# How do we know that the system is metallic from linear Density of states?

In principle, if we have a finite weight of LDOS at the fermi energy, we have a metallic state.

What bin size should we choose around the Fermi energy to know whether the system is metallic?

For eg, fermi energy in my case is 0 and and I have chosen a total bin size of 0.1(-0.05 to 0.05). This gives me a finite weight at 0 but if I choose a narrower bin, like (-0.01 to 0.01) it does not give me any weight, because my minimum eigen energy is around 0.03 on the positive side and maximum is -0.03 on the negative side. Can I call the system metallic?

• Have you experimentally measured or numerically calculated this density of states? In either case how have you done so? Aug 19, 2018 at 20:55
• Hi Annie, your question is a little unclear, I think a bit more setup would help. Are you referring to a numerical model of the LDOS? Is your system so small that the energy levels are quantized? If your system is large, then your energy levels should be so closely spaced that the continuity near the fermi level should be a sufficient determination of your material being a metal. If your system is so small that the spacing between energy levels is large enough, then a definition like metal might be meaningless. Aug 19, 2018 at 20:57