Phase-tunable second-order topological superconductor

Abstract

Two-dimensional second-order topological superconductors (SOTSCs) have gapped bulk and edge states, with zero-energy Majorana bound states localized at corners. Motivated by recent advances in Majorana nanowire experiments, we propose to realize a tunable SOTSC as a two-dimensional nanowire array. We show that the coupling between the Majorana modes of adjacent wires can be controlled by phase-biasing the device, allowing to access a variety of topological phases. We characterize the system using scattering theory, which provides access to its transport properties and its topological invariants. The setup is robust against disorder, both in the nanowires themselves and in the Josephson junctions formed between adjacent wires. Further, we identify a parameter regime in which an initially trivial system is rendered topological upon adding disorder, providing an example of a second-order topological Anderson phase.

Simulating Floquet topological phases in static systems

“…For three-dimensional systems, it would be interesting to successively apply the nested scattering matrix construction twice. Furthermore, for HOTIs where only two of the four corners show zero modes [105][106][107][108], the reflection matrix from one side may show an odd number of topological states, thus simulating a Floquet system which falls outside of the existing, 'tenfold way' [109] classification of topological phases. Finally, it would be interesting to think about how to include many-body effects.…”

“…Time-reversal, particle-hole, and chiral symmetry require that W T V * T = V T W * T = T 2 = ±1, W P W * P = V P V * P = P 2 = ±1, and V C W P = C 2 = 1, respectively. We can choose a basis [33,71,108] such that the symmetries act on the lead modes as U T = V T T = W T T , U P = V T P = W T P , and…”

Floquet Second-Order Topological Phases in Momentum Space

“…The presence of these unique topological matter is usually guaranteed by the coexistence of crystal and non-spatial symmetries, and their classifications go beyond the tenfold way of first-order topological insulators and superconductors [ 9 , 10 , 11 , 12 ]. Besides great theoretical efforts in the study of higher-order topological insulators [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ], superconductors [ 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 ] and semimetals [ 49 , 50 , 51 , 52 , 53 , 54 ], HOTPs have also been observed in solid state materials [ 55 , 56 ,…”

Chiral-Symmetric Higher-Order Topological Phases of Matter

“…Higher-order topological band theory has expanded the classification of topological phases of matter across insulators [1][2][3][4][5][6][7][8][9], semimetals [10][11][12][13], and superconductors [14][15][16][17][18][19][20][21][22][23][24][25][26]. This theory generalizes the bulk-boundary correspondence of topological phases, so that an nthorder topological phase in d dimensions has protected features, such as gapless states or fractional charges, only at its (d − n)-dimensional boundaries.…”