Heidegger wouldn’t start a dictatorship. Let’s get that off the bat straight away.
Martin Heidegger was a philosopher in 1920s and 1930s Germany. It is hardly surprising that he joined the Nazi Party to keep his job, although he may have had some genuine sympathies with National Socialism. His major work was Being and Time published in 1927, examining what it means to be in the world. Here’s a useful link Dasein
Would Erwin Schrödinger be any keener on dictatorships? I doubt it. He fled Nazi-ruled Vienna and travelled to Dublin with his wife and lover.His subject was Physics and he has published many books, such as What is Life, published in 1941.
He is famous for a thought experiment that he devised to explain the theoretical effects of quantum physics. In a sense, he too was interested in ‘being in the world’. The cat in the box thought experiment was intended to ridicule the theory that things can have different states of being and non-being at the same time.