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

Abstract

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.

Can non-local conductance spectra conclusively signal Majorana zero modes? -- Insights from von Neumann entropy

“…Figure 2 shows the eigenspectrum for different setup configurations as a function of µ with constant t and ∆. Figure 2(a) shows the eigenspectrum for a pristine chain of length N = 100 with t = ∆, which corresponds to the Kitaev point [43,44]. As expected, the topological phase (µ/∆ < 2) hosts two MZMs and in the trivial phase (µ/∆ > 2) the MZMs vanish.…”

“…We use the Keldysh non-equilibrium Green's function formalism to evaluate the terminal currents [44,46]. The Keldysh Green's functions are defined over the Keldysh contour, which typically involves the retarded (advanced) Green's function G r(a) and the lesser (greater) Green's function G <(>) .…”

“…The Keldysh Green's functions are defined over the Keldysh contour, which typically involves the retarded (advanced) Green's function G r(a) and the lesser (greater) Green's function G <(>) . The Fourier transform of the Green's function into the energy domain gives the standard steady-state prescription for the transport calculations [44,46] involving the density of states, the correlators, and the currents across the setup. Details of this calculation are presented in the supplementary material.…”

Topological signatures in a weakly dissipative Kitaev chain of finite length

“…Despite the great amount of studies carried out on the Kitaev chain (see, e.g., Ref. [15] and references therein), a complete description of the associated eigenvalue problem for finite N has been achieved only recently [26][27][28][29][30][31].…”

“…For our purposes, it is sufficient to observe that there exist nontrivial values of the parameters t, µ, ∆ leading to the appearance of degeneracies in the excitation spectrum [31]. Therefore, to avoid complications in deriving the master equation in the dissipative scenario [9], we will limit ourselves to the case t = ∆ and µ = 0, which is known to be degeneracy-free, as discussed below.…”