Quantum transport in topological semimetals under magnetic fields (II)

Abstract

We review our recent works on the quantum transport, mainly in topological semimetals and also in topological insulators, organized according to the strength of the magnetic field. At weak magnetic fields, we explain the negative magnetoresistance in topological semimetals and topological insulators by using the semiclassical equations of motion with the nontrivial Berry curvature. We show that the negative magnetoresistance can exist without the chiral anomaly. At strong magnetic fields, we establish theories for the quantum oscillations in topological Weyl, Dirac, and nodal-line semimetals. We propose a new mechanism of 3D quantum Hall effect, via the "wormhole" tunneling through the Weyl orbit formed by the Fermi arcs and Weyl nodes in topological semimetals. In the quantum limit at extremely strong magnetic fields, we find that an unexpected Hall resistance reversal can be understood in terms of the Weyl fermion annihilation. Additionally, in parallel magnetic fields, longitudinal resistance dips in the quantum limit can serve as signatures for topological insulators.

Microscopic theory of magnetoconductivity at low magnetic fields in terms of Berry curvature and orbital magnetic moment

“…In conclusion, we showed the connection between the microscopic theory [1,2] and the Boltzmann theory of magnetotransport at low magnetic fields [5][6][7][8][11][12][13]. We calculated the magnetoconductivity in the linear order of the magnetic field using linear response theory.…”

“…Electric transport in a magnetic field is an extensively studied topic of great importance in solid state physics with a long history [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. A widely used method to calculate conductivity is the semiclassical Boltzmann transport theory with relaxation time approximation [15].…”

“…anomalous Hall effect [16,17] and quantum Hall effect [6]). The Boltzmann theory can also be used to study the magnetoconductivity at low magnetic fields [5,[7][8][9][10][11][12][13]. The Hall conductivity and longitudinal conductivity was shown to have a contribution coming from the Berry curvature in the linear order of the magnetic field [7][8][9][10][11][12][13][14].…”

“…The Boltzmann theory can also be used to study the magnetoconductivity at low magnetic fields [5,[7][8][9][10][11][12][13]. The Hall conductivity and longitudinal conductivity was shown to have a contribution coming from the Berry curvature in the linear order of the magnetic field [7][8][9][10][11][12][13][14]. This gives rise to interesting phenomena such as the negative magnetoresistance without the chiral anomaly [10,12] and the planar Hall effect [11,13] in topological insulators.…”

“…The Hall conductivity and longitudinal conductivity was shown to have a contribution coming from the Berry curvature in the linear order of the magnetic field [7][8][9][10][11][12][13][14]. This gives rise to interesting phenomena such as the negative magnetoresistance without the chiral anomaly [10,12] and the planar Hall effect [11,13] in topological insulators. Such effects were studied in tilted Weyl semimetals [13,14].…”