Majorana Bound States without Vortices in Topological Superconductors with Electrostatic Defects

Abstract

Vortices in two-dimensional superconductors with broken time-reversal and spin-rotation symmetry can bind states at zero excitation energy. These so-called Majorana bound states transform a thermal insulator into a thermal metal and may be used to encode topologically protected qubits. We identify an alternative mechanism for the formation of Majorana bound states, akin to the way in which Shockley states are formed on metal surfaces: An electrostatic line defect can have a pair of Majorana bound states at the end points. The Shockley mechanism explains the appearance of a thermal metal in vortex-free lattice models of chiral p-wave superconductors and (unlike the vortex mechanism) is also operative in the topologically trivial phase. DOI: 10.1103/PhysRevLett.105.046803 PACS numbers: 73.20.At, 73.20.Hb, 74.20.Àz, 74.25.fc Two-dimensional superconductors with spin-polarizedtriplet, p-wave pairing symmetry have the unusual property that vortices in the order parameter can bind a nondegenerate state with zero excitation energy [1][2][3][4]. Such a midgap state is called a Majorana bound state, because the corresponding quasiparticle excitation is a Majorana fermion-equal to its own antiparticle. A pair of spatially separated Majorana bound states encodes a qubit, in a way which is protected from local sources of decoherence [5]. Since such a qubit might form the building block of a topological quantum computer [6], there is an intensive search [7][8][9][10][11][12] for two-dimensional superconductors with the required combination of broken time-reversal and spinrotation symmetries (symmetry class D [13]).The generic Bogoliubov-de Gennes Hamiltonian H of a chiral p-wave superconductor is only constrained by particle-hole symmetry, x H Ã x ¼ ÀH. At low excitation energies E (to second order in momentum p ¼ Ài@@=@r) it has the form H ¼ Áðp x x þ p y y Þ þ ½UðrÞ þ p 2 =2m z ; (1) for a uniform (vortex-free) pair potential Á. The electrostatic potential U (measured relative to the Fermi energy) opens up a band gap in the excitation spectrum. At U ¼ 0 the superconductor has a topological phase transition (known as the thermal quantum Hall effect) between two localized phases, one with and one without chiral edge states [14][15][16][17].Our key observation is that the Hamiltonian (1) on a lattice has Majorana bound states at the two end points of a linear electrostatic defect. The mechanism for the production of these bound states goes back to Shockley [18]: The band gap closes and then reopens upon formation of the defect, and as it reopens a pair of states splits off from the band edges to form localized states at the end points of the defect [see Fig. 1]. Such Shockley states appear in systems as varied as metals and narrow-band semiconductors [19], carbon nanotubes [20], and photonic crystals [21]. In these systems they are unprotected and can be pushed out of the band gap by local perturbations. In a superconductor, particle-hole symmetry requires the spectrum to be AEE symmetric, so an isolated bound state is co...

Scanning tunneling measurements of layers of superconducting 2H-TaSe2: Evidence for a zero-bias anomaly in single layers

“…Broadening of zero-bias conductance peaks in superconductors has been related to impurities, random disorder, or complex gap variations over the Fermi surface. 50,[61][62][63] We do not find evidence for impurities or random disorder. But gap size changes in different parts of the Fermi surface are likely to appear in the involved Fermi surface of 2H -TaSe 2 (Fig.…”

Introduction to topological superconductivity and Majorana fermions

“…Alternatively, MFs can appear if the gap is closed by variations in the chemical potential or electrostatic potential [11]. It is worth noting that isolated MFs can appear even in a spinful p x ± ip y -wave superconductor, in so-called half-quantum vortices [8], where there is a vortex for only one direction of the triplet (note that this also means a breaking of time-reversal symmetry).…”

“…Such quasiparticles do not occur in most types of superconductors and were instead first predicted to occur in the ν = 5/2 fractional quantum Hall state [4]. However, as we will discuss in more detail below, isolated MFs occur in general in vortices and on edges of effectively spinless superconducting systems with triplet pairing symmetry [5,6,7,8,9,10,11,12,13] (p-wave pairing symmetry in one dimension (1D) and p x ± ip y pairing symmetry in two dimensions (2D)). Triplet pairing has been predicted for the ground state of the superconductor Sr 2 RuO 4 [14], but is very sensitive to disorder and has never been observed experimentally.…”

Superconducting proximity effect in inverted InAs/GaSb quantum well structures with Ta electrodes

“…The emergence of Majorana fermions in solid-state systems may have profound implications in quantum computation [8][9][10] and it has triggered an avalanche of research activities [1][2][3][4][5][6][7][11][12][13][14] . Recently, two-dimensional topological insulators (or quantum spin Hall insulators) have attracted a great deal of attention due to being a promising material system for realizing Majorana fermions 9 .…”