By the first-principles electronic structure calculations, we have systematically studied the electronic structures of recently discovered extremely large magnetoresistance (XMR) materials LaSb and LaBi. We find that both LaSb and LaBi are semimetals with the electron and hole carriers in perfect balance. The calculated carrier densities in the order of 10 20 cm −3 are in good agreement with the experimental values, implying long mean free time of carriers and thus high carrier mobilities. With a semiclassical two-band model, the perfect charge compensation and high carrier mobilities naturally explain (i) the XMR observed in LaSb and LaBi; (ii) the non-saturating quadratic dependence of XMR on external magnetic field; and (iii) the resistivity plateau in the turn-on temperature behavior at very low temperatures. The explanation of these features without resorting to the topological effect indicates that they should be the common characteristics of all perfectly electron-hole compensated semimetals.

By using first-principles electronic structure calculations, we have studied the magnetic interactions in a proposed BaZn 2 P 2 -based diluted magnetic semiconductor (DMS). For a typical compound Ba(Zn 0.944 Mn 0.056 ) 2 P 2 with only spin doping, due to the superexchange interaction between Mn atoms and the lack of itinerant carriers, the short-range antiferromagnetic coupling dominates. Partially substituting K atoms for Ba atoms, which introduces itinerant hole carriers into the p orbitals of P atoms so as to link distant Mn moments with the spin-polarized hole carriers via the p-d hybridization between P and Mn atoms, is very crucial for the appearance of ferromagnetism in the compound. Furthermore, applying hydrostatic pressure first enhances and then decreases the ferromagnetic coupling in (Ba 0.75 K 0.25 )(Zn 0.944 Mn 0.056 ) 2 P 2 at a turning point around 15 GPa, which results from the combined effects of the pressure-induced variations of electron delocalization and p-d hybridization. Compared with the BaZn 2 As 2 -based DMS, the substitution of P for As can modulate the magnetic coupling effectively. Both the results for BaZn 2 P 2 -based and BaZn 2 As 2 -based DMSs demonstrate that the robust antiferromagnetic (AFM) coupling between the nearest Mn-Mn pairs bridged by anions is harmful to improving the performance of these II-II-V based DMS materials.

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The Lorentz-invariance-violating Weyl and Dirac fermions have recently attracted intensive interests as new types of particles beyond high-energy physics, and they demonstrate novel physical phenomena such as angle-dependent chiral anomaly and topological Lifshitz transition. Here we predict the existence of Lorentz-invariance-violating Dirac fermions in the YPd2Sn class of Heusler alloys that emerge at the boundary between the electron-like and hole-like pockets in the Brillouin zone, based on the first-principles electronic structure calculations. In combination with the fact that this class of materials was all reported to be superconductors, the YPd2Sn class provides an appropriate platform for studying exotic physical properties distinguished from conventional Dirac fermions, especially for realizing possible topological superconductivity.Conceptually by generalizing topological characterization from insulator to metal, it has been realized that the Dirac [1][2][3][4] and Weyl semimetals [5][6][7][8][9] are new classes of three dimensional (3D) topological materials, different from the well-studied 3D topological insulators (TI) [10][11][12][13]. For Dirac semimetals with both timereversal and space-inversion symmetries, a Dirac point is a linear crossing of two doubly-degenerate bands nearby the Fermi energy with its stability protected by additional symmetry such as a certain crystalline symmetry, while a Weyl point can be obtained by breaking either the time-reversal or the space-inversion symmetry in Dirac semimetals, being a linear crossing of two nondegenerate bands nearby the Fermi energy only available in 3D. A Weyl point acts as a magnetic monopole with either positive or negative charge (chirality) in 3D moment space, while a Dirac point represents a pair of magnetic monopoles with opposite charges. Thus, the Dirac and Weyl semimetals possess a large variety of novel phenomena, such as quantum magnetoresistance [14] and chiral anomaly [15]. In addition, the Dirac and Weyl fermions in condensed matter physics correspond to the relativistic Dirac and Weyl fermions in high-energy physics. Nevertheless, the Lorentz invariance is only strictly required in high-energy physics but not necessary in condensed matter physics [16]. This brings hope for condensed matter physicists to discover new types of fermions in real materials.Very recently, the Lorentz-invariance-violating, namely the type-II, Weyl and Dirac fermions were first conceptually proposed and further predicted in several compounds [16][17][18][19][20][21][22] [48,49]. Although the intensive attention has been paid on half Heusler alloys, the likely topological electronic states of full Heusler alloys are rarely studied [50,51].Here, we predict the existence of type-II Dirac fermions in the full Heusler alloys YPd 2 Sn, ScPd 2 Sn, ZrPd 2 Al, HfPd 2 Al, ZrNi 2 Al, and HfNi 2 Al , namely the YPd2Sn class, by using the first-principles electronic structure calculations. For this class, we find that there are three pairs of symmetry-protected type...

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