Phonons | Detailed Study

PHONONS

Phonon is a quantum of lattice vibrational mechanical energy. They are basically the ground and excited states of quantised lattice vibrations of interacting particles.

The name phonon comes from the Greek word phonē  which means voice or sound, as long wave length phonons give rise to sound.

Atoms in a crystal lattice can be considered to behave as if they are connected by tiny springs which makes mechanical waves that carry heat and sound as a result of executing Simple Harmonic Motion (SHM) by their own thermal vibrations and external forces. A packet of this wave can travel through the crystal with a definite energy and momentum, which in quantum mechanical terms can be considered as a particle (phonon).

So, we can imagine atoms vibrating in SHM as a lattice wave.

Its equation can be written as,

                                

Where:

k= Restoring force, M= Mass of atom

Potential energy =

By Schrödinger’s equation,

On solving, we get the energy Eigen values as,

The energy difference between two allowed states is  . So we define the basic packets of energyand momentumand these fundamental packets of energy exchanged are called phonons.

Phonon is a quasi- particle, that is something that is not a real particle but can behave and be considered as one. They are responsible for acoustic properties, thermal conductivity and heat capacity of solids. Besides, phonons are bosons, that is they follow Bose-Einstein statistics (Indistinguishable, but not obeying Pauli’s exclusion principle), which take the crucial role in the super conducting phenomena (low temperature) as an intermediate particle which makes electrons slightly attract each other whereas they would have normally repelled.