Cusps near Topological Phase Transitions: Signatures of Majorana fermions and interactions with fluctuations

Abstract

In this article, we study non-analyticities or cusps near a topological phase transition driven by changes of global topologies rather than by the formation of conventional (local) order. The particular phase transitions between topologically ordered superfluids and non-topological superfluids studied in this article are always accompanied by the emergence or disappearance of Majorana boundary modes, while at the critical point these boundary modes are liberated and evolve into the bulk. Proliferation of massless Majorana fermions at the transition leaves unique thermodynamic signatures. For a very broad class of isotropic superfluids or superconductors (with or without time reversal symmetry), the resultant transitions in $d$ spatial dimensions will be of $(d+1)$th order. The $(d+1)$th order derivatives of the grand potential are either discontinuous in even dimensions or logarithmically divergent in odd dimensions. Bulk quantities such as compressibility can develop a cusp along with the change of topology of the superfluids. We compute quantitatively the cusp structures and further investigate the effect of interactions induced by massive fluctuation fields. These cusps are direct manifestations of Majorana fermions and their interactions, and can be potentially considered as an alternative approach for detecting these puzzling particles.

19 pages, 9 figures

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Cited by in corpus (9)

• Local and non-local quantum transport due to Andreev bound states in finite Rashba nanowires with superconducting and normal sections
• Majorana bound states in semiconducting nanostructures
• Topological Quantum Critical Points in Strong Coupling limits: Global Symmetries and Strongly Interacting Majorana Fermions
• Topological Quantum Criticality in Superfluids and Superconductors: Surface criticality, Thermal properties, and Lifshitz Majorana fields
• Tricritical physics in two-dimensional $p$-wave superfluids
• Euler--Chern Correspondence via Topological Superconductivity
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• Discrete global symmetries and dynamics of emergent fermions
• Equivalence class of Emergent Single Weyl fermion lattice models in 3 dimensions: gapless superconductors and superfluids versus chiral fermions