Komissarov Ilia, Holder Tobias, Queiroz Raquel
Department of Physics, Columbia University, New York, NY, 10027, USA.
School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel.
Nat Commun. 2024 May 30;15(1):4621. doi: 10.1038/s41467-024-48808-x.
In band insulators, without a Fermi surface, adiabatic transport can exist due to the geometry of the ground state wavefunction. Here we show that for systems driven at a small but finite frequency ω, transport likewise depends sensitively on quantum geometry. We make this statement precise by expressing the Kubo formula for conductivity as the variation of the time-dependent polarization with respect to the applied field. We find that at linear order in frequency, the longitudinal conductivity results from an intrinsic capacitance determined by the ratio of the quantum metric and the spectral gap, establishing a fundamental link between the dielectric response and the quantum metric of insulators. We demonstrate that quantum geometry is responsible for the electronic contribution to the dielectric constant in a wide range of insulators, including the free electron gas in a quantizing magnetic field, for which we show the capacitance is quantized. We also study gapped bands of hBN-aligned twisted bilayer graphene and obstructed atomic insulators such as diamond. In the latter, we find its abnormally large refractive index to have a topological origin.
在能带绝缘体中，由于基态波函数的几何结构，即使没有费米面，绝热输运也可能存在。在此我们表明，对于以小但有限频率ω驱动的系统，输运同样敏感地依赖于量子几何。我们通过将电导率的久保公式表示为随时间变化的极化相对于外加场的变化，使这一表述精确化。我们发现，在频率的线性阶次下，纵向电导率源于由量子度规与能隙之比所确定的本征电容，从而在绝缘体的介电响应与量子度规之间建立了基本联系。我们证明，量子几何在广泛的绝缘体中对介电常数的电子贡献起作用，包括处于量子化磁场中的自由电子气，我们表明其电容是量子化的。我们还研究了hBN取向的扭曲双层石墨烯的带隙以及诸如金刚石等受阻原子绝缘体。在后者中，我们发现其异常大的折射率具有拓扑起源。
