Current focusing in InSb heterostructures

Edge magnetotransport in graphene: A combined analytical and numerical study

“…which can be derived easily by (14) and (23). Of course, mean free path and phase coherence length also have to be comparable with L. To our knowledge in most focusing experiments such system parameters have been used that the regime of coherent electron focusing and the quantum Hall effect are well separated, see e.g.…”

“…It has also been suggested to study by coherent electron focusing the structure of graphene edges [19]. Recently, also the effects of disorder [20] and spin-orbit interaction [21][22][23][24][25] have been investigated in a nonrelativistic 2DEG. On the other hand, graphene stripes in a strong magnetic field show the quantum Hall effect [26,27], which is explained by the transport through edge channels along the boundary of the system, see the red lines in figure 1.…”

Direct observation of exchange-driven spin interactions in one-dimensional system

“…[13][14][15][16] The spin polarization in a 1D quantum wire 13,14 can be measured by means of transverse electron focusing (TEF), [17][18][19] where the height of each focusing peak is proportional to the population of detected electrons. It has been confirmed experimentally in a GaAs hole gas 20,21 and an InSb electron gas 22 that the first focusing peak splits into two sub-peaks and each peak is associated with a spin of an electron. In this work, we provide direct evidence by means of focusing measurements using electrons in the GaAs/AlGaAs heterostructure that the spin-gap can be detected precisely up to the first excited state in agreement with observations of the "0.7" and "1.7" structures.…”

“…The splitting of the first peak, not for the second peak, is predicted to be a sign of the spin-orbit interaction (SOI). 18,19 It may be noted that the observed splitting of 5.5 mT (after scaling against L, it becomes 6.3 mT for 90 geometry) is much smaller than the 40 mT splitting in GaAs hole gas 20,21 or 60 mT in InSb electron gas, 22 which is expected for low SOI in n-GaAs. We made sure that the observed effect is not due to the disorder induced electron branching, 23 because the splitting of the first peak remained preserved when we swapped the role of the injector and the detector (see the discussion in the supplementary material).…”

“…17,25 The linear focusing devices 17,[20][21][22]25 used in previous work share the center gate which may introduce a lateral electric field along the confinement direction. Figure 1 shows the experimental setup along with a typical focusing spectrum obtained using the device shown in the inset.…”