# Can we understand the strong reflectivity of metals from band theory?

I know that solids, including metals, have electronic bands and bandgaps. If we consider some typical metal such as copper, we know that it strongly reflects visible light. From the point of view of bands, this means that the bandgap energy must be large in comparison to the energy of the visible light and therefore, it cannot be absorbed. Is it so? I am not sure.

• You have that backwards - if photons of a particular energy cannot be absorbed, then the material will be transparent to them. – J. Murray Mar 3 '20 at 16:59
• If the photon cannot be absorbed, I think two things are possible. Either reflection or transmission. Isn't it? – mithusengupta123 Mar 3 '20 at 17:00
• When a photon promotes an electron from a low energy state to a high energy state, the electron subsequently loses that energy either by re-emitting it as a photon, or by passing it off to phonons. The former accounts for reflection, the latter accounts for absorption. If the photon cannot be absorbed in the first place, then it will pass right through the material. – J. Murray Mar 3 '20 at 17:22
• Chapter 15 (Band Structure of Metals) in Ashcroft and Mermin discusses optical properties of various metals in light of their band structure. So, yes, it is a core function of band theory to describe optical properties. – Jon Custer Mar 3 '20 at 18:03
• @JonCuster Yes, but there is also the contribution of the Drude peak to the optical conductivity. And the plasmons. It is complicated. – Pieter Mar 3 '20 at 20:23

From the point of view of bands, this means that the bandgap energy must be large in comparison to the energy of the visible light and therefore, it cannot be absorbed.

I don't think so. When there is a large gap and photons can not be absorbed, the material is transparent to visible light. It is the case of some isolators as quartz.

In order to absorb a photon, it is necessary that the energy gap between adjacent electronic bands allows a transition of one of the electrons. Normally, the momentum of the electron ($$\hbar k$$) is much higher than the moment of the photon, and moment conservation requires that there is an available state in a higher energy band with (almost) the same $$k$$.

After being absorbed, the electron returns to the lower energy band, scattering the incoming light, what explains the bright reflective surface of metals.

Metals don't have large band gaps as insulators, and electrons can find available states at high energy band.

J. Murray is correct and yes you can: because most metallic bands are continuous, the promotion of electrons from valence to conduction will occur at a wide range of energies. The relaxation of these electrons then emits a photon resulting in reflection. Metal colours come from differing electron densities at points in their valence bands (DoS).This is also why most metallic materials are opaque and why there is so much interest in transparent materials that are electrically conductive.