  M dwarfs are an important source of information when studying and probing the
lower end of the Hertzsprung-Russell (HR) diagram, down to the hydrogen-burning
limit. Being the most numerous and oldest stars in the galaxy, they carry
fundamental information on its chemical history. The presence of molecules in
their atmospheres, along with various condensed species, complicates our
understanding of their physical properties and thus makes the determination of
their fundamental stellar parameters more challenging and difficult. The aim of
this study is to perform a detailed spectroscopic analysis of the
high-resolution H-band spectra of M dwarfs in order to determine their
fundamental stellar parameters and to validate atmospheric models. The present
study will also help us to understand various processes, including dust
formation and depletion of metals onto dust grains in M dwarf atmospheres. The
high spectral resolution also provides a unique opportunity to constrain other
chemical and physical processes that occur in a cool atmosphere The
high-resolution APOGEE spectra of M dwarfs, covering the entire H-band, provide
a unique opportunity to measure their fundamental parameters. We have performed
a detailed spectral synthesis by comparing these high-resolution H-band spectra
to that of the most recent BT-settl model and have obtained fundamental
parameters such as effective temperature, surface gravity, and metallicity
(Teff, log g and [Fe/H]) respectively.
