Experimentally Motivated Order of Length Scales Affect Shot Noise

Shot noise at a conductance plateau in a quantum point contact (QPC) can be explained by considering equilibrations at the quantum Hall edges. The indication from recent experiments is that the charge equilibration length is much shorter than the thermal equilibration length. We discuss how this discovery gives rise to different thermal equilibration regimes in the presence of full charge equilibration. In this work, we classify these distinct regimes via dc current-current correlations (electrical shot noise) at definite experimentally found (or possible) QPC conductance plateaus for the edges of integer, particle-like, and hole-like filling fractions in a two dimensional electron gas. Our analyses show that distinct universal features arise among the different thermal equilibration regimes for the edges of particle-like and hole-like states.

💡 Research Summary

The paper investigates how the hierarchy of internal length scales—specifically the charge equilibration length (l_ch_eq) and the thermal equilibration length (l_th_eq)—affects shot noise measured at a conductance plateau of a quantum point contact (QPC) in a two‑dimensional electron gas (2DEG) under quantum Hall conditions. Recent experiments have shown that l_ch_eq is much shorter than l_th_eq, implying that charge equilibrates locally while heat can travel over much longer distances before equilibrating. The authors model the QPC geometry with two geometric lengths: the arm length L_A (the distance from the source/drain contacts to the QPC) and the QPC size L_Q (the constriction width). In typical devices L_A ≫ L_Q, and they assume full charge equilibration everywhere (l_ch_eq ≪ L_A, L_Q).

Thermal equilibration, however, can be in one of three regimes: (i) “Full” thermal equilibration where l_th_eq ≪ L_Q ≪ L_A, meaning heat equilibrates in both the arms and the QPC region; (ii) “Hybrid” where L_Q ≪ l_th_eq ≪ L_A, so the arms are thermally equilibrated but the QPC region is not; (iii) “No” thermal equilibration where L_Q ≪ L_A ≪ l_th_eq, i.e., heat does not equilibrate in any segment. Within this framework the authors compute the auto‑correlation noise δ²I₁, δ²I₂ and the cross‑correlation noise δ²I_c using a hydrodynamic description of charge and heat transport along the edge modes. The central formula (Eq. 3) expresses the noise in terms of the bulk filling factor ν, the QPC filling factor ν_i (ν_i < ν), the temperatures of the upstream and downstream edge segments (T_M, T_N), and the stochastic fluctuations of the source and ground currents.

The shot‑noise Fano factors are defined as F_j = δ²I_j /