# Dresden 2006 – wissenschaftliches Programm

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# HL: Halbleiterphysik

## HL 27: Symposium New phenomena in edge transport of QHE systems

### HL 27.2: Fachvortrag

### Mittwoch, 29. März 2006, 15:00–15:30, HSZ 01

**Particle-hole symmetric Luttinger liquids in a quantum Hall circuit** — •Vittorio Pellegrini^{1}, Stefano Roddaro^{1}, Fabio Beltram^{1}, Lucia Sorba^{2}, Giorgio Biasiol ^{2}, Loren N. Pfeiffer^{3}, and K.W. West^{3} — ^{1}NEST CNR-INFM, Scuola Normale Superiore, Pisa — ^{2}TASC CNR-INFM Trieste — ^{3}Lucent Technologies, NJ USA

We report evidence of a novel class of one-dimensional Tomonaga-Luttinger liquids (TLLs) with tunable properties. These electron liquids are induced by a nanocostriction defined with metallic gates on a two-dimensional electron gas in the quantum Hall (QH) regime. TLLs occur in the QH edges and they are usually observed when the occupation of the lowest Landau level of the two-dimensional electron gas subjected to a magnetic field is equal to particular fractional values [1,2]. Our work shows that the observation of TLLs in edge states is not restricted to the extreme quantum limit of the fractional QH effects [3,4]. The evidences are based on the experimental and theoretical analysis of the out-of-equilibrium (finite-bias) current transmission and reflection characteristics through the split-gate constriction. Split-gate biasing drives inter-edge backscattering and is shown to lead to suppressed or enhanced transmission even in the integer QH regime, in marked contrast with the expected linear Fermi-liquid behavior. This evolution is described in terms of particle-hole symmetry and allows us to conclude that an unexpected class of gate-controlled particle-hole-symmetric TLLs can exist at the edges of our integer QH circuit [4]. These results highlight the role of particle-hole symmetry on the properties of TLL edge states.

[1] A.M Chang, Rev. Mod. Phys. 75, 1449 (2003),
[2] S. Roddaro, V. Pellegrini, G. Biasiol, L. Sorba, R. Raimondi, G. Vignale, Phys.Rev.Lett. 90, 046805 (2003),
[3] S. Roddaro, V. Pellegrini, F. Beltram, G. Biasiol, L. Sorba Phys. Rev. Lett. 93, 046801 (2004),
[4] S. Roddaro, V. Pellegrini, F. Beltram, L.N. Pfeiffer, K.W. West Phys. Rev. Lett. 95, 156804 (2005)