Quantum Geometric Friedel Oscillations

Abstract

In conventional Friedel oscillations, the real-space charge density oscillations induced by an impurity are characterized by an oscillation period set by the Fermi momentum. In this work, we demonstrate that in metals with an isolated (nearly) flat band at the Fermi energy, quantum geometry induces a distinct type of oscillations, which we call the \emph{quantum geometric Friedel oscillations} (QGFOs). The period of the QGFOs is set by the momentum-space separation of the quantum metric hot spots of the isolated band. The conventional and quantum metric-induced oscillations can coexist at low temperatures. At higher temperatures, the conventional Friedel oscillation amplitudes away from the impurity site are set by the thermal length such that the oscillations can be easily washed out by temperature effects. Remarkably, the QGFOs decay length is set by the quantum metric length which is defined by the integration of the quantum metric of the isolated band. As a result, the QGFOs can persist even at temperatures much larger than the bandwidth of the isolated flat band. Moreover, the decay length is invariant for a wide range of temperature which is a striking result. In conclusion, we show that the quantum metric induces novel Friedel oscillations. Our work suggests that the measurement of the QGFOs is a powerful way to detect the quantum metric length (which is associated with the integral of the quantum metric) and the quantum metric hot spot separations (which are associated with the distribution of the quantum metric in the momentum space).