Density of states at disorder-induced phase transitions in a multichannel Majorana wire

Abstract

An N-channel spinless p-wave superconducting wire is known to go through a series of N topological phase transitions upon increasing the disorder strength. Here, we show that at each of those transitions the density of states shows a Dyson singularity ν(ε) ∝ ε −1 | ln ε| −3 , whereas ν(ε) ∝ ε |α|−1 has a power-law singularity for small energies ε away from the critical points. Using the concept of "superuniversality" [Gruzberg, Read, and Vishveshwara, Phys. Rev. B 71, 245124 (2005)], we are able to relate the exponent α to the wire's transport properties at zero energy and, hence, to the mean free path l and the superconducting coherence length ξ.

Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains

“…Energy spectrum and Majorana energy splitting Disordered Kitaev chains have formed the topic of active research for over a decade for several reasons [36][37][38][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] . Belonging to the symmetry classes D and BDI (depending on whether they respect time reversal symmetry breaking or not), these systems exhibit behavior that starkly deviates from that of their normal counterparts.…”

“…Several investigations on the distribution of these mid-gap states have explored scaling of density-of-states in Griffiths phases, transport properties and topological phase transitions in the context of disordered Majorana wires. [36][37][38][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] . Here, as a simple illustration, in Fig.…”

“…Subsequent to pioneering work in Ref. 37, several recent works have studied Majorana physics in the presence of disorder 35,36,38,[44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] . Along with some other random-matrix based treatments 59,60 , our present work is one of the few to explicitly address the issue of Majorana mode based fermion parity switches in the presence of disorder.…”

Detecting the existence of Majorana fermions via the Dicke-like effect in a triple quantum-dot system

“…One theoretically explored an interferometry of a chiral Majorana edge channel formed at the interface between a superconductor and a topological insulator under an external magnetic field, quantum-transport properties can manifest the obvious signatures of Majorana modes [29]. Since quantum dots(QDs) as the artificial granules can provide an excellent model system to study quantum transport behaviors, very recently, the searches for Majorana quasi-particles have become a focus of intense attention based on the granular QD devices [20,[31][32][33][34]. A scheme for manipulating the MBS has been addressed based on Coulomb blockaded quantum dots(QDs), it is found that the QDs may be utilized for readout of the state of the Majorana system [35].…”

“…One of the most promising candidate proposals for the full demonstration of MFs is to use semiconducting nanowires(InAS or InSb wires) with a strong spin-orbit interaction, where a nanowire is placed in proximity to a superconductor and biased with a magnetic field. For a one-dimensional topological superconductor(TS) quantum wire, Majorana modes are localized at the edge of the nanowire, some experimental realizations have been recently reported that the search for MFs has been successful in semiconductor wires on superconducting surfaces [18][19][20][21][22]. Certainly, other alternative routes to detect the properties of MFs and manipulate them also are provided including noise measurements [23], resonant Andreev tunneling [24], the 4π-periodic MajoranaJosephson effect [25], the phase-related electric conductance [26], and so forth.…”