Chin. Phys. B, 2020, Vol. 29(11): 117201    DOI: 10.1088/1674-1056/abbbdb
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# Collective modes of Weyl fermions with repulsive S-wave interaction

Xun-Gao Wang(王勋高)1,2, Huan-Yu Wang(王寰宇)1,2, Jiang-Min Zhang(张江敏)3,4, and Wu-Ming Liu(刘伍明)1,2,5, †
1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
3 Fujian Provincial Key Laboratory of Quantum Manipulation New Energy Materials College of Physics and Energy, Fujian Normal University, Fuzhou 350007, China
4 Fujian Provincial Collaborative Innovation Center for Optoelectronic Semiconductors and Efficient Devices, Xiamen 361005, China
5 Songshan Lake Materials Laboratory, Dongguan 523808, China
 Abstract  We calculate the spin and density susceptibility of Weyl fermions with repulsive S-wave interaction in ultracold gases. Weyl fermions have a linear dispersion, which is qualitatively different from the parabolic dispersion of conventional materials. We find that there are different collective modes for the different strengths of repulsive interaction by solving the poles equations of the susceptibility in the random-phase approximation. In the long-wavelength limit, the sound velocity and the energy gaps vary with the different strengths of the interaction in the zero sound mode and the gapped modes, respectively. The particle–hole continuum is obtained as well, where the imaginary part of the susceptibility is nonzero. Keywords:  ultracold gases      collective modes      random-phase approximation Received:  27 August 2020      Revised:  11 September 2020      Accepted manuscript online:  28 September 2020 Fund: the National Natural Science Foundation of China (Grant No. 2016YFA0301500). Corresponding Authors:  †Corresponding author. E-mail: wliu@iphy.ac.cn

 Fig. 1.  Particle–hole continuum (Landau damping regime) in Weyl fermions. The purple region and the yellow region represent intersubband particle–hole excitations (PHEinter) and intrasubband particle–hole excitations (PHEintra), respectively. Fig. 2.  A sketch of the interaction strength dependence of the sound velocity in the long-wave length limit for the zero sound mode. Here we use the cut-off momentum $\bar{\varLambda }=10$. Fig. 3.  A sketch of the interaction strength dependence of the gap in the long-wave length limit for the gapped modes. There are two branches of gapped modes when $g\alpha {\bar{\varLambda }}^{2}\lt 0.7575$, which corresponds to the dimensionless interaction strength g < 0.299, but there is only one branch of gapped mode when $0.7575\lt g\alpha {\bar{\varLambda }}^{2}\lt 1.515$, Here we use $\bar{\varLambda }=10$. Fig. 4.  Dispersion of the collective modes for the zero sound mode. The dispersion is close to the boundary of the intrasubband particle–hole excitations continuum region from above. Here we use g = 10, $\bar{\varLambda }=10$. Fig. 5.  Dispersion of the collective modes for the one branch of gapped mode. Here we use g = 0.46, $\bar{\varLambda }=10$. Fig. 6.  Dispersion of the collective modes for the one branch of mode. The other branch of gapped mode is very close to the boundary of the intersubband particle–hole excitations continuum region. Here we use g = 0.218, $\bar{\varLambda }=10$.