Integer Quantum Hall Effect in Graphene Channel with p-n Junction at Domain Wall in Ferroelectric Substrate

TL;DR

This study investigates how ferroelectric domain walls induce p-n junctions in graphene, affecting the integer quantum Hall effect with unusual, gate-dependent mode sequences linked to ferroelectric phase transitions.

Contribution

It reveals the impact of ferroelectric domain walls on quantum Hall modes in graphene and introduces the observation of irregular mode sequences related to ferroelectric phase transitions.

Findings

Mode number v varies with gate voltage from integers to fractional values.

Unusual v-numbers are due to different carrier concentrations in ferroelectric domains.

Phase transition affects the carrier concentration difference and quantum Hall modes.

Abstract

We revealed that 180 degree ferroelectrics domain walls (FDWs) in a ferroelectric substrate, which induce p-n junctions in a graphene channel, lead to the nontrivial temperature and gate voltage dependences of the perpendicular and parallel modes of the integer quantum Hall effect. In particular the number of perpendicular modes v, corresponding to the p-n junction across the graphene channel varies with gate voltage increase from small integers to higher fractional numbers, e.g.v=1, 1.5, 2, ... 5.1,..9.1, 23 in the vicinity of the transition from ferroelectric to paraelectric phase.These numbers and their irregular sequence principally differ from the sequence of fractional numbers v=1.5,2.5,... reported earlier. The origin of the unusual v-numbers is significantly different numbers of the edge modes, v1 and v2, corresponding to significantly different concentration of carriers in the left (n1) and right (n1) domains of p-n junction boundary. The concentrations n1 and n2 are determined by the gate voltage and polarization contributions, and so their difference originates from the different direction of spontaneous polarization in different domains of ferroelectric substrate. The difference between n1 and n2 disappears with the vanishing of spontaneous polarization in a paraelectric phase. The phase transition from the ferroelectric to paraelectric phase can take place either with the temperature increase (temperature-induced phase transition) or with the decrease of ferroelectric substrate thickness (thickness-induced phase transition).