scholarly journals The self-consistent quantum-electrostatic problem in strongly non-linear regime

2019 ◽  
Vol 7 (3) ◽  
Author(s):  
Pacome Armagnat ◽  
A. Lacerda-Santos ◽  
Benoit Rossignol ◽  
Christoph Groth ◽  
Xavier Waintal
Keyword(s):  
Quantum Hall ◽  
Point Contact ◽  
The Self ◽  
Differential Conductance ◽  
Electrostatic Problem ◽  
Stable Algorithm ◽  
Self Consistent ◽  
Non Linear ◽  
Integer Quantum ◽  
Quantum Point

The self-consistent quantum-electrostatic (also known as Poisson-Schrödinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low temperatures, these fluctuations make the problem highly non-linear which renders iterative schemes deeply unstable. We present a stable algorithm that provides a solution to this problem with controlled accuracy. The technique is intrinsically convergent even in highly non-linear regimes. We illustrate our approach with both a calculation of the compressible and incompressible stripes in the integer quantum Hall regime as well as a calculation of the differential conductance of a quantum point contact geometry. Our technique provides a viable route for the predictive modeling of the transport properties of quantum nanoelectronics devices.

scholarly journals Competing ν = 5/2 fractional quantum Hall states in confined geometry

2016 ◽  
Vol 113 (44) ◽  
pp. 12386-12390 ◽  
Author(s):  
Hailong Fu ◽  
Pengjie Wang ◽  
Pujia Shan ◽  
Lin Xiong ◽  
Loren N. Pfeiffer ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Filling Factor ◽  
Fault Tolerant ◽  
Quantum Hall ◽  
Point Contact ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Topological Quantum ◽  
Quantum Point ◽  
Topological Quantum Computation

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current–tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.

scholarly journals Robust quantum point contact via trench gate modulation

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Dongsung T. Park ◽  
Seokyeong Lee ◽  
Uhjin Kim ◽  
Hyoungsoon Choi ◽  
Hyung Kook Choi
Keyword(s):  
Quantum Hall ◽  
Point Contact ◽  
Primary Component ◽  
Quantum Point Contacts ◽  
Impurity Effects ◽  
Gate Structure ◽  
Important Challenge ◽  
Density Modulation ◽  
High Bias ◽  
Quantum Point

AbstractQuantum point contacts (QPC) are a primary component in mesoscopic physics and have come to serve various purposes in modern quantum devices. However, fabricating a QPC that operates robustly under extreme conditions, such as high bias or magnetic fields, still remains an important challenge. As a solution, we have analyzed the trench-gated QPC (t-QPC) that has a central gate in addition to the split-gate structure used in conventional QPCs (c-QPC). From simulation and modelling, we predicted that the t-QPC has larger and more even subband spacings over a wider range of transmission when compared to the c-QPC. After an experimental verification, the two QPCs were investigated in the quantum Hall regimes as well. At high fields, the maximally available conductance was achievable in the t-QPC due to the local carrier density modulation by the trench gate. Furthermore, the t-QPC presented less anomalies in its DC bias dependence, indicating a possible suppression of impurity effects.

scholarly journals Symmetry Properties of Mixed and Heat Photo-Assisted Noise in the Quantum Hall Regime

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 730 ◽  
Author(s):  
Flavio Ronetti ◽  
Matteo Acciai ◽  
Dario Ferraro ◽  
Jérôme Rech ◽  
Thibaut Jonckheere Thierry Martin ◽  
...  
Keyword(s):  
Quantum Hall ◽  
Point Contact ◽  
Quantum Point Contact ◽  
Dc Voltage ◽  
Quantum Hall States ◽  
Quantum Hall Regime ◽  
Symmetry Properties ◽  
Hall Regime ◽  
Mixed Noise ◽  
Quantum Point

We investigate the photo-assisted charge-heat mixed noise and the heat noise generated by periodic drives in Quantum Hall states belonging to the Laughlin sequence. Fluctuations of the charge and heat currents are due to weak backscattering induced in a quantum point contact geometry and are evaluated at the lowest order in the tunneling amplitude. Focusing on the cases of a cosine and Lorentzian periodic drive, we show that the different symmetries of the photo-assisted tunneling amplitudes strongly affect the overall profile of these quantities as a function of the AC and DC voltage contributions, which can be tuned independently in experiments.

scholarly journals Coherent tunnelling across a quantum point contact in the quantum Hall regime

2013 ◽  
Vol 3 (1) ◽  
Author(s):  
F. Martins ◽  
S. Faniel ◽  
B. Rosenow ◽  
H. Sellier ◽  
S. Huant ◽  
...  
Keyword(s):  
Quantum Hall ◽  
Point Contact ◽  
Quantum Point Contact ◽  
Quantum Hall Regime ◽  
Hall Regime ◽  
Quantum Point

scholarly journals Anomalous integer quantum Hall effect in the ballistic regime with quantum point contacts

1989 ◽  
Vol 62 (10) ◽  
pp. 1181-1184 ◽  
Author(s):  
B. J. van Wees ◽  
E. M. M. Willems ◽  
C. J. P. M. Harmans ◽  
C. W. J. Beenakker ◽  
H. van Houten ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Quantum Point Contacts ◽  
Point Contacts ◽  
Ballistic Regime ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
Quantum Point
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