Longitudinal magnetoconductivity in chiral multifold semimetals exemplified by pseudospin-1 nodal points

TL;DR

This work investigates the longitudinal magnetoconductivity in isotropic pseudospin-1 triple-point semimetals under collinear electric and magnetic fields, incorporating a leading quadratic correction to remove the flat-band artefact. By solving the Boltzmann equation exactly in the linear-response regime and including Berry curvature and orbital magnetic moment corrections, the authors uncover how intra- and inter-node scattering, as well as interband processes, shape the B-dependent transport, with significant contributions arising from the quadratic term even for the s=0 band. The results reveal a rich, tunable magnetoconductivity landscape: the BC- and OMM-induced parts can compete and even flip sign depending on the internode/intranode scattering ratios, and internode scattering typically dominates the response. A key finding is the inadequacy of the relaxation-time approximation to capture these effects, highlighting the importance of beyond-RTA treatments in multifold semimetals. The study lays a foundation for interpreting experiments on multifold fermions and points to future work on noncollinear fields, tilts, and magneto-optical or tunneling phenomena in quadratic-corrected TSMs.

Abstract

We embark on computing the longitudinal magnetoconductivity within the semiclassical Boltzmann formalism, where an isotropic triple-point semimetal (TSM) is subjected to collinear electric ($\boldsymbol E $) and magnetic ($\boldsymbol B$) fields. Except for the Drude part, the $B$-dependence arises exclusively from topological properties like the Berry curvature and the orbital magnetic moment. We solve the Boltzmann equations exactly in the linear-response regime, applicable in the limit of weak/nonquantising magnetic fields. The novelty of our investigation lies in the consideration of the truly multifold character of the TSMs, where the so-called flat-band (flatness being merely an artefact of linear-order approximations) is made dispersive by incorporating the appropriate quadratic-in-momentum correction in the effective Hamiltonian. It necessitates the consideration of interband scatterings within the same node as well, providing a complex interplay of intraband, interband, intranode, and internode processes, offering an overwhelmingly rich set of possibilities. The exact results are compared with those obtained from a naive relaxation-time approximation.

Figures (6)

• Figure 1: Schematics of the scattering processes between two nodes in a TSM, carrying opposite values of chirality. The values of the chemical potential, represented by the yellow planes, have been tuned to cut the positive-energy bands at each node.
• Figure 2: $\delta \sigma_{zz}$ from the $\{s, \tilde{s}\} = \{1,1\}$ bands with no interaction with the $\{s, \tilde{s}\} = \{0,0\}$ bands: While the top panel shows the variation of the full conductivity with $B$ (in eV$^2$) when OMM is taken into account appropriately, the bottom panel represents conductivity versus $B$ when OMM is not considered. The plot-legends indicate the values of the ratio $\beta^{\rm inter}_{1,1} / \beta^{\rm intra}_{1,1}$. The three subfigures represent three distinct sets of parameter values, as indicated in the labels.
• Figure 3: $\delta \sigma_{zz}$ from the $\{s, \tilde{s}\} = \{0,0\}$ bands with no interaction with the $\{s, \tilde{s}\} = \{1,1\}$ bands: The curves demonstrate the variation of conductivity with $B$ (in eV$^2$). Here, the $B$-dependence is entirely caused by the OMM, since BC is zero for these bands. The top, middle, and bottom panels represent the results for the $\chi=+1$ node, $\chi =-1$ node, and sum over both the nodes, respectively. The plot-legends indicate the values of the ratio $\beta^{\rm inter}_{0,0} / \beta^{\rm intra}_{0,0}$. The three subfigures represent three distinct sets of parameter values, as indicated in the labels.
• Figure 4: $\delta \sigma_{zz}$ from the $\{s, \tilde{s}\} = \{1,1\}$ bands interacting mutually and with the $\{s, \tilde{s}\} = \{0,0\}$ bands: While the top panel shows the variation of the full conductivity against $B$ (in eV$^2$) when OMM is taken into account appropriately, the bottom panel represents conductivity versus $B$ when OMM is omitted. The plot-legends indicate the values of the ratios $\lbrace \beta^{\rm inter}_{s,\tilde{s}} / \beta^{\rm intra}_{s,\tilde{s}} \rbrace$. The three subfigures represent three distinct sets of parameter values, as indicated in the labels.
• Figure 5: $\delta \sigma_{zz}$ from the $\{s, \tilde{s}\} = \{0,0\}$ bands interacting mutually and with the $\{s, \tilde{s}\} = \{1,1\}$ bands: The curves demonstrate the variation of conductivity with $B$ (in eV$^2$). The top, middle, and bottom panels represent the results for the $\chi=+1$ node, $\chi =-1$ node, and sum over both the nodes, respectively. The plot-legends indicate the values of the ratios $\lbrace \beta^{\rm inter}_{s,\tilde{s}} / \beta^{\rm intra}_{s,\tilde{s}} \rbrace$. The three subfigures represent three distinct sets of parameter values, as indicated in the labels.