Universal magnetotunnel conductance at a Weyl semimetal-layered Chern insulator junction

Abstract: We investigate electronic transport across a junction between a Weyl semimetal (WSM) and a layered Chern insulator (LCI) in the presence of a magnetic field perpendicular to the interface. The topological mismatch between the gapless Weyl semimetal and the momentum-resolved chiral edge modes of the layered Chern insulator leads to interface Fermi-arc states with a qualitatively distinct connectivity: unlike WSM-WSM junctions, the interface Fermi arcs are forced to reconnect through the Brillouin-zone boundary rather than terminating at the projections of the Weyl nodes. We analyze the spectrum and compute the magneto tunnel conductance mediated by the interface-localized states. We find that the conductance increases linearly with magnetic field at low fields and saturates beyond a critical field to a constant value that is independent of microscopic details such as interface coupling, arc geometry, and lattice-scale parameters. This universal saturation reflects a transport mechanism governed by the topological charge pumping associated with the Chern layers, rather than magnetic breakdown between Fermi arcs. We further show that, under specific conditions, a junction between two distinct Weyl semimetals can exhibit a similar saturation behavior, thereby clarifying the topological origin of the observed universality.

• The paper establishes that interface states reconnect through the Brillouin-zone boundary, a topology-enforced structure caused by the layered Chern insulator’s momentum-resolved Chern number.
• The paper finds conductance grows as G = (e³/h²)A·B at low fields and saturates at G_sat = (e²/h)L_y above B_c = φ₀/L_x, independently of interface coupling and band details.
• The paper shows field-induced Weyl-node gaps can produce conductance oscillations or suppress transport, while effective Chern-insulator phases in WSM–WSM junctions reproduce the same universal plateau.

Overview and physical setup

This paper studies electronic transport across a junction between a Weyl semimetal (WSM) and a layered Chern insulator (LCI) in a perpendicular magnetic field. The LCI is a stack of two-dimensional Chern insulators, characterized by a momentum-resolved Chern number, and is fully gapped in the bulk; it supports chiral edge modes for each conserved momentum along the stacking direction. The junction is built from a minimal two-band cubic-lattice model: the WSM phase hosts two Weyl nodes at $(\pm k_0, 0, 0)$ with $k_0 = \pi/2$, while the LCI is obtained from the same parent Hamiltonian by annihilating the Weyl nodes at the Brillouin-zone (BZ) boundary. The interface coupling is parametrized by a hybridization strength $\kappa$ and a pseudospin imbalance $u$ (fixed at $u = 0.5$); a $\sigma_y$ term is excluded because the interface-localized states are pseudospin-polarized along $y$, so such a term cannot contribute to hybridization.

A $90°$ rotation of the LCI slab about $z$ is imposed so that the two lattices remain commensurate at the interface and the WSM Fermi arcs cross the LCI chiral edge modes at right angles in the interface Brillouin zone (IBZ) in the decoupled limit. This is a modeling convenience rather than a physical requirement, but it avoids supercell constructions that would complicate the numerics without altering the physics.

Topologically enforced interface-state connectivity

At $\kappa = 0$, the IBZ contains two decoupled sets of gapless states: the WSM Fermi arcs connecting the projected Weyl nodes, and the LCI chiral edge modes dispersing along $k_0 = \pi/2$0. Upon turning on finite $k_0 = \pi/2$1, exact diagonalization of the slab Hamiltonian shows that the hybridized interface-localized states form continuous open contours that connect the projected Weyl nodes through the boundary of the BZ, rather than terminating at node projections on both ends as in WSM–WSM junctions. Because the LCI hosts no Weyl nodes, there is no bulk charge on that side to terminate the arcs; this reconnection through the IBZ boundary is a direct consequence of the nontrivial momentum-resolved Chern number inherited from the Weyl-node annihilation. The authors report that this connectivity is robust against changes in $k_0 = \pi/2$2 and other microscopic parameters, provided the bulk topology of the two subsystems is unchanged.

Magnetotunnel conductance and universal saturation

The transport mechanism is as follows. At zero field, the gapped LCI bulk admits no low-energy bulk channel, so transport proceeds only through interface-localized states that are localized in $k_0 = \pi/2$3 but propagate in the interface plane. A magnetic field along $k_0 = \pi/2$4 quantizes the WSM bulk into Landau levels (LLs), including a chiral zeroth LL per Weyl node that carries current toward the interface; the interface states then redirect this current into the chiral edge modes of the LCI. The channel counting is the crux: the number of WSM chiral LL modes grows with flux as $k_0 = \pi/2$5, while the number of LCI chiral edge modes is fixed at $k_0 = \pi/2$6, independent of field. Consequently, the conductance grows linearly at low field and saturates once the LL degeneracy exceeds the available edge channels. The saturation value is

$k_0 = \pi/2$7

with a crossover field obtained by equating the channel counts, $k_0 = \pi/2$8. Two universal results follow: the linear-regime conductance $k_0 = \pi/2$9 (with $\kappa$0 the interface area) and $\kappa$1 are both independent of microscopic details — interface coupling $\kappa$2, Fermi-arc geometry, and lattice-scale band parameters. Since $\kappa$3, the saturation occurs at arbitrarily small field in the thermodynamic limit. KWANT simulations for $\kappa$4, $\kappa$5, and several values of $\kappa$6 confirm the linear-then-saturated behavior.

The authors explicitly contrast this with WSM–WSM junctions, where saturation arises from magnetic breakdown between interface Fermi arcs and its value depends on arc separation, intersection angle, and hybridization gap. Here, saturation reflects a topological charge-pumping constraint set by the finite number of Chern edge modes, not breakdown. One caveat is stated plainly: for small $\kappa$7, the momentum-space separation $\kappa$8 between interface arcs shrinks, making inter-arc scattering strong ($\kappa$9), and the conductance fails to saturate at small $u$0. The saturation is nevertheless recovered for larger systems ($u$1), because $u$2 as the system grows. A further caveat is that the contribution of WSM Fermi arcs propagating toward the interface is neglected in the reported tunneling conductance; the authors argue, based on earlier work, that these states only modify the linear component and become negligible for large systems.

Field-induced bulk gap and anomalous oscillations

A striking, somewhat counterintuitive result concerns the velocity ratio $u$3. For $u$4, the conductance oscillates between the saturation value and zero as a function of field, rather than saturating monotonically. The origin is an orbital magnetic field coupling the two Weyl nodes and opening a bulk gap $u$5 at the Weyl point, which gaps the chiral zeroth LL; whenever $u$6 exceeds the chemical potential $u$7, no states carry current and the conductance vanishes. For $u$8, $u$9 increases monotonically with field, so the zero-conductance windows do not appear at the fields studied, whereas for $u = 0.5$0 the induced gap oscillates with field. The paper does not fully characterize the parameter regime in which the gap oscillates, leaving the precise boundary in $u = 0.5$1 space as an open question. This effect also imposes a practical constraint on observing the universal plateau: the chemical potential must lie above the field-induced gap.

WSM–WSM junctions mimicking the LCI

The paper then shows that the universal saturation is not exclusive to genuine LCIs. A magnetic field perpendicular to the Weyl-node separation can gap the nodes pairwise; for sufficiently large node separation $u = 0.5$2, the field-driven insulating state is a layered Chern insulator rather than a trivial insulator. The authors construct a WSM–WSM junction with node separations $u = 0.5$3 (bottom slab, small induced gap, chiral LL intact) and $u = 0.5$4 (top slab, which becomes an effective LCI beyond a threshold flux $u = 0.5$5 for $u = 0.5$6). Beyond this flux, the junction behaves as a WSM–LCI interface and the conductance saturates to the same $u = 0.5$7, insensitive to node separation, $u = 0.5$8, and band-structure parameters. This demonstrates that the universality is tied to the Chern character of the outgoing edge channels, not to the microscopic realization of the LCI.

Robustness to disorder

The authors comment on disorder via the recent result that interface disorder introduces a finite lifetime $u = 0.5$9 and hence a field scale $\sigma_y$0 at which the Fermi-arc dwell time matches $\sigma_y$1. In the high-field regime $\sigma_y$2, inter-arc scattering is ineffective and the conductance matches the clean result; at low fields, disorder can modify the slope of the linear magnetoconductance. The universal saturation itself remains robust because it is fixed by the number of topologically protected chiral edge modes. This robustness argument is qualitative, however; no numerical disorder-averaged conductance is presented in this paper.

Limitations and open questions

Several limitations are conceded or implicit. The $\sigma_y$3 slab rotation restricts the analysis to commensurate, orthogonally crossed arcs; the generic incommensurate case is unaddressed. The failure of saturation at small $\sigma_y$4 and weak $\sigma_y$5 shows that the universal plateau requires $\sigma_y$6, a condition met only asymptotically for finite systems with strong inter-arc coupling. The conductance collapse due to the field-induced Weyl-node gap constrains the accessible chemical-potential window and is characterized only for two values of $\sigma_y$7; the full dependence of $\sigma_y$8 is not established. The disorder analysis is borrowed from prior work rather than computed here, and the neglect of incoming WSM Fermi-arc contributions is justified only in the thermodynamic limit. Finally, the experimental proposal — heterostructures of WSMs with layered quantum anomalous Hall or magnetic topological insulator multilayers — presumes interface quality sufficient to keep $\sigma_y$9 in the regime where arc scattering is subdominant at the accessible fields.

Conclusion

This paper establishes that the WSM–LCI junction hosts interface Fermi arcs with a topologically enforced BZ-boundary reconnection, and that its magnetotunnel conductance follows a universal two-regime form: linear growth $y$0 at low field, saturating to $y$1 beyond $y$2, with both values independent of microscopic details. The universality stems from the fixed number of momentum-resolved Chern edge modes rather than from magnetic breakdown, and it extends to suitably tuned WSM–WSM junctions where the field drives one side into an effective LCI phase. The main open questions are the full parameter dependence of the field-induced Weyl-node gap that can suppress the conductance, and a quantitative treatment of disorder effects on the plateau onset.