\section{Appendix: Spinor form reflection amplitude in the presence of
interface Rashba spin orbit coupling}

In this appendix, we derive the spinor form reflection amplitude
given by Eq.~(16) in the main text. First, we write down the
following piece-wise scattering wave functions corresponding to the
interfacial potential described by Eq.~(14) in the main text

\begin{equation}
\psi _{\mathbf{k}}\left( \mathbf{r}_{\parallel }\mathbf{,}z>0\right) =\frac{
}{\sqrt{2}}e^{-ik_{z}z}e^{i\mathbf{q\cdot r}_{\parallel }}\chi +\frac{1}
\sqrt{2}}e^{ik_{z}z}e^{i\mathbf{q\cdot r}_{\parallel }}\hat{R}\chi
\tag{A1}
\end{equation
and

\begin{equation}
\psi _{\mathbf{k}}\left( \mathbf{r,}z<0\right)
=\frac{1}{\sqrt{2}}e^{\kappa z}e^{i\mathbf{q\cdot r}_{\parallel
}}\hat{T}\chi   \tag{A2}
\end{equation
where $\mathbf{r}_{\parallel }$ is the in-plane position vector,
$\mathbf{q}$ and $k_{z}$ are the in-plane and perpendicular-to-plane
wave vectors
respectively, $\kappa =\sqrt{k_{b}^{2}-k_{z}^{2}}$with $k_{b}\equiv \sqrt
2m_{e}^{\ast }V_{b}/\hbar ^{2}}$, $\hat{R}$ and $\hat{T}$ are the
$2\times 2$ reflection and transmission amplitude matrices in spin
space, and $\chi $ is an arbitrary spinor.

Now we are ready to determine $\hat{R}$ and $\hat{T}$ matrices by
the following quantum mechanical matching conditions

\begin{equation}
\psi _{\mathbf{k}}\left( \mathbf{r}_{\parallel
}\mathbf{,}0^{+}\right) =\psi _{\mathbf{k}}\left(
\mathbf{r}_{\parallel }\mathbf{,}0^{-}\right)   \tag{A3}
\end{equation
and
\begin{equation}
\psi _{\mathbf{k}}^{\prime }\left( \mathbf{r}_{\parallel }\mathbf{,
0^{+}\right) -\psi _{\mathbf{k}}^{\prime }\left( \mathbf{r}_{\parallel 
\mathbf{,}0^{-}\right) =\left[ \left( k_{b}\lambda _{c}\right) ^{2
\boldsymbol{\sigma }\cdot \left( \mathbf{\hat{p}}\times \mathbf{z}\right)
\right] \psi _{\mathbf{k}}\left( \mathbf{r}_{\parallel
}\mathbf{,}0\right) \tag{A4}
\end{equation
By placing the scattering wave functions into the above two
equations, we find
\begin{equation}
\left( \hat{I}+\hat{R}\right) \chi =\hat{T}\chi   \tag{A5}
\end{equation
and
\begin{equation}
\left( -\kappa \hat{T}-ik_{z}\hat{I}+ik_{z}\hat{R}\right) \chi
=\left[
\left( k_{b}\lambda _{c}\right) ^{2}\boldsymbol{\sigma }\cdot \left( \mathbf
q}\times \mathbf{z}\right) \right] \hat{T}\chi   \tag{A6}
\end{equation
Combining the two equations, we find an equation for $\hat{R}$ only,
\begin{widetext}
\begin{equation}
\left\{ \left[ \left( \kappa -ik_{z}\right) \hat{I}+\left(
k_{b}\lambda
_{c}\right) ^{2}\boldsymbol{\sigma }\cdot \left( \mathbf{q}\times \mathbf{z
\right) \right] \hat{R}+\left( ik_{z}+\kappa \right) \hat{I}+\left(
k_{b}\lambda _{c}\right) ^{2}\boldsymbol{\sigma }\cdot \left( \mathbf{q
\times \mathbf{z}\right) \right\} \chi =0  \tag{A7}
\end{equation
For any $\chi $, the equation is valid if
\begin{equation}
\left[ \left( \kappa -ik_{z}\right) \hat{I}+\left( k_{b}\lambda
_{c}\right)
^{2}\boldsymbol{\sigma }\cdot \left( \mathbf{q}\times \mathbf{z}\right)
\right] \hat{R}+\left( ik_{z}+\kappa \right) \hat{I}+\left(
k_{b}\lambda
_{c}\right) ^{2}\boldsymbol{\sigma }\cdot \left( \mathbf{q}\times \mathbf{z
\right) =0  \tag{A8}  \label{Eq.R=0}
\end{equation
\end{widetext}
From Eq.~(\ref{Eq.R=0}), we find the reflection amplitude matrix
\begin{equation}
\hat{R}=\frac{\left[ -k_{b}^{2}+\left( k_{b}\lambda _{c}\right) ^{4}q^{2
\right] \hat{I}+2i\left( k_{b}\lambda _{c}\right) ^{2}k_{z}\boldsymbol
\sigma }\cdot \left( \mathbf{q}\times \mathbf{z}\right) }{\left(
ik_{z}-\kappa \right) ^{2}-\left( k_{b}\lambda _{c}\right)
^{4}q^{2}} \tag{A9}  \label{R^hat}
\end{equation
. Note that $\hat{R}$ is a unitary matrix as can be easily check via Eq. 
\ref{R^hat}). This unitarity is required by flux conservation.

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