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...

We have studied the transport and low-field magnetotransport of the two-dimensional electron gas in GaAs-Al"Gal As heterostructures in the weak-localization regime and determined the localization parameter (a=0.75 -0.85), the interaction coefficient (1 -F=0.5 -3.2), the inelastic scattering time v;", and its temperature exponent (P=1.0). The experiment shows unambiguously the importance of both the localization effect and the interaction effects. While the observation of a & 1 is explained by the importance of the Maki-Thompson scattering process, also operative in our case of the repulsive electron-electron interaction, several outstanding features of the data remain unexplained.They include the following: (1)~;"being 10 times larger than theory, (2) 1 -F at a high density being 5 times its expected value, and (3) a temperature-sensitive negative magnetoresistance in parallel B.

/ 31Graphene and surface states of topological insulators (TIs) can be described by two-dimensional (2D) massless Dirac Hamiltonian at the low energy excitations, which can be further modulated by adatom adsorption or interfacing with other functional materials [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Owing to the high carrier mobility and unique spin textures, TIs and graphene are promising for high speed electronics and spintronics [16]. Recent theories [8][9][10][11] have predicted the hybridization of graphene and TIs can create nontrivial spin textures in graphene, even leading to quantum spin Hall states [1]. Generally, the rigorous √3 × √3 supercell of graphene stacked with TI is adopted in the calculations [8][9][10][11]. For the incommensurate graphene-TI stacking,Zhang et al. [10] suggested that the renormalized bands of hybrid graphene still acquire the in-plane spin textures from the surface states of TI even in the presence of surface roughness at the heterointerface. The coupling between graphene and TI has been pursued via the angle resolved photoemission spectroscopy (ARPES) Gate-tunable conductivity of the hybrid device is shown in Fig. 1b These observations can be understood in the framework of the graphene-TI proximity effect that was theoretically predicted via band calculations in Refs. [8][9][10][11]. Under the magnetic field perpendicular to the graphene plane, the unevenly spaced energy spectrum is expressed as = ( )√2 ℏ 2 | | , where ℏ is reduced Planck's constant, the Fermi velocity is ~10 6 ⁄ , and the LL index N is positive for electrons and negative for holes [12,13]. The half-filled LLs, such as N = −3, −2, Fig. 3). We should realize that the possible coupling between graphene and TI surface states is the second (or higher) order effect [8][9][10][11]. The hopping process between the orbitals of carbon atoms in graphene and orbitals of the bottom surface states in Bi 2 Se 3 nanoribbons introduces significant influences on the transport properties in graphene near the Dirac point.Anomalous magnetotransport features at Dirac point. Now we discuss the magnetotransport at the Dirac point (or the zeroth LL) in the graphene hybrid device.The evolution of ( * ) curves near the Dirac point at various temperatures andunder negative magnetic fields is shown in Fig. 3a (see Supplementary Fig. 4 for the evolution of ( * )). The curves are shifted for clarity. The resistivity at the Dirac point ( ) versus B is extracted and shown in Fig. 3b,c. In the classical regime, the two-carrier model can be used to describe a zero-gap conductor with the same mobility for electrons and holes, giving Predicted by theoretical models [8][9][10][11], graphene can inherit spin-orbital textures from TI surface states near the Dirac point due to the proximity effect. Accordingly, we summarize the reforming band structures of graphene hybridized with TI surface in Fig. 4. As the interaction between graphene and TI is significant, the fourfold degeneracy of the original graphene bands (Fig. 4a) is par...

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The mobility of the two-dimensional electron gas in GaAs-Alx Ga1−xAs heterostructures was studied systematically in ten samples with density from 1.33×1011 to 7.8×1011 cm−2 in the temperature range T=4.2–300 K. A theoretical calculation using the variational wave function was carried out for scattering by screened impurity ions, optical phonons, and acoustic phonons through deformation and piezoelectric couplings. Good quantitative agreement between theory and experiment was obtained with no adjustable parameters.