Particle-hole symmetry and Luttinger liquids in a quantum Hall circuit*

I shall present recent experimental results on edge-state transport through quantum point contacts in the quantum Hall (QH) regime. Finite-bias backscattering measurements between edge channels at filling factor $\nu=1$ will be presented at different temperatures. Transport through the constriction displays a non-linear Luttinger-like behavior even in the integer QH regime in contrast with the linear tunneling predicted for integer edge states [1,2]. Both zero-bias enhancement and suppression of the inter-edge tunneling will be shown in a controllable way as a function of gate bias [2,3,4]. The observed evolution is connected to the local charge depletion in the constriction region and offers new insight into the link between QH charge-conjugation and Luttinger liquid description of edge channels [2]. I shall discuss the relevance of these experimental results in the context of the dynamics of the highly-correlated edge channels in the fractional QH regime [5]. Finally I shall demonstrate how charge-conjugation can be exploited in the design of new QH circuits where the transport properties of the hole component of a partially filled Landau level can be directly addressed. \newline \newline [1] X.-G. Wen, Phys. Rev. Lett. {\bf 62}, 2206 (1990); P. Fendley {\em et al.} Phys. Rev. Lett. {\bf 74}, 3005 (1995). \newline [2] S. Roddaro, V. Pellegrini, F. Beltram, L. N. Pfeiffer, K. W. West, Phys. Rev. Lett. {\bf 95}, 156804 (2005). \newline [3] S. Roddaro, V. Pellegrini, F. Beltram, G. Biasiol, L. Sorba., Phys. Rev. Lett. {\bf 93}, 046801 (2004). \newline [4] S. Roddaro, V. Pellegrini, F. Beltram, G. Biasiol, L. Sorba, R. Raimondi, G. Vignale, Phys. Rev. Lett. {\bf 90}, 046805 (2003). \newline [5] A. M. Chang, Rev. Mod. Phys. {\bf 75}, 1449 (2003).