We study the linear response of the deformation potential of a chiral two-orbital superconductor Sr\(_2\)RuO\(_4\) to the applied strain. This response rises due to the strain-induced modified interatomic distances. In the linear response theory, the deformation potential–deformation potential correlation function defines the full complex frequency-dependent viscosity tensor. We calculate the anti-symmetric part of this tensor, the phonon Hall viscosity, to consider the static and dynamical Hall responses. The static phonon Hall static enables us to distinguish the different topological phases of Sr\(_2\)RuO\(_4\). We focus on two regimes: (a) the phonon Hall viscosity due to the changes in the hopping energies of the tight-binding Hamiltonian and is termed the normal phonon Hall viscosity and (b) the phonon Hall viscosity due to the variation in the amplitudes of the order parameter of the superconducting state that causes an anomalous momentum transport coefficient and is analogous to the one-dimensional odd isotropic part of the viscosity tensor of an incompressible fluid in two dimension space. In both cases, the tetragonal crystal symmetry which corresponds to the isotropy in the system plays an important role. We also investigate the effect of the crystal symmetry on the stability of the nontrivial topological phase.

我们研究了手性两轨道超导体Sr \（_ 2 \） RuO \（_ 4 \）的形变势对所施加应变的线性响应。由于应变引起的修改的原子间距离，该响应增加。在线性响应理论中，形变电势-形变电势的相关函数定义了完全复数随频率变化的粘度张量。我们计算该张量的反对称部分，即声子霍尔粘度，以考虑静态和动态霍尔响应。静态声子Hall静电使我们能够区分Sr \（_ 2 \） RuO \（_ 4 \）的不同拓扑阶段。我们关注两种情况：（a）由于紧密结合的哈密顿量的跃迁能量的变化而产生的声子霍尔粘度，并且被称为正常声子霍尔粘度，（b）由于振幅的变化而引起的声子霍尔粘度。导致异常动量传输系数的超导状态的阶数参数的近似，类似于二维空间中不可压缩流体的粘度张量的一维奇数各向同性部分。在这两种情况下，对应于系统各向同性的四方晶体对称性都起着重要的作用。我们还研究了晶体对称性对非平凡拓扑相稳定性的影响。