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Table 1 Raman tensors obtained via APR scattering spectra and first-principle calculation

From: Raman tensor of layered black phosphorus

Mode

Experimental

Calculated

\( {A}_g^1 \)

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\( \left(\begin{array}{ccc}0.064{e}^{i0.24\pi }& 0& 0\\ {}0& 0.025{e}^{i0.05\pi }& 0\\ {}0& 0& 0.033\bullet {e}^{i0.01\pi}\end{array}\right) \)

a1/c1 = 3.33

a1/c1 = 1.94

b1/c1 = 0.21

b1/c1 = 0.76

\( {\varphi}_{a_1{c}_1}=0.23\uppi \)

\( {\varphi}_{a_1{c}_1}=0.23\uppi \)

\( {\varphi}_{b_1{c}_1}=0 \)

\( {\varphi}_{b_1{c}_1}=0.03\uppi \)

B2g

/

\( \left(\begin{array}{ccc}0& 0& 0.08\\ {}0& 0& 0\\ {}0.08& 0& 0\end{array}\right) \)

d

d = 0.08

\( {B}_{3g}^1 \)

/

\( \left(\begin{array}{ccc}0& 0& 0\\ {}0& 0& 0.03\\ {}0& 0.03& 0\end{array}\right) \)

f

f = 0.03

\( {A}_g^2 \)

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\( \left(\begin{array}{ccc}0.43{e}^{i0.29\pi }& 0& 0\\ {}0& 0.0045{e}^{i0.04\pi }& 0\\ {}0& 0& 0.28{e}^{i0.3\pi}\end{array}\right) \)

a2/c2 = 1.39

a2/c2 = 1.54

b2/c2 = 0.45

b2/c2 = 0.016

\( {\varphi}_{a_2{c}_2}=0.44\uppi \)

\( {\varphi}_{a_2{c}_2}=0.01\uppi \)

\( {\varphi}_{b_2{c}_2}=0.28\uppi \)

\( {\varphi}_{b_2{c}_2}=0.26\uppi \)