Andreev reflection of fractional quasiparticles in the Quantum Hall Effect

In semiconductor structures, electrons can be confined at the interface between two layers, forming a 2d electron gas. Applying a strong magnetic field, and working at very low temperature, the system reaches a state known as Integer Quantum Hall Effect. There, the conductance (the inverse of the resistance) can only reach very precise quantized values. This quantization can be explained by the topological properties of the system: the electronic current is fully carried by unidimensional electronic edge states along the boundaries of the system, and the value of the conductance is directly related to the number of these edge states. If the magnetic field is increased further, one then reaches the Fractional Quantum Hall Effect. There, electronic interactions play an essential role: the current is still carried by 1d edge states, but the fundamental excitations are not electrons, but quasiparticles having a fractional charge (for example e/3, where e is the electron charge), which are due to the collective behavior of interacting electrons.

The experiment performed in the group of M. Hashisaka at NTT Basic Research Labs. (Atsugi – Japan) studies the electronic transport at the junction between one part of the system which is in the Integer Quantum Hall Effect, and another part of the system which is in the Fractional Quantum Hall Effect (see left figure). As the fundamental excitations are of different nature on the two sides of the junction (electrons on one side, fractional charge e/3 on the other side), the transport is non-trivial. When the coupling between the edge states on both sides of the junction is strong, the basic transport process can be seen as: two e/3 quasiparticles incoming from the fractional side are transmitted as one electron to the integer side, while a hole of charge e/3 is reflected on the fractional side. This process is analogous to the Andreev reflection at the interface between a normal metal and a superconductor, when an electron is reflected as a hole, while a Cooper pair (2 electrons) is transmitted to the superconductor, leading to a conductance larger than the one of the normal metals.

The experiment provides the first observation of this kind of Andreev transport in a fractional Hall system, which had been predicted theoretically twenty years ago. It shows as oscillations in the conductance when the opening of the junction is varied, with a maximum of the conductance clealry larger than the conductance G=⅓ (e²/h) of the fractional system (see right figure). Using a theoretical model where the two edge states are connected in different positions – the number of these positions being proportional to the junction width – the researchers of the Nanophysics Team of the CPT (CNRS/Aix-Marseille Univ.) in Marseille were able to explain theoretically the observed behavior of the conductance, thus showing the complex dynamics of microscopic charges at the interface of interacting electronic systems with non trivial topological properties. This study shows that the Andreev-like reflection is a generic phenomenon in hybrid systems of condensed matter. It is published in Nature Communications.

(left) Scanning electron micrograph of the system, with false colors: the blue and red zones show the electron gas in the regime of Integer Hall Effect (blue) and Fractional Hall Effect (red). The red and blue lines with arrows show the path of the edge states where electronic transport occurs. The junction is the very narrow region between 1/3 and 1 where the blue and red lines overlap. The opening of the junction is controlled by a voltage VS applied to a gate (yellow). The voltage V1 = Vin is applied on the edge incoming on the fractional side, while a voltage V3 = 0 is applied on the edge state on the integer side. Measuring the output current I give access to the conductance, which is measured for different values of the gate voltage VS.

(right) Conductance of the junction as a function of the gate voltage VS which controls its opening (from completely closed on the left of the plot, to widely open on the right of the plot). In the region where VS is close to -1 V, corresponding to a narrow junction, one observes conductance oscillations reaching values much higher than G=⅓ (e²/h), showing the presence of Andreev-like reflection for fractional quasiparticles. The inset shows the predictions given by the theoretical model, which reproduce qualitatively the features of the experimental curve. The different theoretical curves correspond to different random configurations for the positions of the connections between the two edges states.