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arXiv · 2206.11188

Universal properties of boundary and interface charges in multichannel one-dimensional continuum models

Kiryl Piasotski·Niclas Müller·Dante M. Kennes·Herbert Schoeller·Mikhail Pletyukhov
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Abstract

We generalize our recent results for the boundary and interface charges in one-dimensional single-channel continuum [Phys. Rev. B 104, 155409 (2021)] and multichannel tight-binding [Phys. Rev. B 104, 125447 (2021)] models to the realm of the multichannel continuum systems. Using the technique of boundary Green's functions, we give a rigorous proof that the change in boundary charge upon the shift of the system towards the boundary by the distance $x_{\varphi}\in[0, L]$ is given by a perfectly linear function of $x_{\varphi}$ plus an integer-valued topological invariant $I$ -- the so called boundary invariant. For systems with weak potential amplitudes, we additionally develop Green's function-based low-energy theory, allowing one to analytically access the physics of multichannel continuum systems in the low-energy approximation.

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Kiryl Piasotski, Niclas Müller, Dante M. Kennes, Herbert Schoeller, Mikhail Pletyukhov. 2022-06-22. Universal properties of boundary and interface charges in multichannel one-dimensional continuum models. https://doi.org/10.1103/physrevb.106.165405

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