The reason you can't use an electric menorah and  why don't actually need a wick. 

Beis Yitzchok writes that you don't fulfill your obligation with an electric light or a gas light as they are not called a "candle" for the purposes of Chanuka. 

Shalos ve'teshuvos Pekudas Elazar also writes that you don't fulfill your obligation with and electric candle since we are obligated to have the full measure of oil in front of you when you're lighting (enough to burn the requisite time etc). (Shulchan aruch siman 675:5). Here, however, since someone might turn off the light before the measure is complete you don't have it in front of you.

Shalos ve'teshuvos Levushei Mordechai aslo holds that you don't fulfill your obligation with and electric candle for the reason that you it must have some "form of oiliness", like oil or fat or beeswax. Just as you don't fulfill your obligation by lighting light branches or wooden tinder, even if it burns nicely. The reason being that it doesn't have "oil" to it. The same thing applies with the electric candle.

(Another reason why you might think we might be able to use the electric menorah:)
Shu"t Beis Yitzchok explains (first paragraph) that you don't need actually need a wick for the Chanuka light. Its permitted (for example) to light using a small piece of metal placed in oil in a glass, with a thin glass tube in it without a wick. The reason being that it doesn't need to be like the menorah in the temple that had to have a wick. The halacha by the Chanuka candle is that if it goes out your not obligated to relight it, while in the temple you are. So to (by Chanuka), you don't need to exchange the old wicks to new each night, while in the temple you do. So, also in this way, without a wick it can be considered a "candle" even though it is certainly more proper to use oil and a wick.

brought down in Sharim Metzuyanim be'halacha chelek 3, siman 139

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