Vortex-lattice structure and topological superconductivity in the quantum Hall regime

Abstract

Chiral topological superconductors are expected to appear as intermediate states when a quantum anomalous Hall system is proximity coupled to an s-wave superconductor and the magnetization direction is reversed. In this paper we address the edge state properties of ordinary quantum Hall systems proximity coupled to s-wave superconductors, accounting explicitly for Landau quantization. We find that the appearance of topological superconducting phases with an odd number of Majorana edge modes is dependent on the structure of the system's vortex lattice. More precisely, vortex lattices containing odd number of superconducting flux quanta per unit cell, always support an even number of chiral edge channels and are therefore adiabatically connected to normal quantum Hall insulators. We discuss strategies to engineer chiral topological superconductivity in proximity-coupled quantum Hall systems by manipulating vortex lattice structure. arXiv:1903.12249v3 [cond-mat.mes-hall] 9 Jan 2020

Nonequilibrium edge transport in quantum Hall based Josephson junctions

“…(25) and (26) in Eq. (8). In this model, the transmission is strongly dependent on the angle α that determines the distance between the leads, as opposed to the chiral model.…”

“…The possibility of marrying superconductivity with the quantum Hall (QH) effect has brought to the table a plethora of novel physical phenomena: from the emergence of Andreev edge states [1,2] and crossed Andreev conversion [3,4] to realizations of non-Abelian anyons [5,6] and chiral Majorana fermions [7,8]. In a series of recent experiments [9][10][11][12][13][14][15], superconducting correlations were successfully induced at the edges of integer quantum Hall samples, paving the way to a new generation of such promising hybrid devices.…”

Quantum Hall Superconductivity from Moir{é} Landau Levels

“…Because these prerequisites for quantum Hall superconductivity are rarely satisfied, twisted bilayer graphene provides a rare opportunity to pursue exotic quantum Hall pair states. A number of proposals to engineer topological superconducting states rely on pairing of Landau quantized electrons [13][14][15]. The widespread interest in topological superconductivity and * gchaudhary@anl.gov…”

Hall effect for Dirac electrons in graphene exposed to an Abrikosov flux lattice

“…Introduction. -A promising strategy for creating particles obeying non-Abelian braiding statistics, which may be useful for quantum computation [1], is to integrate superconductivity into the integer quantum Hall (QH) effect, which can produce topological superconductivity (TS) supporting Majorana particles [2][3][4][5][6][7][8][9][10][11][12][13]. One of the (many) practical challenges toward achieving this goal is that the strong magnetic field required for QH effect usually kills superconductivity.…”

“…Even if systems can be found wherein superconductivity survives to sufficiently high magnetic fields, a fundamental difficulty is that a gapped QH state does not couple to a superconductor in a meaningful manner. One can overcome this impediment by considering non-uniform magnetic fields, which produce "dispersive" Landau levels and thus allow, when partially filled, proximity coupling to superconductivity [12,13] This motivates, as a first step, the need to gain an understanding of QH effect in the presence of non-uniform magnetic fields. In practice, such non-uniform fields are naturally produced by the nearby superconductor itself, in the form of an Abrikosov flux lattice.…”