Can't override a style of a deeply nested component (Material-UI Jss Styling)

The &$ syntax references a rule in the same style sheet, you need to create an expanded rule and pass it into the classes object e.g.

const styles = theme => ({
  expandIcon: {
    "&$expanded": {
      transform: "translateY(-50%) rotate(90deg)"
    }
  },
  expanded: {},
});

<ExpansionPanelSummary
  expandIcon={<ExpandMoreIcon />}
  classes={{
    expandIcon: classes.expandIcon,
    expanded: classes.expanded,
  }}
>

Codesandbox example: https://codesandbox.io/s/x256q3xz44