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arXiv:1201.2238 · Physical Review Letters

Searching for Majorana Fermions in 2D Spin-Orbit Coupled Fermi Superfluids at Finite Temperature

Ming Gong, Gang Chen, Suotang Jia, Chuanwei Zhang

Published Sep 5, 2012• 105 citations
arXivHTMLPDF

Abstract

Recent experimental breakthroughs in realizing spin-orbit (SO) coupling for cold atoms have spurred considerable interest in the physics of two-dimensional SO coupled Fermi superfluids, especially topological Majorana fermions (MFs) which were predicted to exist at zero temperature. However, it is well known that long-range superfluid order is destroyed in two dimensions by phase fluctuations at finite temperature, and the relevant physics is the BKTs transition. In this Letter, we examine finite temperature effects on SO coupled Fermi gases and show that finite temperature is indeed necessary for the observation of MFs. Majorana fermions are topologically protected by a quasiparticle energy gap which is found to be much larger than the temperature. The restrictions to the parameter region for the observation of MFs have been obtained.

DOI
10.1103/physrevlett.109.105302

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Recent experimental breakthroughs in realizing spin-orbit (SO) coupling for cold atoms have spurred considerable interest in the physics of two-dimensional SO coupled Fermi superfluids, especially topological Majorana fermions (MFs) which were predicted to exist at zero temperature. However, it is well known that long-range superfluid order is destroyed in two dimensions by phase fluctuations at finite temperature, and the relevant physics is the BKTs transition. In this Letter, we examine finite temperature effects on SO coupled Fermi gases and show that finite temperature is indeed necessary for the observation of MFs. Majorana fermions are topologically protected by a quasiparticle energy gap which is found to be much larger than the temperature. The restrictions to the parameter region for the observation of MFs have been obtained.
The experimental observation of traditional Zeeman-field induced Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by various challenges, in particular, the requirement of low dimensional systems. In 2D, finite temperature phase fluctuations lead to extremely small Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for FFLO superfluids, raising serious concerns regarding their experimental observability. Recently, it was shown that FFLO superfluids can be realized using a Rashba spin-orbit coupled Fermi gas subject to Zeeman fields, which may also support topological excitations such as Majorana fermions in 2D. Here we address the finite temperature BKT transition issue in this system, which may exhibit gapped, gapless, topological, and gapless topological FF phases. We find a large BKT transition temperature due to large effective superfluid densities, making it possible to observe 2D FF superfluids at finite temperature. In addition, we show that gapless FF superfluids can be stable due to their positive superfluid densities. These findings pave the way for the experimental observation of 2D gapped and gapless FF superfluids and their associated topological excitations at finite temperature.
Abstract : Majorana fermions (MFs) are quantum particles that are their own anti-particles, and satisfy non-Abelian exchange statistics. The latter is the key for their potential use in fault-tolerant topological quantum computation. In this project, we proposed to investigate the possibility of realizing MFs in much more physically robust s-wave superfluids by utilizing two additional components: spin-orbit coupling and Zeeman fields. In the last year grant period, we have made the following important achievements: 1)We found a large BKT transition temperature due to large effective superfluid densities in a spin-orbit coupled Fulde-Ferrell superfluid, making it possible to observe 2D Fulde-Ferrell superfluids at finite temperature;2) Collaborated with Ian Speilmans group, we demonstrated the tunable spin-orbit coupling through the modulation of the Raman coupling strength in experiments; 3)We found that the spin-orbit coupled Fulde-Ferrell superfluids can support Weyl points or rings with nontrivial topological structures; 4)We proposed and experimentally realized a new type of tunable spin-orbit coupling using optical lattice band pseudospins. The research leads to 23 peer-reviewed publications, including 4 in Physical Review Letters and 1 in Nature Communications.
The experimental observation of traditional Zeeman-field induced Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by various challenges, in particular, the requirement of low dimensional systems. In 2D, finite temperature phase fluctuations lead to an extremely small Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for FFLO superfluids, raising serious concerns regarding their experimental observability. Recently, it was shown that FFLO superfluids can be realized using a Rashba spin-orbit coupled Fermi gas subject to Zeeman fields, which may also support topological excitations such as Majorana fermions in 2D. Here we address the finite temperature BKT transition issue in this system, which may exhibit gapped, gapless, topological, and gapless topological FF phases. We find a large BKT transition temperature due to large effective superfluid densities, making it possible to observe 2D FF superfluids at finite temperature. In addition, we show that gapless FF superfluids can be stable due to their positive superfluid densities. These findings pave the way for the experimental observation of 2D gapped and gapless FF superfluids and their associated topological excitations at finite temperature.
We show that Majorana fermions (MFs) exist in twoand three-dimensional (2D,3D) fermionic optical lattices with strictly 1D spin-orbit coupling (SOC) which has already been realized in experiments. For a quasi-1D topological BCS superfluid, there are multiple MFs at each end which are topologically protected by a chiral symmetry. In the generalization to higher dimensions, the multiple MFs form a zero energy flat band. An additional experimentally tunable in-plane Zeeman field drives the system to a topological Fulde-Ferrell (FF) superfluid phase. We find that even though the multiple MFs are robust against the in-plane Zeeman field if the order parameters at the different chains are enforced to be identical, they are destroyed in the self-consistently obtained FF phase where the order parameters are inhomogeneous on the boundaries. Our results are useful to guide the experimentalists on searching for MFs in the context of ultracold fermionic atoms.
We study Majorana fermions (MFs) in quasi-one dimensional (quasi-1D) and higher-dimensional fermionic optical lattices with a strictly 1D spin-orbit coupling, which has already been realized in cold atom experiments. We show that when the superfluid order parameters are homogeneous and are enforced to be identical along different chains, there are multiple MFs at each end with or without an experimentally tunable in-plane Zeeman field Vy{V}_{y}Vy​. For Vy=0{V}_{y}=0Vy​=0 the multiple MFs are topologically protected by a chiral symmetry; however, for ${V}_{y}\ensuremath{\ne}0$ the existence of multiple MFs is related to the peculiar spectrum properties of the system despite the broken chiral symmetry. In the generalization to higher dimensions, the multiple MFs form a zero-energy flat band. Furthermore, when the superfluid order parameters are solved self-consistently, the multiple MFs are usually destroyed because of the inhomogeneous order parameters of either Bardeen-Cooper-Schrieffer (Vy=0{V}_{y}=0Vy​=0) type or Fulde-Ferrell (${V}_{y}\ensuremath{\ne}0$) type. Our results are useful to guide the experimentalists on searching for MFs in ultracold spin-orbit coupled fermionic superfluids.
We theoretically study trapped one-dimensional Fermi gases in the presence of spin-orbit coupling induced by Raman lasers. The gas changes from a conventional (nontopological) superfluid to a topological superfluid as one increases the intensity of the Raman lasers above a critical chemical-potential-dependent value. Solving the Bogoliubov-de Gennes equations self-consistently, we calculate the density of states in real and momentum space at finite temperatures. We study Majorana fermions (MFs) which appear at the boundaries between topologically trivial and topologically nontrivial regions. We linearize the trap near the location of a MF, finding an analytic expression for the localized MF wave function and the gap between the MF state and other edge states.