# Why Landau Level quantization is observed only in low temperature and strong magnetic field in real experiment?

I know that Quantum Hall Effect and Fractional Quantum Hall Effect origin from Landau Level quantization.

In magnetic field, the energy of in-plane(plane perpendicular to magnetic field) degree of motion is quantized, which is $E=(n+1/2)\hbar\omega$, $n$ is integer.

In experiment, both QHE and FQHE are observed in low temperature and strong magnetic field, suggesting that landau level quantization is observable under the condition $k_B T<<\hbar\omega$, where $k_B$ is Boltzman constant.

I am not sure why this condition is important in experiment.

• The first questions to ask yourself are always "What is the data?" and "What is the experimental signature of the thing we are looking for?". Once you have those answers (and I don't because I don't know these experiments) it is likely that the answer is clear. – dmckee Dec 16 '13 at 19:58

In general, both IQHE and FQHE are rigid quantum states, whose rigidness is protected by the finite energy gap ($h\omega$ for IQHE) between the ground state(s) and the exited states. Finite temperature can support excitations to overcome the gap, which destroys the rigidness of the state. Under finite temperature, the quantization of the Hall conductivity is no longer exact. If the energy scale of temperature $k_BT$ is greater than the gap, the rigidness will be completely destroyed, and the quantization effect can not be observed anymore.