ($\alpha$, $\beta$, $\gamma$) are probed up to $14$~T magnetic field in dHvA oscillations. The $\alpha$-branch corresponding to $21$~T frequency possesses non-trivial topological character with $\pi$ Berry phase and a linear dispersion along $\Gamma$ to $Z$ direction with a small effective mass of $0.069~m_e$ with second-lowest Landau-level up to $14$~T. For $B~\parallel$~[010] direction, the 295~T frequency exhibits non-trivial $2D$ character with $1.24\pi$ Berry phase and a high Fermi velocity of $6.7 \times 10^5$~ms$^{-1}$. The band structure calculations reveal multiple nodal crossings in the vicinity of Fermi energy $E_f$ without spin-orbit coupling (SOC). Inclusion of SOC opens a small gap in the nodal crossings and results in nonsymmorphic symmetry enforced Dirac points at some high symmetry points, suggesting YSi to be a symmetry enforced topological metal., Comment: 6 pages, 5 figures