Understanding the three-dimensional quantum Hall effect in generic multi-Weyl semimetals

Abstract

The quantum Hall effect in three-dimensional Weyl semimetal (WSM) receives significant attention for the emergence of the Fermi loop where the underlying two-dimensional Hall conductivity, namely, sheet Hall conductivity, shows quantized plateaus. Considering the tilted lattice models for multi Weyl semimetals (mWSMs), we systematically study the Landau levels (LLs) and magneto-Hall conductivity in the presence of parallel and perpendicular (with respect to the Weyl node's separation) magnetic field, i.e., $\mathbf{B}\parallel z$ and $\mathbf{B}\parallel x$, to explore the impact of tilting and non-linearity in the dispersion. We make use of two (single) node low-energy models to qualitatively explain the emergence of mid-gap chiral (linear crossing of chiral) LLs on the lattice for $\mathbf{B}\parallel z$ ($\mathbf{B}\parallel x$). Remarkably, we find that the sheet Hall conductivity becomes quantized for $\mathbf{B}\parallel z$ even when two Weyl nodes project onto a single Fermi point in two opposite surfaces, forming a Fermi loop with $k_z$ as the good quantum number. On the other hand, the Fermi loop, connecting two distinct Fermi points in two opposite surfaces, with $k_x$ being the good quantum number, causes the quantization in sheet Hall conductivity for $\mathbf{B}\parallel x$. The quantization is almost lost (perfectly remained) in the type-II phase for $\mathbf{B}\parallel x$ ($\mathbf{B}\parallel z$). Interestingly, the jump profiles between the adjacent quantized plateaus change with the topological charge for both of the above cases. The momentum-integrated three-dimensional Hall conductivity is not quantized; however, it bears the signature of chiral LLs as resulting in the linear dependence on $\mu$ for small $\mu$. The linear zone (its slope) reduces (increases) as the tilt (topological charge) of the underlying WSM increases.

19 pages and 9 figures

References in corpus (28)

• Topological response in Weyl semimetals and the chiral anomaly
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator
• Anomalous Hall Effect in Weyl Metals
• Novel electric field effects on Landau levels in Graphene
• Chiral Decomposition in the Electronic Structure of Graphene Multilayers
• Thermoelectric properties of Weyl and Dirac semimetals
• Observation of the quantum Hall effect in confined films of the three-dimensional Dirac semimetal Cd3As2
• Quantum Hall states observed in thin films of Dirac semimetal Cd3As2
• Plasmon mode as a detection of the chiral anomaly in Weyl semimetals
• Algebraic solution of a graphene layer in a transverse electric and perpendicular magnetic fields
• Anomalous Nernst and Thermal Hall Effects in Tilted Weyl Semimetals
• Theory for the Charge-Density-Wave Mechanism of 3D Quantum Hall Effect
• Nonlinear transport in Weyl semimetals induced by Berry curvature dipole
• 3D Quantum Hall Effect Manipulated by Chiral Landau Levels in Weyl Semimetals
• Weyl fermions with arbitrary monopole in magnetic fields: Landau levels, longitudinal magnetotransport, and density-wave ordering
• Signature of tilted Dirac cones in Weiss oscillations of $8-Pmmn$ borophene
• Origin of the quasi-quantized Hall effect in ZrTe5
• Anomalous thermoelectric phenomena in lattice models of multi-Weyl semimetals
• Absorption of circular polarized light in tilted Type-I and II Weyl semimetals
• Role of time reversal symmetry and tilting in circular photogalvanic responses
• Electronic structure and unconventional non-linear response in double Weyl semimetal SrSi${}_2$
• Theory for magnetic-field-driven 3D metal-insulator transitions in the quantum limit
• Topological Magnus responses in two and three dimensional systems
• Three-dimensional quantum Hall effect and magnetothermoelectric properties in Weyl semimetals
• Quantum Hall effect originated from helical edge states in Cd${}_3$As${}_2$
• Distinct signatures of particle-hole symmetry breaking in transport coefficients for generic multi-Weyl semimetals
• Time-reversal-broken Weyl semimetal in the Hofstadter regime

Cited by in corpus (16)

• Effect of chirality imbalance on Hall transport of PrRhC${}_2$
• Landau level spectrum and magneto-optical conductivity in tilted Weyl semimetal
• Entropy and Temperature in finite isolated quantum systems
• Two Types of 3D Quantum Hall Effects in Multilayer WTe${}_2$
• Magnetic field driven Lifshitz transition and one-dimensional Weyl nodes in three-dimensional pentatellurides
• Quantum oscillations of the nonlinear planar effects signifying chiral anomaly in Weyl Semimetals
• Fractional Quantum Hall Effect Based on Weyl Orbits
• Distinct quasiparticle interference patterns for surface impurity scattering on various Weyl semimetals
• Magneto-Seebeck coefficient of Fermi-liquid in three-dimensional Dirac/Weyl semimetal
• Topological semimetal with coexisting nodal points and nodal lines
• Quantum Hall Effect in a Weyl-Hubbard Model: Interplay between Topology and Correlation
• Fano resonances in tilted Weyl semimetals in an oscillating quantum well
• Three-Dimensional Quantum Hall Effect in Topological Amorphous Metals
• Transitions from Composite Fermi Liquid to Moore-Read States in Weyl Semimetals
• Impact of Broken Inversion Symmetry on Molecular States in multi-Weyl fermions
• The orbital-driven topological phase transition and planar Hall responses in ternary tellurides Weyl semi-metals