Quantization through dissipation: impurity states and the optical quantum Hall effect
Abstract
The integer quantum Hall effect remains the most paradigmatic and remarkable example of exact quantization in condensed matter physics. Its Hall conductivity σxy is fixed to e2/h times an integer to a precision limited only by measurement and independent of disorder or interactions. This robustness has several explanations, each capturing a strikingly different piece of the physics. In Laughlin's gauge argument, flux insertion pumps an integer charge between edges, so quantization follows from gauge invariance alone. The edge-channel picture instead attributes transport to chiral, ballistic 1D channels at the sample boundary, one per filled Landau level. Bulk arguments tie σxy to a topological invariant of the disordered system, with extended states compensating exactly for the current not carried by localized ones. Here we demonstrate an additional route to understanding quantization, rooted in the finite-frequency dissipative electrodynamics of the bulk. Using high-precision terahertz Faraday rotation and numerics, we show that the cyclotron resonance alone does not give quantized plateaus under Kramers-Kronig transformation. Quantization is recovered only once a faint, low-frequency, topologically enforced dissipative contribution from impurity states is included. This dynamical mechanism, hiding in plain sight within the dissipative response, ties the DC value to the finite-frequency optical response and offers a new route to quantization through the optical Hall effect, complementary to previous pictures.
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BibTeX
@misc{tagay2026quantization,
title = {{Quantization through dissipation: impurity states and the optical quantum Hall effect}},
author = {Zhenisbek Tagay and Ahmed Abouelkomsan and Yugo Onishi and Adbhut Gupta and Loren Pfeiffer and Liang Fu and N. P. Armitage},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.40337},
eprint = {2609.40337},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40337},
}
RIS
TY - UNPB
TI - Quantization through dissipation: impurity states and the optical quantum Hall effect
AU - Zhenisbek Tagay
AU - Ahmed Abouelkomsan
AU - Yugo Onishi
AU - Adbhut Gupta
AU - Loren Pfeiffer
AU - Liang Fu
AU - N. P. Armitage
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2609.40337
UR - https://arxiv.org/abs/2609.40337
AB - The integer quantum Hall effect remains the most paradigmatic and remarkable example of exact quantization in condensed matter physics. Its Hall conductivity σ_xy is fixed to e^2/h times an integer to a precision limited only by measurement and independent of disorder or interactions. This robustness has several explanations, each capturing a strikingly different piece of the physics. In Laughlin's gauge argument, flux insertion pumps an integer charge between edges, so quantization follows from gauge invariance alone. The edge-channel picture instead attributes transport to chiral, ballistic 1D channels at the sample boundary, one per filled Landau level. Bulk arguments tie σ_xy to a topological invariant of the disordered system, with extended states compensating exactly for the current not carried by localized ones. Here we demonstrate an additional route to understanding quantization, rooted in the finite-frequency dissipative electrodynamics of the bulk. Using high-precision terahertz Faraday rotation and numerics, we show that the cyclotron resonance alone does not give quantized plateaus under Kramers-Kronig transformation. Quantization is recovered only once a faint, low-frequency, topologically enforced dissipative contribution from impurity states is included. This dynamical mechanism, hiding in plain sight within the dissipative response, ties the DC value to the finite-frequency optical response and offers a new route to quantization through the optical Hall effect, complementary to previous pictures.
ER -