Schottky anomaly in a cavity-coupled double quantum well

We present a theoretical study of a mesoscopic two-dimensional electron gas confined in a double quantum well that is coupled to a uniform quasistatic cavity mode via fluctuations of the dipole moment. We focus on the regime of large number of electrons participating in the virtual intersubband transitions. In this regime, the effective photonic potential is no longer quadratic but, instead, it contains large number of minima. Each minimum represents a nearly harmonic oscillator with the renormalized cavity frequency that is much greater than its bare value. The energy offset of a minimum scales quadratically with respect to the photon coordinate corresponding to this minimum. These energy offsets determine the statistical weight of each minimum, and altogether they result in the additive correction to the heat capacity of the system. This correction exhibits a Schottky anomaly and a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>0.5</a:mn><a:msub><a:mi>k</a:mi><a:mtext>B</a:mtext></a:msub></a:mrow></a:math> plateau at low temperatures. This behavior can be associated with the emergence of a new degree of freedom. This degree of freedom does not manifest in the optical conductivity and can only be observed via the heat capacity measurement.