So something like that would be great

The Martian Chronicles are quite unlike anythign else (and they’re amazing, imho). You may want to read his other short stories. He wrote quite a few of them. If I had to pick a single one, I’m a fan of ‘All Summer in a Day’. It’s not the best short story he has written but, I don’t know, it works so well.

Not knowing what you liked in the Martian Chronicles (the style, the themes,…), it’s hard to suggest something else that may fit. So, here a few very wide suggestions:

Classical writers, in no order: Richard Matheson. Fritz Leiber. Cordwainer Smith. Isaac Asimov… if you don’t know Asimov already, he wrote a lot (and not just fiction), his most notable SF work would be his Foundation series (the same Foundation Apple butchered in their series adaptation, imho) and his Robots series (that is composed of novels and many, many short stories) he also devised the classical ‘3 laws’ of Robotics. I would suggest you read his Robots short stories. Algernon Blackwood. P.K. Dick (I’m a fan of his novels and short stories, but not all are… work of art so you should be ok with reading some duds next to real true gems). Frederic Brown. Ursula K. Le Guin.

Contemporary writers, I would suggest Paolo Bacigalupi. ‘Pump Six and other stories’ was the very first of his books I read, I was an instant fan. Then there is also Rich Larson, Tade Thompson that are also amazing.

Very personal, I’m a real fan of Robert Reed’s short stories. I stumbled upon him by accident in a French newspaper many, many years ago, as they were publishing a series of SF short stories that summer, and was blown away by his story. So, I started hunting for all he has published ;)

For many years, science fiction prospered as a short story genre, published in the many magazines available (Bradbury also write at that time). So, there is a lot a lot of great work available from that era. Nowadays, a lot of writers keep on publishing great short stories alas there is a lot less magazines to publish them.

If you want to easily find a lot of those great writers (certainly not all of them, but a real good selection that will keep you busy for a while) you may want to get your hands on used copies of the many ‘Year’s Best SF’ anthologies that Gardner Dozois edited from 1984 or so up to his death in 2017, or 2018. There are many more anthologies, mind you but I was never disappointed by his anthologies.

Then, next to SF there are many other genres. Horror for example, a genre that I think thrives in the short story format but is sadly under-appreciated, beside a few mega stars. Stephen King is sure more than worth reading (there is a reason why he is so successful, be it with his very long novels as well as with his short stories) and I enjoy reading him anytime, but there are so, so many more ‘horror’ writers that are worth reading. But since you only mentioned science fiction, and since a few of those authors I consider the most talented can also be quite disturbing to read, I will not go the ‘horror’ road.