The function takes an input string and increments the second character by 1. If the second character is 'z', it becomes 'a'. If the string has only one character, it returns the same character.

[CODE]:
```python
def increment_second_char(s: str) -> str:
    if len(s) > 1:
        second_char = chr(((ord(s[1]) - ord('a') + 1) % 26) + ord('a'))
        return s[0] + second_char + s[2:]
    else:
        return s
```

Please note that this implementation only considers lowercase alphabets and might not work correctly for uppercase or other characters.