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The Early Data Release (EDR) of the Dark Energy Spectroscopic Instrument (DESI) comprises spectroscopy obtained from 2020 December 14 to 2021 June 10. White dwarfs were targeted by DESI both as calibration sources and as science targets and were selected based on Gaia photometry and astrometry. Here, we present the DESI EDR white dwarf catalogue, which includes 2706 spectroscopically confirmed white dwarfs of which approximately 60 per cent have been spectroscopically observed for the first time, as well as 66 white dwarf binary systems. We provide spectral classifications for all white dwarfs, and discuss their distribution within the Gaia Hertzsprung–Russell diagram. We provide atmospheric parameters derived from spectroscopic and photometric fits for white dwarfs with pure hydrogen or helium photospheres, a mixture of those two, and white dwarfs displaying carbon features in their spectra. We also discuss the less abundant systems in the sample, such as those with magnetic fields, and cataclysmic variables. The DESI EDR white dwarf sample is significantly less biased than the sample observed by the Sloan Digital Sky Survey, which is skewed to bluer and therefore hotter white dwarfs, making DESI more complete and suitable for performing statistical studies of white dwarfs. [ABSTRACT FROM AUTHOR]

A total of 1–3 per cent of white dwarfs are orbited by planetary dusty debris detectable as infrared emission in excess above the white dwarf flux. In a rare subset of these systems, a gaseous disc component is also detected via emission lines of the Ca  ii 8600 Å triplet, broadened by the Keplerian velocity of the disc. We present the first statistical study of the fraction of debris discs containing detectable amounts of gas in emission at white dwarfs within a magnitude and signal-to-noise ratio limited sample. We select 7705 single white dwarfs spectroscopically observed by the Sloan Digital Sky Survey (SDSS) and Gaia with magnitudes g  ≤ 19. We identify five gaseous disc hosts, all of which have been previously discovered. We calculate the occurrence rate of a white dwarf hosting a debris disc detectable via Ca  ii emission lines as |$0.067\, \pm \, ^{0.042}_{0.025}$|  per cent. This corresponds to an occurrence rate for a dusty debris disc to have an observable gaseous component in emission as 4 ±  |$_{2}^{4}$|  per cent. Given that variability is a common feature of the emission profiles of gaseous debris discs, and the recent detection of a planetesimal orbiting within the disc of SDSS J122859.93+104032.9, we propose that gaseous components are tracers for the presence of planetesimals embedded in the discs and outline a qualitative model. We also present spectroscopy of the Ca  ii triplet 8600 Å region for 20 white dwarfs hosting dusty debris discs in an attempt to identify gaseous emission. We do not detect any gaseous components in these 20 systems, consistent with the occurrence rate that we calculated. [ABSTRACT FROM AUTHOR]