  Terrestrial extrasolar planets around low-mass stars are prime targets when
searching for atmospheric biosignatures with current and near-future
telescopes. The habitable-zone Super-Earth LHS 1140 b could hold a
hydrogen-dominated atmosphere and is an excellent candidate for detecting
atmospheric features. In this study, we investigate how the instellation and
planetary parameters influence the atmospheric climate, chemistry, and spectral
appearance of LHS 1140 b. We study the detectability of selected molecules, in
particular potential biosignatures, with the upcoming James Webb Space
Telescope (JWST) and Extremely Large Telescope (ELT). In a first step we use
the coupled climate-chemistry model, 1D-TERRA, to simulate a range of assumed
atmospheric chemical compositions dominated by H$_2$ and CO$_2$. Further, we
vary the concentrations of CH$_4$ by several orders of magnitude. In a second
step we calculate transmission spectra of the simulated atmospheres and compare
them to recent transit observations. Finally, we determine the observation time
required to detect spectral bands with low resolution spectroscopy using JWST
and the cross-correlation technique using ELT. In H$_2$-dominated and
CH$_4$-rich atmospheres O$_2$ has strong chemical sinks, leading to low
concentrations of O$_2$ and O$_3$. The potential biosignatures NH$_3$, PH$_3$,
CH$_3$Cl and N$_2$O are less sensitive to the concentration of H$_2$, CO$_2$
and CH$_4$ in the atmosphere. In the simulated H$_2$-dominated atmosphere the
detection of these gases might be feasible within 20 to 100 observation hours
with ELT or JWST, when assuming weak extinction by hazes. If further
observations of LHS 1140 b suggest a thin, clear, hydrogen-dominated
atmosphere, the planet would be one of the best known targets to detect
biosignature gases in the atmosphere of a habitable-zone rocky exoplanet with
upcoming telescopes.
