  The power-law emission and reflection component provide valuable insights
into the accretion process around a black hole. In this work, thanks to the
broadband spectra coverage of \emph{the Nuclear Spectroscopic Telescope Array},
we study the spectral properties for a sample of low-mass black hole X-ray
binaries (BHXRBs). We find that there is a positive correlation between the
photon index $\Gamma$ and the reflection fraction $R$ (the ratio of the coronal
intensity that illuminates the disk to the coronal intensity that reaches the
observer), consistent with previous studies, but except for MAXI J1820+070. It
is quite interesting that this source also deviates from the well-known
``V"-shaped correlation between the photon index $\Gamma$ and the X-ray
luminosity log$L_{\rm X}$, when it is in the bright hard state. More
specifically, the $\Lambda$-shaped correlation between $\Gamma$ and log$L_{\rm
X}$ is observed, as the luminosity decreases by a factor of 3 in a narrow range
from $\sim 10^{38}$ to $10^{37.5}$ $\rm erg~s^{-1}$. Furthermore, we discover a
strong positive correlation between $R$ and the X-ray luminosity for BHXRBs in
the hard state, which puts a constraint on the disk-corona coupling and the
evolution.
