Proximity effects and a topological invariant in a Chern insulator connected to leads

The observed robustly quantized Hall conductance in quantum Hall systems and Chern insulators (CI) have so far been understood in terms of the topology of isolated systems, which are not coupled to leads. It is assumed that the leads act as inert reservoirs that simply supply/absorb electrons to/from the sample. Within a model of a CI coupled to leads with a cylindrical geometry, we show that this is not true. In the proximity of the CI, the edge current leaks into the leads, with the Hall conductance quantized only if this novel proximity effect is taken into account. For a special choice of leads, we identify the conductance with a topological invariant of the system, in terms of the winding number of the phase of the reflection coefficients of the scattering states.

💡 Research Summary

The paper investigates how the Hall conductance of a Chern insulator (CI) is affected when it is coupled to metallic leads, a situation that more closely resembles experimental setups than the idealized isolated systems traditionally considered in topological band theory. Using a two‑dimensional spinless Bernevig‑Hughes‑Zhang (SBHZ) model placed on a cylindrical lattice, the authors attach semi‑infinite leads at the two ends along the longitudinal (x) direction while imposing periodic boundary conditions in the transverse (y) direction. This geometry allows a Fourier transform in y, reducing the problem to a set of independent one‑dimensional chains, each equivalent to a Rice‑Mele model with k‑dependent onsite potentials and alternating hoppings.

The transport properties are calculated with two complementary microscopic approaches: the non‑equilibrium Green’s function (NEGF) formalism and a scattering‑state analysis based on transfer‑matrix techniques. Within NEGF, the steady‑state two‑point correlation matrix yields the longitudinal current, and the Hall conductance G_H = ∂J_y/∂μ is expressed in terms of the Green’s function of each 1D chain, G̃_m(ω) =