Decaying spectral oscillations in a Majorana wire with finite coherence length

Abstract

Motivated by recent experiments, we investigate the excitation energy of a proximitized Rashba wire in the presence of a position dependent pairing. In particular, we focus on the spectroscopic pattern produced by the overlap between two Majorana bound states that appear for values of the Zeeman field smaller than the value necessary for reaching the bulk topological superconducting phase. The two Majorana bound states can arise because locally the wire is in the topological regime. We find three parameter ranges with different spectral properties: crossings, anticrossings and asymptotic reduction of the energy as a function of the applied Zeeman field. Interestingly, all these cases have already been observed experimentally. Moreover, since an increment of the magnetic field implies the increase of the distance between the Majorana bound states, the amplitude of the energy oscillations, when present, gets reduced. The existence of the different Majorana scenarios crucially relies on the fact that the two Majorana bound states have distinct k-space structures. We develop analytical models that clearly explain the microscopic origin of the predicted behavior.

Interaction-induced zero-energy pinning and quantum dot formation in Majorana nanowires

“…The Majorana overlap, which is a measurement of the degree of non-locality of the two Majorana wave functions, mostly depends on the length of the nanowire (and to a lesser extent on other parameters, such as the induced superconductor gap and the Rashba coupling), but it is not necessarily correlated to the Majorana energy splitting. Different mechanisms can reduce this splitting, such as interactions with the environment as studied here, smooth potential or gap profiles [21,26–28 30], or orbital magnetic effects [31], and still leave the Majorana overlap unaffected. The behavior of the Majorana wave functions in this case is illustrated in Fig.…”

“…Conspicuously, in most of the available experimental data the emergence of a robust zero-bias conductance peak is observed above some critical Zeeman field without the expected oscillatory pattern [12,19,24–25]. Several mechanisms have been proposed to account for the reduction or lack of oscillations, such as smooth confinement [21,26–28], strong spin–orbit coupling [29], position-dependent pairing [30], orbital magnetic effects [31], Coulomb repulsion among the carriers in the nanowire [22], or the presence of the normal drain lead connected to the hybrid wire [32]. …”

Subband occupation in semiconductor-superconductor nanowires

“…While many experimental results are consistent with the presence of Majorana zero modes, there are concerns that at least some of the observations of zerobias conductance peaks are actually associated with nontopological low-energy Andreev bound states (ABSs). Such low-energy ABSs can be produced by several sources, including soft confinement 24,25 , inhomogeneous superconducting pairing 26 , disorder [27][28][29][30] , accidental quantum dots 31,32 , and inter-subband coupling 33 . This is especially concerning in the case of trivial low-energy states that mimic very faithfully the local phenomenology of Majorana zero modes, the so-called quasi-Majorana 34 , or partially-separated ABS states 35 .…”

Fractional charge oscillations in quantum dots with quantum spin Hall effect

“…Its low energy properties are well described by Dirac-like Hamiltonians [2]: Klein tunneling has been theoretically predicted [3] and experimentally observed [4] and Zitterbewegung is believed to matter for the motion of its electrons [5]. More recently, it has been shown that the chiral anomaly [6][7][8] is crucial in the understanding of the electromagnetic response of Weyl semimetals [9][10][11][12][13][14][15][16][17][18][19][20][21] and the behavior of two-dimensional topological insulators in the presence of magnetic barriers [22]. Another connection between high energy and condensed matter physics is charge fractionalization due to the Jackiw-Rebbi mechanism [23], which has been shown to play a role in polyacetylene [24].…”

“…Fractional charges with charge e/2 have also been recently proposed to appear in carbon nanotubes under the influence of non-uniform strain and magnetic fields [25]. More general fractional charges, corresponding to complex solitons, [26] are hosted by magnetically defined quantum dots defined at the edges of two dimensional topological insulators [22,[27][28][29], even in the presence of weak interactions [28,29]. A different type of charge fractionalization is known to take place in strongly interacting condensed matter systems.…”