Conductance quantization and finite-size effects in cleaved edge overgrowth GaAs quantum wires

Cleaved Edge Overgrowth (CEO) quantum wires (QW) are among the cleanest 1D systems available, showing conductance quantization and Luttinger liquid effects such as charge fractionalization and spin-charge separation.
Previously, we studied the conductance quantization of CEO QWs as a function of temperature in Scheller et al. PRL112, 066801 (2014), finding that the first conductance plateau goes from 2 e²/h at high T > 10K to 1 e²/h at low T < 0.1K. he results are consistent with helical nuclear spin order as proposed by Braunecker et al. PRB80, 165119 (2009).
Here we present the dependence on wire length, and observe a steeper slope over increasing temperatures in short 2 μm wires compared to 6 μm wires, which agrees with theory from Aseev et al. PRBB95, 125440 (2017).
Further, we report on finite-size effects in CEO QWs. Though seen before in Y. Tserkovnyak et al. PRB68, 125312 (2003) as a function of magnetic field and bias voltage, we also study the gate voltage and gate length dependence, and can now resolve the discrete level spacing due to the finite length of the QW. Single particle simulations give excellent agreement with data, explaining most of the observed features.