Casimir-Lifshitz Torque Sign Reversal In Topological Nodal-Line Semimetal System

In quantum theory,vacuum is not a real void,there is a zero-point energy quantum fluctuation of electromagnetic field in vacuum.In 1948,Casimir pointed out that the quantum fluctuation would cause an attraction between ideal metal plates placed parallel in a vacuum.In 1956,Lifshitz extended the theory to all practical metal and dielectric materials,showing that the Casimir effect and van der Waals interaction had the same physical origin.In the past half century,the Casimir effect has been studied extensively,revealing some interesting physical phenomena such as critical Casimir effect,thermal Casimir effect and dynamic Casimir effect.In recent years,people have been interested in the Casimir effect in topological quantum materials,and have studied the repulsive Casimir effect in topological insulator,magnetic insulator,Weyl semimetal and other topological quantum materials.Different from other topological quantum materials,topological nodal line semimetal is a special semimetal.From band structures,topological nodal line semimetal has non-trivial valence and conduction bands,which the Fermi surface is an overlapping line or ring in the three-dimensional Brillouin zone,i.e.,the intersection of energy bands will form a continuous closed curve in the lattice momentum space.From the physical properties,the particularity of topological nodal line semimetal is a one-dimensional line nodal and two-dimensional surfaces states(drum-head state)with almost no dispersion.The topological nodal line semimetal quasiparticles have both the properties of relativistic and non relativistic particles,which dispersion relation is significantly different in different directions.In some special directions,the quasiparticles behave like relativistic particles with constant velocity.In the other directions,the quasiparticles behave as non relativistic particles similar to traditional normal two-dimensional electron gas.In view of the unique energy band structure of topological nodal-line semimetal,we systematically studied and calculated the Casimir effect between topological semi-metal Ca3P2 and liquid crystal material 4-cyano-4-n-pentyl cyclohexylphenyl(5 PCH).It is found that the relativistic and non-relativistic properties of the quasiparticles in topological nodal-line semimetal determine the relative strength of polarizability along different principal axes.When near the energy degeneracy point,relativistic particles have higher energy than non relativistic particles,relativistic particles dominate.while far away from the energy degeneracy point,the energy of non relativistic particles will be higher than relativistic particles,at which point the non relativistic particles dominate and the sign of the Casimir-Lifshitz torque is reversed.In short,the competition of relativistic and non relativistic particles of quasiparticles in topological semimetal can change the relative intensity of polarization along different principal axes,leading to a reversal of the Casimir-Lifshitz torque.In this paper,obtain an analytical solution for the dielectric function of the topological nodal-line semimetal by using the flow-flow correlation function,discuss the Casimir-Lifshitz torque between materials with different spatial parameters,and show that the band structure of topological nodal line semimetal can be used to manipulate the Casimir-Lifshitz torque,which proposed three different approaches to generate this symbol reversal,i.e.,tuning the spatial anisotropic parameters or chemical potential in nodal-line semimetal,changing the distance between the topological nodal line semimetal and substrate birefringent material.This paper qualitatively explains the basic reason and physical principle of Casimir-Lifshitz torque symbol reversal of topological nodal-line semimetal,which lays a foundation for realizing torque reversal experimentally,and provides help for finding new topological nodal-line semimetal and observing more topological effects in the future.