Topological semimetals are well known for the linear energy band dispersion in the bulk state and topologically protected surface state with arc-like Fermi surface. The angle resolved photoemission spectroscopy experiments help confirm the existence of linear Dirac (Weyl) cone and Fermi arc. Meantime, the transport experiments are very important for its intimate relationship with possible applications. In this concise review, recent developments of quantum transport in two typical topological semimetals, namely Dirac and Weyl semimetals, are described. The 3D Dirac semimetal phase is revealed by the Shubnikov-de Haas oscillations. The Weyl Fermions-related chiral anomaly effect is evident by negative magnetoresistance, thermal power suppression, and nonlocal measurements. The Fermi arc mechanism is discussed and several corresponding transport evidences have been described. The point contact-induced superconductivity in Dirac and Weyl semimetal is also introduced. Perspectives about the development of topological semimetals and topological superconductors are provided.

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Dirac semimetals [1], such as Cd 3 As 2 or Na 3 Bi [2][3][4][5][6][7][8][9][10], show a linear electronic dispersion in three dimensions described by two copies of the Weyl equation. Applying a magnetic field can break the time reversal symmetry, and the Dirac semimetal is transformed into a Weyl semimetal with the two Weyl nodes separated in the momentum space [10,11]. Chiral charge pumping between the Weyl nodes with different chirality is predicted, which brings the Weyl fermions into the experimental realm. Recently, anomalous transport properties signaled by a pronounced negative magnetoresistance are observed as the evidence for the chiral anomaly effect [10,12].Besides this, the surface dispersion-relation of a Weyl semimetal is topologically equivalent to a non-compact Riemann surface without equal-energy contour that encloses the projection of the Weyl point [13], leading to the emergence of surface Fermi arcs [14]. Lots of angle-resolved photoemission spectroscopy (ARPES) experiments [7,[15][16][17][18] [16,19,[32][33][34][35][36][37][38]. Although the one-dimensional helical transport has been demonstrated in topological insulator nanowires through measuring the AB oscillations is the flux quantum and , where is the measured magnetic field periodicity ( in this case) and S is the cross-sectional area.From the magnetic field periodicity, we can deduce the cross-sectional area to be , which is consistent with the nanowire diameter ~58 nm. In To further clearly present the conductance oscillations, we plot the mapping of ∆G versus gate voltage and magnetic field in Fig. 1d. Clearly there are two kinds of phase modulations on the interference. One is tuned by gate voltage, and the other is influenced by the magnetic field. At a fixed gate voltage, if the conductance reaches the minimum at zero magnetic field, the conductance will be the maximum at half integer multiple of ; if the conductance is maximum at zero magnetic field, the conductance will be the maximum at integer multiple of . The phase of the AB interference is strongly dependent on gate voltage. while when the chirality is -1, the energy dispersion has a similar form with a sign 6 change. This physics picture is depicted in Fig. 2. At zero magnetic field, that is =0, the original linear energy dispersion becomes gapped with a series of sub-bands, as shown in Fig. 2a. The red and blue lines represent the chirality to be +1 and -1, respectively. According to the surface band splitting, there should emerge a periodic oscillation when the Fermi level crosses the sub-bands continuously. This is what happens in our Cd 3 As 2 nanowires, as shown in Fig. 1b.When a magnetic field is applied, the corresponding AB oscillation term should be considered. The surface energy band diagrams at the magnetic flux and are depicted in Fig. 2b, where the letter L and R denote the chirality of Weyl nodes to be +1 or −1. Apparently, when the magnetic flux is half integer of Ф 0 , the linear energy band with specified chirality emerges. The quantum transport can be...