Type-II pumping beyond resonance principle: From energetic to geometric rules

TL;DR

This paper explores geometric pumping (GP) beyond the traditional resonance principle, highlighting its unique features, relation to topological phase transitions, and experimental detection in ZrTe$_5$ using ultrafast spectroscopy.

Contribution

It introduces the concept of geometric pumping beyond resonance, detailing its fractional, irreversible nature and its connection to topological phase transitions, with experimental validation.

Findings

GP is non-directional and depends on a different probability function than FGR.

GP exhibits fractional and irreversible characteristics.

Experimental detection achieved via ultrafast spectrum in ZrTe$_5$.

Abstract

Conventionally, pumping relies on energetic resonance: energy quanta ${\hbar}{\omega}$ matches the gap $\Delta$. Under linear approximation, this is known as the Fermi golden rule (FGR). However, this principle becomes challenging to apply in the "0/0" limit, where ${\omega},{\Delta}{\rightarrow}0$ simultaneously. In "0/0" scenarios, such as topological phase transition (TPT), a type-II pumping, geometric pumping (GP), is recognized subject to geometric rules, distinguished from type-I dictated by FGR. Type-I features an "arrow of energy", sending particles higher in energy, reflected by FGR's dependence on Fermi distribution $f_v-f_c$ (probabilities of valence and conduction bands). While GP is non-directional, its probability relies on $f_v+f_c-2f_v f_c$ instead, a key signature for detection. In this work, we address: (1) the concept of GP; (2) its features of fractionality, irreversibility, and dependence on TPT; (3) experimental detection with ultra-fast spectrum in coherent phonon driving of ZrTe$_5$.