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Let $X$ be a mixed graph and $\omega=\frac{1+\i \sqrt{3}}{2}$. We write$i\rightarrow j$, if there is an oriented edge from a vertex $v_i$ to anothervertex $v_j$, and $i\sim j$ for an un-oriented edge between the vertices $v_i$and $v_j$. The degree of a vertex $v_i$ is denoted by $d_i$. We propose theHermitian Randi\'c matrix of second kind $R^\omeg(X)\coloneqq(R^\omeg_{ij})$,where $R^\omeg_{ij}=\frac{1}{\sqrt{d_id_j}}$ if $i \sim j$, $R^\omeg_{ij}=\frac{\omega}{\sqrt{d_id_j}}$ and $R^\omeg_{ji}=\frac{\overline{\omega}}{\sqrt{d_id_j}}$ if $i\rightarrow j$, and 0 otherwise.In this paper, we investigate some spectral features of this novel Hermitianmatrix and study a few properties like positiveness, bipartiteness,edge-interlacing etc. We also compute the characteristic polynomial for thisnew matrix and obtain some upper and lower bounds for the eigenvalues and theenergy of this matrix.

On spectra of Hermitian Randi\'c matrix of second kind