12  Electronic Contributions to Thermal Properties

NoteLearning Objectives

By the end of this lecture, you should be able to:

• explain why the classical Drude model fails for the electronic heat capacity of metals;
• derive the linear-in-\(T\) electronic heat capacity in the Sommerfeld model and interpret the Sommerfeld coefficient \(\gamma\);
• combine the electronic and phononic low-temperature contributions into \(C = \gamma T + \beta T^{3}\);
• distinguish energy current from heat current and write the coupled transport equations for charge and heat;
• derive the Sommerfeld form of the Wiedemann–Franz law and summarize the Seebeck, Peltier, and Thomson effects;
• identify the main thermal limitations of the free-electron model and motivate the transition to Bloch electrons.