A single crystal producing method for growing a single crystal, comprises the steps of: placing a material at one focal point in a light-condensing and heating furnace having an ellipse in section; placing a heat light source at another focal point; and emitting a laser beam has a wavelength of not less than about 160 nm and not greater than about 1,000 nm, on or near the one focal point to form a melt zone; and moving the melt zone to grow a single crystal.