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Register a new userCross-over between Magnetic and Electric Edges in Quantum Hall Systems
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We report on the transition from magnetic edge to electric edge transport in a split magnetic gate device which applies a notch magnetic field to a two-dimensional electron gas. The gate bias allows tuning the overlap of magnetic and electric edge wavefunctions on the scale of the magnetic length. Conduction at magnetic edges - in the 2D-bulk - is found to compete with conduction at electric edges until magnetic edges become depleted. Current lines then move to the electrostatic edges as in the conventional quantum Hall picture. The conductivity was modelled using the quantum Boltzmann equation in the exact hybrid potential. The theory predicts the features of the bulk-edge cross-over in good agreement with experiment.
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The edge of a two-dimensional electron system (2DES) in a magnetic field consists of one-dimensional (1D) edge-channels that arise from the confining electric field at the edge of the specimen$^{1-3}$. The crossed electric and magnetic fields, E x B, cause electrons to drift parallel to the sample boundary creating a chiral current that travels along the edge in only one direction. Remarkably, in an ideal 2DES in the quantum Hall regime all current flows along the edge$^{4-6}$. Quantization of the Hall resistance, $R_{xy}= h/Ne^{2}$, arises from occupation of N 1D edge channels, each contributing a conductance of $e^{2}/h^{7-11}$. To explore this unusual one-dimensional property of an otherwise two-dimensional system, we have studied tunneling between the edges of 2DESs in the regime of integer quantum Hall effect (QHE). In the presence of an atomically precise, high-quality tunnel barrier, the resultant interaction between the edge states leads to the formation of new energy gaps and an intriguing dispersion relation for electrons traveling along the barrier. The absence of tunneling features due to the electron spin and the persistence of a conductance peak at zero bias are not consistent with a model of weakly interacting edge states.
The interplay between different orders is of fundamental importance in physics. The spontaneous, symmetry-breaking charge order, responsible for the stripe or the nematic phase, has been of great interest in many contexts where strong correlations are present, such as high-temperature superconductivity and quantum Hall effect. In this article we show the unexpected result that in an interacting two-dimensional electron system, the robustness of the nematic phase, which represents an order in the charge degree of freedom, not only depends on the orbital index of the topmost, half-filled Landau level, but it is also strongly correlated with the magnetic order of the system. Intriguingly, when the system is fully magnetized, the nematic phase is particularly robust and persists to much higher temperatures compared to the nematic phases observed previously in quantum Hall systems. Our results give fundamental new insight into the role of magnetization in stabilizing the nematic phase, while also providing a new knob with which it can be effectively tuned.
We study a two-terminal graphene Josephson junction with contacts shaped to form a narrow constriction, less than 100nm in length. The contacts are made from type II superconducting contacts and able to withstand magnetic fields high enough to reach the quantum Hall (QH) regime in graphene. In this regime, the device conductance is determined by edge states, plus the contribution from the constricted region. In particular, the constriction area can support supercurrents up to fields of ~2.5T. Moreover, enhanced conductance is observed through a wide range of magnetic fields and gate voltages. This additional conductance and the appearance of supercurrent is attributed to the tunneling between counter-propagating quantum Hall edge states along opposite superconducting contacts.
We study the effect of backward scatterings in the tunneling at a point contact between the edges of a second level hierarchical fractional quantum Hall states. A universal scaling dimension of the tunneling conductance is obtained only when both of the edge channels propagate in the same direction. It is shown that the quasiparticle tunneling picture and the electron tunneling picture give different scaling behaviors of the conductances, which indicates the existence of a crossover between the two pictures. When the direction of two edge-channels are opposite, e.g. in the case of MacDonalds edge construction for the $ u=2/3$ state, the phase diagram is divided into two domains giving different temperature dependence of the conductance.
A two-dimensional (2D) topological insulator (TI) exhibits the quantum spin Hall (QSH) effect, in which topologically protected spin-polarized conducting channels exist at the sample edges. Experimental signatures of the QSH effect have recently been reported for the first time in an atomically thin material, monolayer WTe2. Electrical transport measurements on exfoliated samples and scanning tunneling spectroscopy on epitaxially grown monolayer islands signal the existence of edge modes with conductance approaching the quantized value. Here, we directly image the local conductivity of monolayer WTe2 devices using microwave impedance microscopy, establishing beyond doubt that conduction is indeed strongly localized to the physical edges at temperatures up to 77 K and above. The edge conductivity shows no gap as a function of gate voltage, ruling out trivial conduction due to band bending or in-gap states, and is suppressed by magnetic field as expected. Interestingly, we observe additional conducting lines and rings within most samples which can be explained by edge states following boundaries between topologically trivial and non-trivial regions. These observations will be critical for interpreting and improving the properties of devices incorporating WTe2 or other air-sensitive 2D materials. At the same time, they reveal the robustness of the QSH channels and the potential to engineer and pattern them by chemical or mechanical means in the monolayer material platform.
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