Fermion parity switches of the ground state of Majorana billiards

Pekerten, Barış; Bozkurt, Ayhan; Adagideli, İnanç

doi:10.1103/physrevb.100.235455

Cited by 4 publications

(3 citation statements)

References 81 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The exact zero energy solutions of the isolated Kitaev chain represent fermion parity switches, 36,[46][47][48] and for given t, ∆ occur for discrete values of µ. Close to the Majorana lines one always finds eigenstates with exponentially small energy, as seen in Fig.…”

Section: The Isolated Kitaev Chainmentioning

confidence: 89%

Linear and non-linear transport across a finite Kitaev chain: an exact analytical study

Leumer,

Marganska,

Muralidharan

et al. 2020

Preprint

View full text Add to dashboard Cite

We present exact analytical results for the differential conductance of a finite Kitaev chain in an N-S-N configuration, where the topological superconductor is contacted on both sides with normal leads. Our results are obtained with the Keldysh non-equilibrium Green's functions technique, using the full spectrum of the Kitaev chain without resorting to minimal models. A closed formula for the linear conductance is given, and the analytical procedure to obtain the differential conductance for the transport mediated by higher excitations is described. The linear conductance attains the maximum value of e 2 /h only for the exact zero energy states. Also the differential conductance exhibits a complex pattern created by numerous crossings and anticrossings in the excitation spectrum. We reveal the crossings to be protected by the inversion symmetry, while the anticrossings result from a pairing-induced hybridization of particle-like and hole-like solutions with the same inversion character. Our comprehensive treatment of the Kitaev chain allows us also to identify the contributions of both local and non-local transmission processes to transport at arbitrary bias voltage. Local Andreev reflection processes dominate the transport within the bulk gap and diminish for higher excited states, but reemerge when the bias voltage probes the avoided crossings. The non-local direct transmission is enhanced above the bulk gap, but contributes also to the transport mediated by the topological states.

show abstract

Section: The Isolated Kitaev Chainmentioning

confidence: 89%

Linear and non-linear transport across a finite Kitaev chain: an exact analytical study

Leumer,

Marganska,

Muralidharan

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…The exact zero-energy solutions of the isolated Kitaev chain represent fermion parity switches [36,[45][46][47] and, for given t, occur for discrete values of μ. Although the finite size effects may raise the energy of the topological states so high that they do not contribute to the zero-bias conductance (see, e.g., the low conductance regions in Fig.…”

Section: The Isolated Kitaev Chainmentioning

confidence: 99%

Linear and nonlinear transport across a finite Kitaev chain: An exact analytical study

et al. 2021

View full text Add to dashboard Cite

We present exact analytical results for the differential conductance of a finite Kitaev chain in an N-S-N configuration, where the topological superconductor is contacted on both sides with normal leads. Our results are obtained with the Keldysh nonequilibrium Green's function technique, using the full spectrum of the Kitaev chain without resorting to minimal models. A closed formula for the linear conductance is given, and the analytical procedure to obtain the differential conductance for the transport mediated by higher excitations is described. The linear conductance attains the maximum value of e 2 /h only for the exact zero-energy states. Also, the differential conductance exhibits a complex pattern created by numerous crossings and anticrossings in the excitation spectrum. We reveal the crossings to be protected by inversion symmetry, while the anticrossings result from a pairing-induced hybridization of particlelike and holelike solutions with the same inversion character. Our comprehensive treatment of the Kitaev chain allows us also to identify the contributions of both local and nonlocal transmission processes to transport at arbitrary bias voltage. Local Andreev reflection processes dominate the transport within the bulk gap and diminish for higher excited states but reemerge when the bias voltage probes the avoided crossings. The nonlocal direct transmission is enhanced above the bulk gap but contributes also to the transport mediated by the topological states.

show abstract

“…The topological charge determines whether the system is in the trivial (Q = 1) or topological (Q = −1) phase. [71][72][73][74][75][76]…”

Section: B Topological Gap and Topological Chargementioning

confidence: 99%

Anisotropic topological superconductivity in Josephson junctions

Pekerten,

Pakizer,

Hawn

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We investigate the effects of magnetic and crystalline anisotropies on the topological superconducting state of planar Josephson junctions (JJs). In junctions where only Rashba spin-orbit coupling (SOC) is present, the topological phase diagram is insensitive to the supercurrent direction, but exhibits a strong dependence on the magnetic field orientation. However, when both Rashba and Dresselhaus SOCs coexist, the topological phase diagram strongly depends on both the magnetic field and junction crystallographic orientations. We examine the impact of the magnetic and crystalline anisotropy on the current-phase relation (CPR), energy spectrum, and topological gap of phase-biased JJs, where the junction is connected in a loop and the superconducting phase difference is fixed by a loop-threading magnetic flux. The anisotropic CPR can be used to extract the ground-sate phase (i.e. the superconducting phase difference that minimizes the system free energy) behavior in phase-unbiased JJs with no magnetic flux. Under appropriate conditions, phase-unbiased JJs can self-tune into or out of the topological superconducting state by rotating the in-plane magnetic field. The magnetic field orientations at which topological transitions occur strongly depends on both the junction crystallographic orientation and the relative strength between Rashba and Dresselhaus SOCs. We find that for an optimal practical application, in which the junction exhibits topological superconductivity with a sizeable topological gap, a careful balancing of the magnetic field direction, the junction crystallographic orientation, and the relative strengths of the Rashba and Dresselhaus SOCs is required. We discuss the considerations that must be undertaken to achieve this balancing for various junction types and parameters.

show abstract

Fermion parity switches of the ground state of Majorana billiards

Cited by 4 publications

References 81 publications

Linear and non-linear transport across a finite Kitaev chain: an exact analytical study

Linear and non-linear transport across a finite Kitaev chain: an exact analytical study

Linear and nonlinear transport across a finite Kitaev chain: An exact analytical study

Anisotropic topological superconductivity in Josephson junctions

Contact Info

Product

Resources

About