Quantized transconductance emerges from non-symmetric quantum fluctuations: theoretical prediction

Abstract

We show theoretically that weak quantum fluctuations induced by a non-symmetric electromagnetic environment may lead to a quantized transconductance of a multi-terminal quantum contact rather than to a blockade of transport in the contact. The result suggests the possibility to realize Quantum Hall phenomenology without its common ingredients and/or a topological quantum state.

Figures (4)

• Figure 1: (a) The N-terminal scatterer (N=3 in the Figure) embedded in a linear electromagnetic environment which is characterized by the generally non-symmetric $N\times N$ impedance matrix $\hat{Z}(\omega)$. (b) Sketch of a general (high-energy) scattering matrix: an incoming electron wave is scattered back and to both terminals. (c) Insulating fixed point: all incoming waves are reflected in the low-energy limit. (d) Predicted QTC fixed point: all incoming waves are fully transmitted to different terminals realizing IQHE phenomenology in the low-energy limit.
• Figure 2: One channel per terminal. Energy dependence of transmission coefficients for two different choices of time-reversible $\hat{s}_{\rm in}$. (a) Realization of the insulating fixed point. (b) Realization of a QTC fixed point. We choose $c = 1.5$ where both fixed points occur with comparable probabilities.
• Figure 3: One channel per terminal. (a) The fraction of $\hat{s}_{\rm in}$ flowing to QTC fixed point $P_1$ versus asymmetry parameter $c$. $10^4$ runs per point in $c$. (b) The pseudo-potential $\varepsilon$ of the insulating fixed point (red) and $P_1$ (blue). $c_{s}, c_{c}$ indicate the stability and pseudo-potential crossing thresholds, respectively.
• Figure 4: 3 channels per terminal. (a),(b) The probabilities for the realization of QTC fixed points $P_n$ versus $c$. $10^4$ runs per point in $c$. (b) Zoom in of the same data as in (a) in the vicinity of $c_c$. (c) The pseudo-potential for $P_n$ and the insulating point. 10 channels per terminal. (d) The probabilities for the realization of QTC fixed points $P_n$ versus $c$. $10^3$ runs per point in $c$.