A path integral approach to electronic friction of a nanometer-sized tip scanning a metal surface

• 作者: Yang Wang Yu Jia
• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2021,（4）
• 所属期刊栏目: CONDENSED MATTER THEORY
• 页码范围: 111-120
• 页数: 10页
• 语种: 英文

摘要

In this work,we study the dissipation mechanism and frictional force of a nanometer-sized tip scanning a metal surface via a path integral approach.The metal,with internal degrees of freedom (c,c+) and a tip with an internal degree of freedom (d,d+) couple with one another by means of an exchanged potential,V.Having integrated out all internal degrees of freedom,we obtain the in-out amplitude.Moreover,we calculate the imaginary part of the in-out amplitude and the frictional force.We find the imaginary part of the in-out amplitude to be positive,and correlated to the sliding velocity in most cases.The frictional force is proportional to the sliding velocity for the case where v ＜ 0.01.However,for cases where v ＞ 0.01,the frictional force demonstrates nonlinear dependence on sliding velocity.