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

Armagnat, Pacome; Lacerda-Santos, Antonio; Rossignol, Benoît; Groth, Christoph; Waintal, Xavier

doi:10.21468/scipostphys.7.3.031

Cited by 22 publications

(21 citation statements)

References 42 publications

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“…Solving the full self-consistent electrostatic-quantum problem, beyond the above approximations and at low temperature, is a difficult task however, as the presence of the Landau levels (and the associated Dirac comb for the density of states) makes the set of equations highly nonlinear. In this letter, we use a newly developped numerical technique capable of handling this problem [35] and explore how the LB channels present at low field evolve into CSG compressible stripes at high magnetic field. Using the solution of the full self-consistent problem, we find that in a large region of the parameter space the system is in an 'hybrid' phase that borrows features from both the LB and CSG pictures.…”

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confidence: 99%

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Reconciling edge states with compressible stripes in a ballistic mesoscopic conductor

Armagnat

Waintal

2020

J. Phys. Mater.

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The well-known Landauer-Buttiker (LB) picture used to explain the quantum Hall effect uses the concept of (chiral) edge states that carry the current. In their seminal 1992 article, Chklovskii, Shklovskii and Glazman (CSG) showed that the LB picture does not account for some very basic properties of the gas, such as its density profile, as it lacks a proper treatment of the electrostatic energy. They showed that, instead, one should consider alternated stripes of compressible and incompressible phases. In this letter, we revisit this issue using a full solution of the quantum-electrostatic problem of a narrow ballistic conductor, beyond the CSG approach. We recover the LB channels at low field and the CSG compressible/incompressible stripes at high field. Our calculations reveal the existence of a third 'hybrid' phase at intermediate field. This hybrid phase has well defined LB type edge states, yet possesses a Landau level pinned at the Fermi energy as in the CSG picture. We calculate the magnetoconductance which reveals the interplay between the LB and CSG regimes. Our results have important implications for the propagation of edge magneto-plasmons.Electrostatic energy is very often the largest energy scale in a physical situation. Yet, the electrostatic landscape is equally often taken for granted as an external potential, which may result in a wrong physical picture. A well known example is the quantum Hall effect [1] (QHE) that has been largely discussed using the concept of edge states in a non-interacting Landauer-Buttiker (LB) picture [2, 3]. Despite being very successful for the understanding of e.g. the quantification of the Hall resistance and the vanishing longitudinal resistance, the LB picture also fails spectacularly to describe basic physics such as the density profile of the electron gas. In a series of articles [4-6] that culminated with the work of Chklovskii, Shklovskii and Glazman (CSG) [7-9], it was recognized that the LB picture should be revisited. It was shown that the interplay between quantum mechanics and electrostatics leads to the emergence of compressible and incompressible stripes, a concept related, yet somehow different, to the original edge states. An important effort has been devoted to the experimental observation of these stripes [10][11][12][13][14][15][16][17][18][19][20]. CSG work, as well as a large fraction of the subsequent litterature [21][22][23][24][25][26][27][28][29][30] was based on the Thomas-Fermi approximation which is suitable at high magnetic field but inadequate at low field where the LB approach is expected to work well. The self-consistent problem can also be tackled directly in presence of a finite temperature [31]. More recent works improved on Thomas-Fermi by incorporating a Gaussian broadening of the Landau levels [32][33][34]. Solving the full self-consistent electrostatic-quantum problem, beyond the above approximations and at low temperature, is a difficult task however, as the presence of the Landau levels (and the associated Dirac comb for the den...

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“…In the QHE regime, equations (1), (3), (4) and (5) form a highly nonlinear set of equations that we solve numerically. We refer to [35] for details of the calculations. A more precise model would replace the 2D electronic density n(x) by a 3D density…”

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Reconciling edge states with compressible stripes in a ballistic mesoscopic conductor

Armagnat

Waintal

2020

J. Phys. Mater.

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“…Finally, our treatment of the bias voltage dependence of the tunnel region is phenomenological. Future work could include computing finite-bias conductances with more realistic electrostatic potentials obtained by solving the self-consistent Schrödinger-Poisson equations [43,[52][53][54]. However, we expect that this will not change our qualitative findings.…”

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confidence: 97%

Conductance asymmetries in mesoscopic superconducting devices due to finite bias

et al. 2021

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Tunneling conductance spectroscopy in normal metal-superconductor junctions is an important tool for probing Andreev bound states in mesoscopic superconducting devices, such as Majorana nanowires. In an ideal superconducting device, the subgap conductance obeys specific symmetry relations, due to particle-hole symmetry and unitarity of the scattering matrix. However, experimental data often exhibits deviations from these symmetries or even their explicit breakdown. In this work, we identify a mechanism that leads to conductance asymmetries without quasiparticle poisoning. In particular, we investigate the effects of finite bias and include the voltage dependence in the tunnel barrier transparency, finding significant conductance asymmetries for realistic device parameters. It is important to identify the physical origin of conductance asymmetries: in contrast to other possible mechanisms such as quasiparticle poisoning, finite-bias effects are not detrimental to the performance of a topological qubit. To that end we identify features that can be used to experimentally determine whether finite-bias effects are the source of conductance asymmetries.

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“…The hybrid nanowire is placed on a dielectric layer of thickness 10 nm, and a backgate and two side gates are applied below or beside the nanowire. To obtain the electrostatic potential φ(r) for the setup, we solve the self-consistent Thomas Fermi-Poisson equation [31,32,[38][39][40][41]…”

Section: B Thomas Fermi-poisson Approachmentioning

confidence: 99%

Electronic properties of InAs/EuS/Al hybrid nanowires

et al. 2021

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We study the electronic properties of InAs/EuS/Al heterostructures as explored in a recent experiment [S. Vaitiekėnas et al., Nat. Phys. 17, 43 (2020)], combining both spectroscopic results and microscopic device simulations. In particular, we use angle-resolved photoemission spectroscopy to investigate the band bending at the InAs/EuS interface. The resulting band offset value serves as an essential input to subsequent microscopic device simulations, allowing us to map the electronic wave function distribution. We conclude that the magnetic proximity effects at the Al/EuS as well as the InAs/EuS interfaces are both essential to achieve topological superconductivity at zero applied magnetic field. Mapping the topological phase diagram as a function of gate voltages and proximity-induced exchange couplings, we show that the ferromagnetic hybrid nanowire with overlapping Al and EuS layers can become a topological superconductor within realistic parameter regimes. Our work highlights the need for a combined experimental and theoretical effort for faithful device simulations.

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

Cited by 22 publications

References 42 publications

Reconciling edge states with compressible stripes in a ballistic mesoscopic conductor

Reconciling edge states with compressible stripes in a ballistic mesoscopic conductor

Conductance asymmetries in mesoscopic superconducting devices due to finite bias

Electronic properties of InAs/EuS/Al hybrid nanowires

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