I'm not too sure on the details of theory, but yes, "we" have created heavier elements. These lighter or heavier elements are formed through types of radioactive decay such as [tex]\alpha[/tex] and [tex]\beta[/tex] decay. Just a situation where there are not enough neutrons, too many neutrons, too little protons. Generally [tex]\alpha[/tex] decay occurs when there are too many protons, and [tex]\beta[/tex] decay when there are too many neutrons. This is induced of course. Some examples : fission of U-235 produces a source of neutrons, which are then bombarded into other elements to create heavier isotopes. Like Cobalt-60, Iodine-123, Strontium-90.
As far as I know we can't actually "create" these new heavier or lighter elements. We just slightly alter existing ones and call them isotopes. And that too elements very, very close to each other. I don't know if we can actually just "create" something.
Hope that helped.
Here is an example:
1.) [tex]^{238}_{92}U+ ^{1}_{0}n\xrightarrow~ ^{239}_{92}U[/tex]
2.) [tex]^{239}_{92}U\xrightarrow~ ^{239}_{93}Np+ ^{0}_ {-1}e[/tex]
3.) [tex]^{239}_{93}Np\xrightarrow~ + ^{239}_{94}Pu + ^{0}_{-1}e[/tex]