The recent realization of two-dimensional (2D) synthetic spin-orbit (SO) coupling opens a broad avenue to study novel topological states for ultracold atoms. Here, we propose a new scheme to realize exotic chiral Fulde-Ferrell superfluid for ultracold fermions, with a generic theory being shown that the topology of superfluid pairing phases can be determined from the normal states. The main findings are two fold. First, a semimetal is driven by a new type of 2D SO coupling whose realization is even simpler than the recent experiment, and can be tuned into massive Dirac fermion phases with or without inversion symmetry. Without inversion symmetry the superfluid phase with nonzero pairing momentum is favored under an attractive interaction. Furthermore, we show a fundamental theorem that the topology of a 2D chiral superfluid can be uniquely determined from the unpaired normal states, with which the topological chiral Fulde-Ferrell superfluid with a broad topological region is predicted for the present system. This generic theorem is also useful for condensed matter physics and material science in search for new topological superconductors.
We theoretically find that finite size Fulde-Ferrell (FF) superconductor (which is characterized by spatially nonuniform ground state $Ψ\sim \text{exp}(-i{\bf q}_{FF}{\bf r})$ and $|Ψ|(r)=const$ in the bulk case, where $Ψ$ is a superconducting order parameter) has paramagnetic Meissner, vortex and 'onion' ground states with $|Ψ|(r) \neq const$. These states are realized due to boundary effect when the lateral size of superconductor $L \sim 1/q_{FF}$. We argue, that predicted states could be observed in thin disk/square made of superconductor-ferromagnet-normal metal trilayer with $L \simeq 150…
We theoretically study magnetic response of a superconductor/ferromagnet/normal-metal (SFN) strip in an in-plane Fulde--Ferrell (FF) state. We show that unlike to ordinary superconducting strip the FF strip can be switched from diamagnetic to paramagnetic and then back to diamagnetic state by {\it increasing} the perpendicular magnetic field. Being in paramagnetic state FF strip exhibits magnetic field driven second order phase transition from FF state to the ordinary state without spatial modulation along the strip. We argue that the global paramagnetic response is connected with peculiar dep…
We demonstrate that the Fulde-Ferrell (FF) phase can be induced uniquely by the orbital effect in a cylindrical metallic nanowire. In the external magnetic field the two-fold degeneracy with respect to the orbital quantum number $m$ is lifted what leads to a Fermi wave vector mismatch between the subbands with opposite orbital momenta in the paired state. This mismatch can be compensated by the nonzero total momentum of the Cooper pairs created by electrons from split subbands what results in the formation of the FF phase. With increasing magnetic field a series of FF stability regions appear …
We propose an Andreev interferometer, based on a branched Y-junction, to detect the finite momentum pairing in Fulde-Ferrell (FF) superconductors. In this interferometer, the oscillation of subgap conductance is a unique function of phase difference between the two channels of the Y-junction, which is determined by the phase modulation of the order parameter in the FF superconductors. This interferometer has the potential not only to determine the magnitude but also the direction of the momentum of Cooper pairs in the FF superconductor. The possible applications of the interferometer in the id…
We consider a free-standing metallic nanofilm with a predominant intersubband paring which emerges as a result of the confinement in the growth direction. We show that the Fermi wave vector mismatch between the subbands, detrimental to the intersubband pairing, can be compensated by the non-zero center of mass momentum of the Cooper pairs. This leads to the spontaneous appearance of the intersubband Fulde-Ferrell (IFF) state, even in the absence of an external magnetic field. Our study of the intrasubband pairing channel on the stability of the IFF phase shows that the former strongly competes…
We propose that the long-sought Fulde-Ferrell superfluidity with nonzero momentum pairing can be realized in ultracold two-component Fermi gases of $^{40}$K or $^{6}$Li atoms by optically tuning their magnetic Feshbach resonances via the creation of a closed-channel dark state with a Doppler-shifted Stark effect. In this scheme, two counterpropagating optical fields are applied to couple two molecular states in the closed channel to an excited molecular state, leading to a significant violation of Galilean invariance in the dark-state regime and hence to the possibility of Fulde-Ferrell superf…
The Higgs mode associated with amplitude fluctuations of the superconducting gap in uniform superconductors usually is heavy, which makes its excitation and detection difficult. We report on the existence of a gapless Higgs mode in the Fulde-Ferrell-Larkin-Ovchinnikov states. This feature is originated from the Goldstone mode associated with the translation symmetry breaking. The existence of the gapless Higgs mode is demonstrated by using both a phenomenological model and microscopic Bardeen-Cooper-Schrieffer (BCS) theory. The gapless Higgs mode can avoid the decay into other low energy excit…
We show that the behaviour of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductors near a surface is considerably different from the usual case. The order parameter of the FF state is strongly deformed near the surface, which leads to a number of unusual features in the linear magnetic response, such as "anti-screening" or "over-screening" of the applied field. In a fully isotropic FF case, the Meissner effect is still present, despite the vanishing of the transverse superfluid density in the bulk. We also calculate the surface critical field Hc3, which exhibits a peculiar temperature d…
We study the superconducting properties of the thin film BCS superconductor proximity coupled to a magnetically doped topological insulator(TI). Using the mean field theory, we show that Fulde-Ferrell(FF) pairing can be induced in the conventional superconductor by having inverse proximity effect(IPE). This occurs when the IPE of the TI to the superconductor is large enough that the normal band of the superconductor possesses a proximity induced spin-orbit coupling and magnetization. We find that the energetics of the different pairings are dependent on the coupling strength between the TI and…
In superconducting nanofilms the energy quantization induced by the confinement in the direction perpendicular to the film leads to a multiband character of the system which results in the thickness-dependent oscillations of the in-plane critical field (shape resonances). In this paper, we study the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase in nanofilms and examine its interplay with the shape resonances as well as the influence of the multiband effects on its stability. We demonstrate that the range of the magnetic field for which the FFLO state is stable oscillates as a function of the fi…
The exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states have been actively searched for experimentally since the mean-field based FFLO theories were put forward half a century ago. Here we investigate the stability of FFLO states against unavoidable pairing fluctuations, and conclude that FFLO superfluids cannot exist due to their intrinsic instability in three and two dimensions. This explains their absence in experimental observations in both condensed matter systems and the most recent, more promising ultracold atomic Fermi gases with a population imbalance.
We theoretically study the orbital destructive effect against superconductivity in a parallel magnetic field in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO or LOFF) phase at zero temperature in a quasi-two-dimensional (Q2D) conductor. We demonstrate that at zero temperature a special parameter, $λ= l_{\perp}(H)/d$, is responsible for strength of the orbital effect, where $l_{\perp}(H)$ is a typical "size" of the quasi-classical electron orbit in a magnetic field and $d$ is the inter-plane distance. We discuss applications of our results to the existing experiments on the FFLO phase in the organ…
We study exotic superconducting states in SrTiO$_3$ heterostructures on the basis of the three-orbital model, which reproduces the band structure of two-dimensional electron gases. We show various Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states induced by the broken inversion symmetry and orbital degree of freedom. In particular, a novel orbital-dependent FFLO state is stabilized in a magnetic field along the [110]-axis. The field angle dependence of the FFLO state is clarified on the basis of the spin and orbital texture in the momentum space. It is shown that the orbital degree of freedom in …
We find the angular Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states (or the twisted kink crystals) in which a phase and an amplitude of a pair potential modulate simultaneously in a quasi-onedimensional superconducting ring with a static Zeeman magnetic field applied on the ring and static Aharonov-Bohm magnetic flux penetrating the ring. The superconducting ring with magnetic flux produces a persistent current, whereas the Zeeman split of Fermi energy results in the spatial modulation of the pair potential. We show that these two magnetic fields stabilize the FFLO phase in a large parameter re…
We show that in the presence of magnetic field, two superconducting phases with the center-of-mass momentum of Cooper pair parallel to the magnetic field are induced in spin-orbit-coupled superconductor Li$_2$Pd$_3$B. Specifically, at small magnetic field, the center-of-mass momentum is induced due to the energy-spectrum distortion and no unpairing region with vanishing singlet correlation appears. We refer to this superconducting state as the drift-BCS state. By further increasing the magnetic field, the superconducting state falls into the Fulde-Ferrell-Larkin-Ovchinnikov state with the emer…
