For English (and many other languages), you can just use Character.toLowerCase as @aleph_null proposes. This compares characters based on their (lower case) Unicode code points. For some languages, however, this will be wrong. (For instance, in German, ß — eszett — comes between 's' and 't'. However, its Unicode value is U+00DF, which would make it come after 'z'.)

The only way comparing two characters makes sense is with reference to a locale. One way to do this is to use a Collator:

/**
 * Compares two characters, ignoring all but primary differences. (Case
 * is a tertiary difference.)
 * @return true if ch1 is alphabetically smaller than ch2; false otherwise
 */
public static boolean smallestCharacter(char ch1, char ch2, Locale locale) {
    Collator collator = Collator.getInstance(locale);
    collator.setStrength(Collator.PRIMARY); // Collator.SECONDARY would work
    return 0 > collator.compare(Character.toString(ch1),
                                Character.toString(ch2)
                               );
}

(P.S., new String(ch1) is not the way to create a String object containing a given char value.)

Take a look at the String.compareTo method.

s1.compareTo(s2)

From the javadocs:

The result is a negative integer if this String object lexicographically precedes the argument string. The result is a positive integer if this String object lexicographically follows the argument string. The result is zero if the strings are equal; compareTo returns 0 exactly when the equals(Object) method would return true.