Editing Drude model (section)

== Accuracy of the model ==
The Drude model provides a very good explanation of DC and AC conductivity in metals, the [[Hall effect]], and the [[magnetoresistance]]<ref name=":2" group="Ashcroft & Mermin" /> in metals near room temperature. The model also explains partly the [[Wiedemann–Franz law]] of 1853.

Drude formula is derived in a limited way, namely by assuming that the charge carriers form a [[Classical physics|classical]] [[ideal gas]]. When quantum theory is considered, the Drude model can be extended to the [[free electron model]], where the carriers follow [[Fermi–Dirac distribution]]. The conductivity predicted is the same as in the Drude model because it does not depend on the form of the electronic speed distribution. However, Drude's model greatly overestimates the electronic heat capacity of metals. In reality, metals and insulators have roughly the same heat capacity at room temperature. Also, the Drude model does not explain the scattered trend of electrical conductivity versus frequency above roughly 2&nbsp;THz.<ref name="Dressel">{{cite journal |author1=M. Dressel |author2=M. Scheffler |year=2006 |title=Verifying the Drude response |journal=[[Annalen der Physik]] |volume=15 |issue=7–8 |pages=535–544 |bibcode=2006AnP...518..535D |doi=10.1002/andp.200510198 |s2cid=14153937}}</ref><ref>{{cite journal |last1=Jeon |first1=Tae-In |last2=Grischkowsky |first2=D. |last3=Mukherjee |first3=A. K. |last4=Menon |first4=Reghu |date=2000-10-16 |title=Electrical characterization of conducting polypyrrole by THz time-domain spectroscopy |url=http://dx.doi.org/10.1063/1.1319188 |journal=Applied Physics Letters |volume=77 |issue=16 |pages=2452–2454 |doi=10.1063/1.1319188 |bibcode=2000ApPhL..77.2452J |issn=0003-6951|hdl=11244/19868 |hdl-access=free }}</ref>

The model can also be applied to positive (hole) charge carriers.

=== Drude response in real materials ===
The characteristic behavior of a Drude metal in the time or frequency domain, i.e. exponential relaxation with time constant {{mvar|τ}} or the frequency dependence for {{math|''σ''(''ω'')}} stated above, is called Drude response. In a conventional, simple, real metal (e.g. sodium, silver, or gold at room temperature) such behavior is not found experimentally, because the characteristic frequency {{math|{{itco|''τ''}}<sup>−1</sup>}} is in the infrared frequency range, where other features that are not considered in the Drude model (such as [[Electronic band structure|band structure]]) play an important role.<ref name="Dressel" /> But for certain other materials with metallic properties, frequency-dependent conductivity was found that closely follows the simple Drude prediction for {{math|''σ''(''ω'')}}. These are materials where the relaxation rate {{math|{{itco|''τ''}}<sup>−1</sup>}} is at much lower frequencies.<ref name="Dressel" /> This is the case for certain [[Doping (semiconductor)|doped semiconductor]] single crystals,<ref>{{cite journal |author1=M. van Exter |author2=D. Grischkowsky |year=1990 |title=Carrier dynamics of electrons and holes in moderately doped silicon |url=https://shareok.org/bitstream/11244/19898/1/okds_Grischkowsky_PRB_1990-06-15.pdf |journal=[[Physical Review B]] |volume=41 |issue=17 |pages=12140–12149 |bibcode=1990PhRvB..4112140V |doi=10.1103/PhysRevB.41.12140 |pmid=9993669 |hdl-access=free |hdl=11244/19898}}</ref> high-mobility [[2DEG|two-dimensional electron gases]],<ref>{{cite journal |author1=P. J. Burke |author2=I. B. Spielman |author3=J. P. Eisenstein |author4=L. N. Pfeiffer |author5=K. W. West |year=2000 |title=High frequency conductivity of the high-mobility two-dimensional electron gas |url=https://authors.library.caltech.edu/2073/1/BURapl00b.pdf |journal=[[Applied Physics Letters]] |volume=76 |issue=6 |pages=745–747 |bibcode=2000ApPhL..76..745B |doi=10.1063/1.125881}}</ref> and [[Heavy fermion|heavy-fermion metals]].<ref>{{cite journal |author1=M. Scheffler |author2=M. Dressel |author3=M. Jourdan |author4=H. Adrian |year=2005 |title=Extremely slow Drude relaxation of correlated electrons |journal=[[Nature (journal)|Nature]] |volume=438 |issue=7071 |pages=1135–1137 |bibcode=2005Natur.438.1135S |doi=10.1038/nature04232 |pmid=16372004 |s2cid=4391917}}</ref>