Spin and charge signatures of topological superconductivity in Rashba nanowires

Abstract

We consider a Rashba nanowire with a proximity gap which can be brought into the topological phase by tuning external magnetic field or chemical potential. We study spin and charge of the bulk quasiparticle states when passing through the topological transition for open and closed systems. We show, analytically and numerically, that the spin of bulk states around the topological gap reverses its sign when crossing the transition due to band inversion, independent of the presence of Majorana fermions in the system. This spin reversal can be considered as a bulk signature of topological superconductivity that can be accessed experimentally. We find a similar behavior for the charge of the bulk quasiparticle states, also exhibiting a sign reversal at the transition. We show that these signatures are robust against random static disorder. DOI: 10.1103/PhysRevB.96.041401Introduction. Topological phases of condensed matter systems [1,2] have attracted a lot of attention over many years due to their high promise for applications such as topological quantum computation [3,4]. One of the hallmarks of such phases, in particular of topological superconductivity, are zero-energy modes such as Majorana fermions (MF) that emerge at the edges of the system. Various candidate materials can host such topological states [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] but one of the most promising platforms are semiconducting nanowires of InAs or InSb material, with strong Rashba spin orbit interaction (SOI), subjected to an external magnetic field and in proximity to an s-wave superconductor [22,23]. Experimental evidence has been reported for topological phases in such wires [24][25][26][27][28][29][30][31] as well as in magnetic atomic chains on superconducting substrates [32][33][34]. However, most of the work so far has focused on the detection of the MFs in these nanowires and not on their bulk properties. This is quite surprising given the fact that the unambiguous identification of MFs from transport data alone can be challenging [35][36][37][38][39][40][41][42][43]. It is thus of great interest to look for alternative signatures of topological phases and to address the question how the bulk states change when passing from trivial to topological phase and if these changes appear in physically observable quantities.In this work, we show that the phase of a topological superconductor can be monitored by bulk states, in particular by certain spin and charge degrees of freedom. Quite remarkably, we find that the sign of the spin component along the magnetic field reverses for low-momentum states close to the Fermi level when the system passes through the phase transition, and similarly for the charge of such bulk states. This sign reversal is a direct consequence of the band inversion at the transition point and is directly accessible by spin-and energy resolved measurements. Another remarkable feature is that this signature is independent of boundary effects and thus unrelated to the presence of MFs. To demons...

Leakage of Majorana mode into correlated quantum dot nearby its singlet-doublet crossover

“…Upon entering the topological phase, there appear two Majorana quasiparticles simultaneously in both spin channels but with different spectral weights, what has been indeed reported in the STM measurements using a ferromagnetic tip [12]. Such issue has been recently addressed by several groups [11,13,14]. J. Klinovaja with co-workers [8] have shown that spin up and down tunneling amplitudes between MBSs and quantum dot depend on the spin-orbit interaction length.…”

“…For instance, in a weak coupling limit the Majorana modes show up either by the constructive or destructive interferometric lineshapes [7]. True leakage of Majorana mode into nontopological region is possible only in strongly hybridized structures [8][9][10][11] as indeed reported experimentally [1][2][3][4]. But even under such conditions, leakage of the Majorana mode into the side-coupled QD region could be affected by various effects, e.g.…”

Controlling the bound states in a quantum-dot hybrid nanowire

“…Increase of V g (o → p) leads to position of the QD energy level with majority ↑(↓)-spin character near (far above) the topological gap respectively. Additionally, dominant spin component reverses during the topological phase transition [81].…”

Distinguishing a Majorana zero mode using spin-resolved measurements

“…(14)), arguably, no unique experimental signature of MZMs is yet to be reported. Here we describe how spin-polarized spectroscopic mesurements (15)(16)(17)(18)(19)(20)(21) can be used to distinguish MZM from trival localized quasiparticles by showing features in such experiments that are a direct consequence of the nonlocality of the Hilbert space of MZMs emerging from a topological band structure. The spin polarization not only provides a litmus test for the existence of MZM, but also is a unique property of these novel qausi-particles that can be utilized for long-range transfer of quantum information between spin qubits (22,23).…”