Majorana spintronics

For Josephson junctions based on s-wave superconductors, time-reversal symmetry is known to allow for powerful relations between the normal-state junction properties, the excitation spectrum, and the Josephson current. Here we provide analogous relations for Josephson junctions involving one-dimensional time-reversal invariant topological superconductors supporting Majorana-Kramers pairs, considering both topological-topological and s-wave-topological junctions. Working in the regime where the junction is much shorter than the superconducting coherence length, we obtain a number of analytical and numerical results that hold for arbitrary normal-state conductance and the most general forms of spin-orbit coupling. The signatures of topological superconductivity we find include the fractional AC Josephson effect, which arises in topological-topological junctions provided that the energy relaxation is sufficiently slow. We also show, for both junction types, that robust signatures of topological superconductivity arise in the DC Josephson effect in the form of switches in the Josephson current due to zero-energy crossings of Andreev levels. The junction spinorbit coupling enters the Josephson current only in the topological-topological case and in a manner determined by the switch locations, thereby allowing quantitative predictions for experiments with the normal-state conductance, the induced gaps, and the switch locations as inputs.

“…∆ − > 0), the superconductor is nontopological. From the secular equation (17), the Andreev energies for a nontopological junction are given by the solutions to the two equations…”

Section: Nontopological Variantmentioning

confidence: 99%

Signatures of time-reversal-invariant topological superconductivity in the Josephson effect

Mellars

Béri

2016

“…We have constructed a lattice Hamiltonian from which the continuum Hamiltonian is derived. In the lattice Hamiltonian (17), N represents the number of the nearest adjacent sites. Hence, the case for N = 2 can be embedded into the layered square lattice, while the case for N = 3 can be embedded into the layered triangular lattice 15,16 .…”

Section: Fermi Arcsmentioning

confidence: 99%

“…Double-and triple-Weyl semimetals are generalization of Weyl semimetals, where the monopole charges are 2 and 3, respectively [15][16][17][18][19][20] . It has theoretically been proposed that quadratic-and cubic-Dirac insulators are also possible based on the symmetry considerations 16 .…”

mentioning

confidence: 99%

Merging of momentum-space monopoles by controlling Zeeman field: From cubic-Dirac to triple-Weyl fermion systems

Ezawa

2017

We analyze a generalized Dirac system, where the dispersion along the kx and ky axes is N -th power and linear along the kz axis. When we apply magnetic field, there emerge N monopole-antimonopole pairs beyond a certain critical field in general. As the direction of the magnetic field is rotated toward the z axis, monopoles move to the north pole while antimonopoles move to the south pole. When the magnetic field becomes parallel to the z axis, they merge into one monopole or one antimonopole whose monopole charge is ±N . The resultant system is a multiple-Weyl semimetal. Characteristic properties of such a system are that the anomalous Hall effect and the chiral anomaly are enhanced by N times and that N Fermi arcs appear. These phenomena will be observed experimentally in the cubic-Dirac and triple-Weyl fermion systems (N = 3).Introduction: Topological objects in the momentum space play intriguing roles in the field of condensed matter physics [1][2][3][4] . Examples are monopoles, skyrmions and merons. They have fascinating properties that are not shared by the corresponding ones in the real space, since they are purely static because of the absence of the kinetic energy. For instance, a monopole carrying a large magnetic charge cannot exist in the real space due to a large Coulomb repulsion but can in the momentum space. It is an interesting problem if we may generate N monopole-antimonopole pairs and successively make them merged into one monopole-antimonopole pair each of which carries monopole charge ±N just by controlling an external parameter.

“…It is protected by a monopole charge in the momentum space 3 . Multiple Weyl semimetal is a generalization of a Weyl semimetal which has a monopole charge larger than the unit charge [4][5][6][7] .There exist another class of novel semimetals. They are line nodal semimetals whose Fermi surfaces form one-dimensional lines [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] .…”

mentioning

confidence: 99%

Photoinduced topological phase transition from a crossing-line nodal semimetal to a multiple-Weyl semimetal

Ezawa

2017

We propose a simple scheme to construct a model whose Fermi surface is comprised of crossing-line nodes. The Hamiltonian consists of a normal hopping term and an additional term which is odd under the mirror reflection. The line nodes appear along the mirror-invariant planes, where each line node carries the quantized Berry magnetic flux. We explicitly construct a model with the N -fold rotational symmetry, where the 2N line nodes merge at the north and south poles. Photoirradiation induces a topological phase transition. When we apply photoirradiation along the kz axis, there emerge point nodes carrying the monopole charge ±N at these poles, while all the line nodes disappear. The resultant system describes anisotropic multiple-Weyl fermions.Introduction: Weyl semimetal is one of the hottest topics in condensed matter physics 1,2 . It is protected by a monopole charge in the momentum space 3 . Multiple Weyl semimetal is a generalization of a Weyl semimetal which has a monopole charge larger than the unit charge [4][5][6][7] .There exist another class of novel semimetals. They are line nodal semimetals whose Fermi surfaces form one-dimensional lines [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] . A line node is protected by a quantized Berry magnetic flux. Recently, line nodal semimetals are generalized into two species. One is a loop node forming a nontrivial link such as the Hopf link [26][27][28][29] . The other is a crossing-line node, where several line nodes cross at a point [30][31][32][33][34][35] . Photoirradiation is a powerful tool to modify the band structure [36][37][38][39][40][41] . According to the Floquet theory an additional term emerges due to the second-order process of photoirradiation. A typical example is the generation of a Weyl point from a Dirac semimetal [42][43][44][45] . It is shown that a Weyl node can also be generated by applying photoirradiation to a loop nodal semimetal 46,47 . In this paper, we first propose a simple scheme to construct models for crossing-line nodal semimetals. We then investigate how a crossing-line nodal semimetal is modified by way of photoirradiation. The model Hamiltonian consists of a normal hopping term and a mirror-odd interaction term. A line node emerges on the mirror-invariant plane. Each line node is topologically protected by the quantized Berry magnetic flux. Explicitly, we construct an N -fold rotational symmetric model, where the crossing of 2N -fold line nodes occurs at the north pole and also at the south pole. There are no magnetic monopoles at these poles. Next, we derive a photoinduced term based on the Floquet theory. It induces a topological phase transition. Indeed, by applying photoirradiation along the z direction, the Fermi surface is found to disappear by the emergence of gap except for two nodal points carrying the N (−N ) units of the monopole charge at the north (south) pole. The resultant system is the anisotropic N -fold multiple-Weyl semimetal. On the other hand, by applying photoirradiation perpendicu...