There are variations of the Quantum Hall effect (QHE) such as the Quantum Spin Hall effect...

Transcribed Image Text:

There are variations of the Quantum Hall effect (QHE) such as the Quantum Spin Hall effect (QSHE) and Quantum Anomalous Hall effect (QAHE), where they show quantized conductances in the absence of applied external magnetic field. When dealing with quantized conductances, it is often useful to refer to the Landauer-Buttiker equation: Σ(TjiVi - TijVj) I₁ = = 6 e² (1) where I, is the current flowing from the ith electrode and V; is the voltage on the ith electrode, and Tj; is the transmission probability from the ith to the jth electrode. (a) Describe QSHE and QAHE (* feel free to read up on relevant papers). (b) A Hall-bar device, said to have been made of a 2D QAHE crystal is shown in Fig. 2. You have several electronic measurement hardware in your arsenal for current (voltage) sourcing and voltage (current) measurements. How will you design the electronic circuit such that you can verify the QSHE nature of the sample? Describe the 2-probe, 4-probe conductance you would observe using the Landauer-Buttiker formalism. (* Assume that the contact resistance is negligible) (c) What do you expect to observe if this was instead, a QSHE system? There are variations of the Quantum Hall effect (QHE) such as the Quantum Spin Hall effect (QSHE) and Quantum Anomalous Hall effect (QAHE), where they show quantized conductances in the absence of applied external magnetic field. When dealing with quantized conductances, it is often useful to refer to the Landauer-Buttiker equation: Σ(TjiVi - TijVj) I₁ = = 6 e² (1) where I, is the current flowing from the ith electrode and V; is the voltage on the ith electrode, and Tj; is the transmission probability from the ith to the jth electrode. (a) Describe QSHE and QAHE (* feel free to read up on relevant papers). (b) A Hall-bar device, said to have been made of a 2D QAHE crystal is shown in Fig. 2. You have several electronic measurement hardware in your arsenal for current (voltage) sourcing and voltage (current) measurements. How will you design the electronic circuit such that you can verify the QSHE nature of the sample? Describe the 2-probe, 4-probe conductance you would observe using the Landauer-Buttiker formalism. (* Assume that the contact resistance is negligible) (c) What do you expect to observe if this was instead, a QSHE system?

Answer rating: 100% (QA)

Explanation a The Quantum Spin Hall Effect QSHE and Quantum Anomalous Hall Effect QAHE are variations of the Quantum Hall Effect QHE that exhibit quan... View the full answer