Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1201.0177 · Physical Review Letters

Emergence of Majorana and Dirac Particles in Ultracold Fermions via Tunable Interactions, Spin-Orbit Effects, and Zeeman Fields

Kangjun Seo, Han Li, C. A. R. Sá de Melo

Published Sep 6, 2012• 58 citations
arXivHTMLPDF

Abstract

We discuss the emergence of rings of zero-energy excitations in momentum space for superfluid phases of ultracold fermions when spin-orbit effects, Zeeman fields, and interactions are varied. We show that phases containing rings of nodes possess nontrivial topological invariants, and that phase transitions between distinct topological phases belong to the Lifshitz class. Upon crossing phase boundaries, existing massless Dirac fermions in the gapless phase annihilate to produce bulk zero-mode Majorana fermions at phase boundaries, and then become massive Dirac fermions in the gapped phase. We characterize these tunable topological phase transitions via several spectroscopic properties, including excitation spectrum, spectral function, and momentum distribution.

DOI
10.1103/physrevlett.109.105303

Related papers

Topological phase transitions in ultracold Fermi superfluids: The evolution from Bardeen-Cooper-Schrieffer to Bose-Einstein-condensate superfluids under artificial spin-orbit fields

Kangjun Seo, Han Li, C. A. R. Sá de Melo

We discuss topological phase transitions in ultracold Fermi superfluids induced by interactions and artificial spin-orbit fields. We construct the phase diagram for population-imbalanced systems at zero and finite temperatures, and analyze spectroscopic and thermodynamic properties to characterize various phase transitions. For balanced systems, the evolution from Bardeen-Cooper-Schrieffer to Bose-Einstein-condensate superfluids in the presence of spin-orbit effects is only a crossover as the system remains fully gapped, even though a triplet component of the order parameter emerges in the helicity basis. However, for imbalanced populations, spin-orbit fields induce a triplet component for the order parameter in the helicity basis, and may produce nodes in the quasiparticle excitation spectrum leading to bulk topological phase transitions of the Lifshitz type. Additionally a fully gapped phase exists, where a crossover from indirect to direct gap occurs, but a topological transition to a gapped phase possessing Majorana fermion edge states does not occur.

arXiv:1108.4068•Physical Review A•Mar 2, 2012•54 citations

Artificial spin-orbit coupling in ultra-cold Fermi superfluids

Kangjun Seo, Han Li, C. A. R. Sá de Melo

We develop a theory for interacting fermions in the presence of spin-orbit coupling and Zeeman fields, and show that many new superfluids phases, which are topological in nature, emerge. Depending on values of spin-orbit coupling, Zeeman fields, and interactions, initially gapped s-wave superfluids acquire p-wave, d-wave, f-wave and higher angular momentum components, which produce zeros in the excitation spectrum, rendering the superfluid gapless. Several multi-critical points, which separate topological superfluid phases from normal or non-uniform, are accessible depending on spin-orbit coupling, Zeeman fields or interactions, setting the stage for the study of tunable topological superfluids.

arXiv:1110.6364•Oct 28, 2011•1 citation

Quantum phases of interacting three-component fermions under the influence of spin-orbit coupling and Zeeman fields

Dog̃a Murat Kürkçüog̃lu, C. A. R. Sá de Melo

We describe the quantum phases of interacting three component fermions in the presence of spin-orbit coupling, as well as linear and quadratic Zeeman fields. We classify the emerging superfluid phases in terms of the loci of zeros of their quasi-particle excitation spectrum in momentum space, and we identify several Lifshitz-type topological transitions. In the particular case of vanishing quadratic Zeeman field, a quintuple point exists where four gapless superfluid phases with surface and line nodes converge into a fully gapped superfluid phase. Lastly, we also show that the simultaneous presence of spin-orbit and Zeeman fields transforms a momentum-independent scalar order parameter into an explicitly momentum-dependent tensor in the generalized helicity basis.

arXiv:1612.02365•Dec 7, 2016•0 citations

Gapless topological Fulde-Ferrell superfluidity induced by an in-plane Zeeman field

Hui Hu, Lin Dong, Ye Cao +2 more

Topological superfluids are recently discovered quantum matter that hosts topologically protected gapless edge states known as Majorana fermions---exotic quantum particles that act as their own antiparticles and obey non-Abelian statistics. Their realizations are believed to lie at the heart of future technologies such as fault-tolerant quantum computation. To date, the most efficient scheme to create topological superfluids and Majorana fermions is based on the Sau-Lutchyn-Tewari-Das Sarma model with a Rashba-type spin-orbit coupling on the x-y plane and a large out-of-plane (perpendicular) Zeeman field along the z direction. Here we propose an alternative setup, where the topological superfluid phase is driven by applying an in-plane Zeeman field. This scheme offers a number of different features, notably Cooper pairings at finite center-of-mass momentum (i.e., Fulde-Ferrell pairing) and gapless excitations in the bulk. As a result, gapless topological quantum matter with an inhomogeneous pairing order parameter appears. It features unidirectional Majorana surface states at boundaries, which propagate in the same direction and connect two Weyl nodes in the bulk. We demonstrate the emergence of such exotic topological matter and the associated Majorana fermions in spin-orbit coupled atomic Fermi gases, and we determine its parameter space. The implementation of our scheme in semiconductor/superconductor heterostructures is briefly discussed.

arXiv:1404.2442•Physical Review A•Sep 24, 2014•23 citations

Thermodynamic signatures for topological phase transitions to Majorana and Weyl superfluids in ultracold Fermi gases

Kangjun Seo, Chuanwei Zhang, Sumanta Tewari

We discuss the thermodynamic signatures for the topological phase transitions into Majorana and Weyl superfluid phases in ultracold Fermi gases in two and three dimensions (2D and 3D) in the presence of Rashba spin-orbit coupling and a Zeeman field. We analyze the thermodynamic properties exhibiting the distinct nature of the topological phase transitions linked with the Majorana fermions (2D Fermi gas) and Weyl fermions (3D Fermi gas) which can be observed experimentally, including pressure, chemical potential, isothermal compressibility, entropy, and specific heat, as a function of the interaction and the Zeeman field at both zero and finite temperatures. We conclude that among the various thermodynamic quantities, the isothermal compressibility and the chemical potential as functions of the artificial Zeeman field have the strongest signatures of the topological transitions in both two and three dimensions.

arXiv:1302.4747•Physical Review A•Jun 19, 2013•21 citations

Three-dimensional spin–orbit coupled Fermi gases: Fulde–Ferrell pairing, Majorana fermions, Weyl fermions, and gapless topological superfluidity

Xia-Ji Liu, Hui Hu, Han Pu

We theoretically investigate a three-dimensional Fermi gas with Rashba spin–orbit coupling in the presence of both out-of-plane and in-plane Zeeman fields. We show that, driven by a sufficiently large Zeeman field, either out-of-plane or in-plane, the superfluid phase of this system exhibits a number of interesting features, including inhomogeneous Fulde–Ferrell pairing, gapped or gapless topological order, and exotic quasi-particle excitations known as Weyl fermions that have linear energy dispersions in momentum space (i.e., massless Dirac fermions). The topological superfluid phase can have either four or two topologically protected Weyl nodes. We present the phase diagrams at both zero and finite temperatures and discuss the possibility of their observation in an atomic Fermi gas with synthetic spin–orbit coupling. In this context, topological superfluid phase with an imperfect Rashba spin–orbit coupling is also studied.

arXiv:1411.2993•Chinese Physics B•Apr 30, 2015•16 citations
We discuss the emergence of rings of zero-energy excitations in momentum space for superfluid phases of ultracold fermions when spin-orbit effects, Zeeman fields, and interactions are varied. We show that phases containing rings of nodes possess nontrivial topological invariants, and that phase transitions between distinct topological phases belong to the Lifshitz class. Upon crossing phase boundaries, existing massless Dirac fermions in the gapless phase annihilate to produce bulk zero-mode Majorana fermions at phase boundaries, and then become massive Dirac fermions in the gapped phase. We characterize these tunable topological phase transitions via several spectroscopic properties, including excitation spectrum, spectral function, and momentum distribution.
We discuss topological phase transitions in ultracold Fermi superfluids induced by interactions and artificial spin-orbit fields. We construct the phase diagram for population-imbalanced systems at zero and finite temperatures, and analyze spectroscopic and thermodynamic properties to characterize various phase transitions. For balanced systems, the evolution from Bardeen-Cooper-Schrieffer to Bose-Einstein-condensate superfluids in the presence of spin-orbit effects is only a crossover as the system remains fully gapped, even though a triplet component of the order parameter emerges in the helicity basis. However, for imbalanced populations, spin-orbit fields induce a triplet component for the order parameter in the helicity basis, and may produce nodes in the quasiparticle excitation spectrum leading to bulk topological phase transitions of the Lifshitz type. Additionally a fully gapped phase exists, where a crossover from indirect to direct gap occurs, but a topological transition to a gapped phase possessing Majorana fermion edge states does not occur.
We develop a theory for interacting fermions in the presence of spin-orbit coupling and Zeeman fields, and show that many new superfluids phases, which are topological in nature, emerge. Depending on values of spin-orbit coupling, Zeeman fields, and interactions, initially gapped s-wave superfluids acquire p-wave, d-wave, f-wave and higher angular momentum components, which produce zeros in the excitation spectrum, rendering the superfluid gapless. Several multi-critical points, which separate topological superfluid phases from normal or non-uniform, are accessible depending on spin-orbit coupling, Zeeman fields or interactions, setting the stage for the study of tunable topological superfluids.
We describe the quantum phases of interacting three component fermions in the presence of spin-orbit coupling, as well as linear and quadratic Zeeman fields. We classify the emerging superfluid phases in terms of the loci of zeros of their quasi-particle excitation spectrum in momentum space, and we identify several Lifshitz-type topological transitions. In the particular case of vanishing quadratic Zeeman field, a quintuple point exists where four gapless superfluid phases with surface and line nodes converge into a fully gapped superfluid phase. Lastly, we also show that the simultaneous presence of spin-orbit and Zeeman fields transforms a momentum-independent scalar order parameter into an explicitly momentum-dependent tensor in the generalized helicity basis.
Topological superfluids are recently discovered quantum matter that hosts topologically protected gapless edge states known as Majorana fermions---exotic quantum particles that act as their own antiparticles and obey non-Abelian statistics. Their realizations are believed to lie at the heart of future technologies such as fault-tolerant quantum computation. To date, the most efficient scheme to create topological superfluids and Majorana fermions is based on the Sau-Lutchyn-Tewari-Das Sarma model with a Rashba-type spin-orbit coupling on the x-y plane and a large out-of-plane (perpendicular) Zeeman field along the z direction. Here we propose an alternative setup, where the topological superfluid phase is driven by applying an in-plane Zeeman field. This scheme offers a number of different features, notably Cooper pairings at finite center-of-mass momentum (i.e., Fulde-Ferrell pairing) and gapless excitations in the bulk. As a result, gapless topological quantum matter with an inhomogeneous pairing order parameter appears. It features unidirectional Majorana surface states at boundaries, which propagate in the same direction and connect two Weyl nodes in the bulk. We demonstrate the emergence of such exotic topological matter and the associated Majorana fermions in spin-orbit coupled atomic Fermi gases, and we determine its parameter space. The implementation of our scheme in semiconductor/superconductor heterostructures is briefly discussed.
We discuss the thermodynamic signatures for the topological phase transitions into Majorana and Weyl superfluid phases in ultracold Fermi gases in two and three dimensions (2D and 3D) in the presence of Rashba spin-orbit coupling and a Zeeman field. We analyze the thermodynamic properties exhibiting the distinct nature of the topological phase transitions linked with the Majorana fermions (2D Fermi gas) and Weyl fermions (3D Fermi gas) which can be observed experimentally, including pressure, chemical potential, isothermal compressibility, entropy, and specific heat, as a function of the interaction and the Zeeman field at both zero and finite temperatures. We conclude that among the various thermodynamic quantities, the isothermal compressibility and the chemical potential as functions of the artificial Zeeman field have the strongest signatures of the topological transitions in both two and three dimensions.
We theoretically investigate a three-dimensional Fermi gas with Rashba spin–orbit coupling in the presence of both out-of-plane and in-plane Zeeman fields. We show that, driven by a sufficiently large Zeeman field, either out-of-plane or in-plane, the superfluid phase of this system exhibits a number of interesting features, including inhomogeneous Fulde–Ferrell pairing, gapped or gapless topological order, and exotic quasi-particle excitations known as Weyl fermions that have linear energy dispersions in momentum space (i.e., massless Dirac fermions). The topological superfluid phase can have either four or two topologically protected Weyl nodes. We present the phase diagrams at both zero and finite temperatures and discuss the possibility of their observation in an atomic Fermi gas with synthetic spin–orbit coupling. In this context, topological superfluid phase with an imperfect Rashba spin–orbit coupling is also studied.