Longitudinal conductivity in Si/SiGe heterostructure at integer filling factors

TL;DR

This study examines how the longitudinal conductivity in Si/SiGe heterostructures varies with temperature at different integer quantum Hall filling factors, revealing distinct behaviors for odd and even levels due to quantum corrections and energy gaps.

Contribution

It provides a detailed analysis of temperature-dependent conductivity at various filling factors, highlighting the different mechanisms governing odd and even levels in Si/SiGe heterostructures.

Findings

Odd levels show quantum corrections due to electron-electron interactions.

Even levels exhibit exponential temperature dependence related to energy gaps.

Conductivity tends to a residual value at very low temperatures.

Abstract

We have investigated temperature dependence of the longitudinal conductivity $\sigma_{xx}$ at integer filling factors $\nu =i$ for Si/SiGe heterostructure in the quantum Hall effect regime. It is shown that for odd $i$, when the Fermi level $E_{F}$ is situated between the valley-split levels, $\Delta \sigma_{xx}$ is determined by quantum corrections to conductivity caused by the electron-electron interaction: $\Delta\sigma_{xx}(T)\sim \ln T$. For even $i$, when $E_{F}$ is located between cyclotron-split levels or spin-split levels, $\sigma_{xx}\sim \exp[-\Delta_{i}/T]$ for $i=6,10,12$ and $\sim \exp [-(T_{0i}/T)]^{1/2}$ for $i=4,8$. For further decrease of $T$, all dependences $\sigma_{xx}(T)$ tend to almost temperature-independent residual conductivity $\sigma_{i}(0)$. A possible mechanism for $\sigma_{i}(0)$ is discussed.