Majorana fermions (MFs), quantum particles that are their own antiparticles, are not only of fundamental importance in elementary particle physics and dark matter, but also building blocks for fault-tolerant quantum computation. Recently MFs have been intensively studied in solid state and cold atomic systems. These studies are generally based on superconducting pairing with zero total momentum. On the other hand, finite total momentum Cooper pairings, known as Fulde-Ferrell (FF) Larkin-Ovchinnikov (LO) states, were widely studied in many branches of physics. However, whether FF and LO superconductors can support MFs has not been explored. Here we show that MFs can exist in certain types of gapped FF states, yielding a new quantum matter: topological FF superfluids/superconductors. We demonstrate the existence of such topological FF superfluids and the associated MFs using spin-orbitcoupled degenerate Fermi gases and derive their parameter regions. The implementation of topological FF superconductors in semiconductor/superconductor heterostructures is also discussed.

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase was first predicted in 2D superconductors about 50 years ago, but so far unambiguous experimental evidences are still lacked. The recently experimentally realized spin-imbalanced Fermi gases may potentially unveil this elusive state, but require very stringent experimental conditions. In this Letter, we show that FFLO phases may be observed even in a 3D degenerate Fermi gas with spin-orbit coupling and in-plane Zeeman field. The FFLO phase is driven by the interplay between asymmetry of Fermi surface and superfluid order, instead of the interplay between magnetic and superconducting order in solid materials. The predicted FFLO phase exists in a giant parameter region, possesses a stable long-range superfluid order due to the 3D geometry, and can be observed with experimentally already achieved temperature (T ∼ 0.05EF ), thus opens a new fascinating avenue for exploring FFLO physics. The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, characterized by Cooper pairs with finite total momentum and spatially modulated order parameters, was predicted to exist in certain region of 2D superconductors in high Zeeman fields [1][2][3]. This fascinating state arises from the interplay between magnetic and superconducting order, and now is a central concept for understanding many exotic phenomena in different physics branches [4][5][6][7][8][9][10][11][12]. Despite tremendous experimental and theoretical efforts in the past five decades, there is still no unambiguous experimental evidence for FFLO states [11]. The experimental difficulty may arise from several different aspects, such as the depairing of Cooper pairs due to orbital or Pauli effects in strong magnetic fields and unavoidable disorder effects in solid state materials.The recent experimental realization of spin-imbalanced Fermi gases [13][14][15][16][17] provides a new excellent platform for exploring FFLO physics. In Fermi gases, the effective Zeeman field is generated through the population imbalance between two spins, therefore the orbital effects (e.g., vortices induced by the magnetic field) are absent even in 3D. The Fermi gases are also free of disorder and all experimental parameters are highly controllable. These advantages have sparked tremendous recent interest in exploring FFLO physics in spin-imbalanced Fermi gases [18][19][20][21][22][23][24][25][26][27][28]. However, the FFLO phase only exists in a narrow parameter regime in 3D due to the Pauli depairing effect [18,22,23]. Furthermore, the free energy difference between the FFLO state and the BCS superfluid is extremely small. As a result, only the transition from the BCS superfluid to the normal gas [13][14][15] has been observed in experiments in 3D spin-imbalanced Fermi gases. Current experimental and theoretical efforts on the FFLO state have focused on low dimensions (1D or 2D) [29][30][31][32][33], where quantum and thermal (at finite temperature) fluctuations may become crucial and the physics is much more complicated [34][35][36].In this Lett...

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We show that the combination of spin-orbit coupling and in-plane Zeeman field in a two-dimensional degenerate Fermi gas can lead to a larger parameter region for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases than that using spin-imbalanced Fermi gases. The resulting FFLO superfluids are also more stable due to the enhanced energy difference between FFLO and conventional Bardeen-Cooper-Schrieffer (BCS) excited states. We clarify the crucial role of the symmetry of Fermi surface on the formation of finite momentum pairing. The phase diagram for FFLO superfluids is obtained in the BCS-BEC crossover region and possible experimental observations of FFLO phases are discussed.

Nanomotors in nanotechnology are as important as engines in daily life. Many ATPases are nanoscale biomotors classified into three categories based on the motion mechanisms in transporting substrates: linear, rotating, and the recently discovered revolving motion. Most biomotors adopt a multisubunit ring-shaped structure that hydrolyzes ATP to generate force. How these biomotors control the motion direction and regulate the sequential action of their multiple subunits is intriguing. Many ATPases are hexameric with each monomer containing a conserved arginine finger. This review focuses on recent findings on how the arginine finger controls motion direction and coordinates adjacent subunit interactions in both revolving and rotating biomotors. Mechanisms of intersubunit interactions and sequential movements of individual subunits are evidenced by the asymmetrical appearance of one dimer and four monomers in high-resolution structural complexes. The arginine finger is situated at the interface of two subunits and extends into the ATP binding pocket of the downstream subunit. An arginine finger mutation results in deficiency in ATP binding/hydrolysis, substrate binding, and transport, highlighting the importance of the arginine finger in regulating energy transduction and motor function. Additionally, the roles of channel chirality and channel size are discussed as related to controlling one-way trafficking and differentiating the revolving and rotating mechanisms. Finally, the review concludes by discussing the conformational changes and entropy conversion triggered by ATP binding/hydrolysis, offering a view different from the traditional concept of ATP-mediated mechanochemical energy coupling. The elucidation of the motion mechanism and direction control in ATPases could facilitate nanomotor fabrication in nanotechnology.