FFLO-Phase in Quantum Liquids, Quantum Gases, and Nuclear Matter

In a magnetic field superconductors (SC) with small orbital effect exhibit the Fulde-Ferrell-Larkin- Ovchinnikov (FFLO) phase bleow the Pauli limiting field. It has Cooper pairs with finite center of mass momentum and is stabilized by the gain in Zeeman energy of depaired electrons in the imbalanced Fermi gas. The ground state is a coherent superposition of paired and depaired states. This concept, although central to the FFLO state lacks a direct experimental confirmation. We propose that STM quasiparticle interference can give a direct momentum space image of the depaired states in the FFLO wave function. For a proof of principle we investigate a 2D single orbital tight binding model with a SC s-wave order parameter. For the equilibrium values of pair momentum and SC gap we calculate the spectral function of quasiparticles and associated QPI spectrum as function of magnetic field. We show that the characteristic depaired Fermi surface parts appear as a fingerprint in the QPI spectrum of the FFLO phase and we demonstrate its evolution with field strength. Its observation in STM experiments would constitute a direct proof for FFLO ground state wave function.

Superconductivity occurs when it becomes energetically favorable to form Cooper pairs consisting of two electrons with opposite momenta and oppositely aligned spins (magnetic moments). One would expect that due to its spin, an electron could orient in a magnetic field in a manner analogous to a compass needle, and destroy the superconducting state when the spin magnetic energy exceeds the binding energy of the Cooper pairs. However in most cases, superconductivity is destroyed in an external magnetic field due to vortices - non-superconducting regions containing a magnetic field line shielded by circulating electrons - which increase in density as the magnetic field is increased and ultimately displace the superconducting phase. Clogston and Chandrasakar were the first to recognize that if the formation of vortices could be suppressed, superconductivity could persist to a magnetic field limit which arises from the Pauli paramagnetism of the electrons, and is denoted as HP. Some 50 years ago, Fulde and Farrell and Larkin and Ovchinnikov predicted that in electronically clean materials, a new, spatially inhomogeneous, superconducting phase (FFLO state) with paramagnetic spin domains could exist for fields even above HP. We report here calorimetric and magnetocaloric measurements that demonstrate the existence of a magnetic-field-induced first-order phase transition from a traditional superconducting state into a paramagnetic, higher-entropy, high field superconducting state above HP. Our superconducting phase diagram agrees with that established by RF penetration and NMR. Our observations of a first-order phase transition into a high entropy superconducting state provide a "smoking gun proof" of the long sought after FFLO state.

FFLO-like physics[1, 2, 3, 4] leads to the appearance of the oscillating order parameter in proximized ferromagnet in superconducting-ferromagnet (SF) hybrid structures. In Josephson SFS or SIFS (I is an insulator) structures, the oscillating order parameter in F leads to the oscillating critical current Ic(dF ), wheredF isthethicknessoftheF-layer.Thus,bychoosingdF properly,onecanfabricateconventionalas well as ? Josephson junctions (JJs), i.e., the JJs having the phase drop of ? in the ground state. Such ? JJs were demonstrated by several groups[5, 6, 7, 8] and can be used as (not dischargeable) ?-phase batteries, providing self-bias to various (classical or quantum) superconducting electronic circuits such as RSFQ logic circuits[9] or flux qubits[10]. By special combination of 0 and ? segments we were able to fabricate the so-called ? JJ — a JJ having a degenerate ground state phase ? = ±?, where 0 < ? < ?[11, 12, 13]. This system has 2?-periodic double-well Josephson energy profile with asymmetry tunable by an externally applied magnetic field[14]. We present several recent experiments with such a ? JJ. We demonstrate their unusual properties, e.g., two critical currents that can be used to read out an unknown state of the ? JJ[15], while magnetic field can be used to write the desired state. Combining these two properties, we demonstrate the application of a ? JJ as a memory cell[16]. Finally, we study the retrapping of the phase by the ? JJ and discover a buttery effect[17], which was recently measured experimentally[18] in our group. References [1] P. Fulde and R. A. Ferrell, Phys. Rev. 135, A550 (1964). [2] A. Larkin and Y. N. Ovchinnikov, Sov. Phys. JETP 20, 762 (1965). [3] L. N. Bulaevski ?i, V. V. Kuzi ?i, and A. A. Sobyanin, JETP Lett. 25, 290 (1977), [Pis’ma Zh. Eksp. Teor. Fiz. 25, 314 (1977)]. [4] A. I. Buzdin, L. N. Bulaevskii, and S. V. Panyukov, JETP Lett. 35, 178 (1982). [5] T. Kontos et al., Phys. Rev. Lett. 89, 137007 (2002). [6] V. A. Oboznov, V. V. Bol’ginov, A. K. Feofanov, V. V. Ryazanov, and A. I. Buzdin, Phys. Rev. Lett. 96, 197003 (2006). [7] M. Weides et al., Appl. Phys. Lett. 89, 122511 (2006). [8] J. W. A. Robinson, S. Piano, G. Burnell, C. Bell, and M. G. Blamire, Phys. Rev. B 76, 094522 (2007). [9] T. Ortlepp et al., Science 312, 1495 (2006). [10] A. K. Feofanov et al., Nat. Phys. 6, 593 (2010). [11] A. Buzdin and A. E. Koshelev, Phys. Rev. B 67, R220504 (2003). [12] E. Goldobin, D. Koelle, R. Kleiner, and A. Buzdin, Phys. Rev. B 76, 224523 (2007). [13] S. V. Bakurskiy, N. V. Klenov, T. Y. Karminskaya, M. Y. Kupriyanov, and A. A. Golubov, Supercond. Sci. Technol. 26, 015005 (2013). [14] E. Goldobin, D. Koelle, R. Kleiner, and R. G. Mints, Phys. Rev. Lett. 107, 227001 (2011). [15] H. Sickinger et al., Phys. Rev. Lett. 109, 107002 (2012). [16] E. Goldobin et al., Appl. Phys. Lett. 102, 242602 (2013). [17] E. Goldobin, R. Kleiner, D. Koelle, and R. G. Mints, Phys. Rev. Lett. 111, 057004 (2013). [18] R. Menditto et al., Phys. Rev. B 93, 174506 (2016).

We study a Josephson junction formed by connecting two superconductors through the helical edge states of a quantum spin-Hall insulator or through a semiconducting nanowire with Rashba spin-orbit coupling. In the presence of a suitably oriented magnetic field, such system displays the anomalous Josephson effect: a nonzero supercurrent in the absence of a superconducting phase difference between the leads. We show that this anomalous current can be increased significantly by tuning the superconducting parts of the junction into the topologically nontrivial phase, in which they host Majorana bound states.

Solitonic patterns play important role in various quasi one-dimensional systems: from the FFLO state in superconductors and atomic gases to its analogs in electronic systems with charge density waves. The new trend is to introduce a high concentration of solitons by means an optical pumping or by a strong electric field. The ordered solitonic structures are formed via series of dynamical phase transitions, when understanding calls for studies of statistical properties of ensembles of solitons. Here we present the results of Monte-Carlo simulation of phase transitions in an ensemble of amplitude solitons in three- and two-dimensional systems. The first phase transition brings about the confinement of solitons into bisoliton pairs. At the second one the unconfined solitons appear again, but at a macroscopic scale: aggregated into domain walls forming stripe structures embedded to the gas of remnant confined pairs. We analyze also the influence of Coulomb interactions in case of charged solitons. We show that even a weak Coulomb interaction, which does not affect the solitons locally, can nevertheless prevent the formation of macroscopic domain walls.

High-$T_c$ cuprate superconductivity contradicts the conventional wisdom that BCS-like pairing or usual Bose-Einstein condensation (BEC) causes this phenomenon, because the high-Tc cuprates undergo a $\?ambda$-like superconducting (SC)transition, which is different from the BCS/BEC transition. Here we identify the novel mechanisms that are responsible for the pseudogap (PG) phenomena, high-$T_c$ superconductivity, gapless quasiparticle excitations and halfinteger flux quantization in doped cuprates. We show that the unconventional electron-phonon coupling and polaronic effects are more relevant to these systems than other factors and control the new physics. We find that polaronic effects and related PG weaken with increasing the doping $x$ and disappear at the quantum critical point (QCP) $x = x_p>0.2$ in high-$T_c$ cuprates. We identify the PG and vortex-like states above $T_c$, the PG-QCP, the novel SC state and two distinct SC phases of high-$T_c$ cuprates like the $A$ and $B$ phases of superfluid 3^$He$. We present the real phase diagrams of the cuprates and explain the rich cuprate phenomenology from lightly doped to overdoped region.

We present the Usadel theory describing the superconducting proximity effect in heterostructures with a half-metallic layer. It is shown that the full spin polarization inside the half-metals gives rise to an additional triplet component of the Green function which results in the giant triplet spin-valve effect in superconductor (S) -- ferromagnet (F) -- half-metal (HM) trilayers and provides a natural explanation for the $\varphi_0$-junction formation in the S/F/HM/F/S systems. We also show that this additional component provides favorable conditions for the in-plane Fulde-Ferrell-Larkin-Ovchinnikov instability which results in the formation of the non-uniform states with the order parameter modulated along the layers.

In standard theory of the superconductivity one uses and idea of the Cooper pairs. In the BCS theory these pairs have zero total momentum. However, it turns out that in some situation the Cooper pair can have non-zero total momentum. This phase, called Fulde-Ferrell-Larkin-Ovchinnikov phase, can be realized in low temperatures and high magnetic fields. One expects a realization of this phase in organic or heavy fermions superconductors. Some experimental and theoretical works (see Ref. [1] and reference therein) suggest also a possibility of the realization of this phase in iron-based superconductors. Multiband character of this chemical compound provides some theoretical and technical troubles. In my seminary, I will show some result founded in three orbital tight binding model and ab-initio method studying superconductivity using the Cooper pairs susceptibility. [1] Multiple phase transitions in Pauli limited iron-based superconductors, A. Ptok, Journal of Physics: Condensed Matter 27, 482001 (2015)

We study topological Fermi superfluidity using interacting spin-1/2 particles loaded in a one dimensional optical lattice. The system collective excitations, specially at low temperatures, behave as quasiparticles with properties that may differ from their constitutive fermions. In particular, there are exotic excitations called Majorana fermions, edge modes with the special characteristic of being their own anti-particles proposed on 1937 but experimentally reported on 2012 in the condensed matter context. On the other hand, the interplay between pairing and population density imbalance of the internal degrees of freedom, leads to a rich scenario which includes the possibility of exotic superconducting Cooper-pair-like states with finite center-of-mass momenta such as the Fulde-Ferrel (FF) state. In this work, we start from an interacting Fermi gas in the superfluid regime. With an increasing Zeeman field a Fulde-Ferrel state is achieved for weak enough fields while for strong fields the system undergoes ferromagnetic. Furthermore, in the presence of a spin-orbit coupling, the system may become topological establishing Majorana fermions in real space. Topologically ordered states are many-body ground-states exhibiting an order that does not rely on symmetry-breaking mechanisms. This robustness makes them suitable for fault-tolerant quantum-computation because of their immunity to local perturbations. This interacting system is analyzed solving the Bogoliubov-de Gennes Hamiltonian to retrieve the order parameter. We also use the matrix product state formalism to analyze the different phases and in particular the topological order which is characterized by specific entanglement properties. These methods also allow us to distinguish the topological from the trivial phases.

In structures made up of superconducting (S) and ferromagnet (F) layers, it is known that the Cooper pair wave function of the ground state changes its phase difference across the F layer from 0 to $\pi$ under certain geometrical conditions. We present a joint experimental and theoretical study of 0 - $\pi$ phase transition in diffusive SFS trilayers composed of thin superconductor (S) and ferromagnet (F) layers. Measurements of the critical temperature Tc of Nb / Cu1-x Nix / Nb (x$\approx$ 0.65) trilayers were performed by a local near-field nonlinear microwave technique [1]. A sudden, unusual increase of the critical temperature was detected with decreasing thickness of Nb layers. On the basis the Ginzburg–Landau theory developed in [2] we compute the in-plane critical current density jc of SFS structure in the vicinity of the 0 - $\pi$ transition. Since the pair-breaking proximity effect depends on the structure of the Copper pair wave function in the ferromagnetic layer, the critical current density jc is different for 0 and $\pi$ states. A jump of the critical current density during the 0 - $\pi$ transition is shown to provoke the nonmonotonous, reentrant behavior of the measured critical temperature Tc with decreasing thickness of the S layers. This work was supported by the Russian Scientific Foundation Grant No. 15-12-10020. [1] S. V. Baryshev, et al., PRB 76, 054520 (2007). [2] A. V. Samokhvalov and A. I. Buzdin, PRB 92, 054511 (2015)

Proximity-induced superconductivity in ferromagnets [1,2] reveal rich spin-triplet pairing scenarios that play an important role in superconducting spintronics [3,4]. We propose an electrically controllable platform for Cooper-pair spintronics based on topological insulator (TI)/superconductor hybrids carrying a supercurrent (a dissipationless transport current or a diamagnetic current in response to an external magnetic field). The proposal utilizes a robust locking of the electron spin and momentum directions in the TI to generate spin-polarized triplet Cooper pairs through the coupling to the superconducting phase gradient, ${\bf q}$, associated with the supercurrent. This is a nonunitary triplet pairing characterized by a complex ${\bf d}({\bf q})$ vector, allowing one to realize the "supercurrent spintronics" when the Cooper-pair spin is manipulated by switching the direction of ${\bf q}$. As an example, we predict a spin valve effect in a TI/ferromagnet contact, which manifests itself in the asymmetry of the electric conductance under the switching ${\bf q} \to -{\bf q}$ parallel to the interface. This dependence is caused by a supercurrent-induced spin transfer torque exerted on the magnetization by Andreev tunneling of triplet Cooper pairs. Our results uncover an unexplored area of orbital spin-polarization phenomena in superconducting spintronics, suggesting, at the same time, a direct experimental probe of triplet superconductivity in TI materials. This work has been done in collaboration with F. S. Bergeret (Centro de Fisica de Materiales, San Sebastian, Spain) with the financial support of the German Research Foundation (DFG) through grants TK60/1-1 and TK60/4-1. 1. A. I. Buzdin, Rev. Mod. Phys. 77, 935 (2005). 2. F. S. Bergeret, A. F. Volkov, K. B. Efetov, Rev. Mod. Phys. 77, 1321 (2005). 3. M. Eschrig, Phys. Today 64 (1), 43–49 (2011). 4. J. Linder and J. W. A. Robinson, Nat. Physics 11, 307–315 (2015).

The quasiparticle attraction and pairing is inherent not only to superconductors and superfluids but also to exotic phases in quantum magnets. In particular, magnon pairing may appear as a result of competition between ferro- and antiferromagnetic exchange bonds in frustrated spin systems. As a result bound magnon pairs are formed in the fully polarized magnetic state at high fields. Upon decreasing external field magnon pairs undergo a condensation into a state, which is bosonic analog of a BCS superconductor. The magnon-pair condensate lacks a conventional transverse magnetic order and is described by a quadrupolar or spin-nematic order parameter. The magnon-pairing mechanism will be considered in detail for two spin models: frustrated chains weakly coupled by interchain interactions and frustrated square-lattice antiferromagnet both exhibiting high-field spin-nematic states. The theory predicts the long-range spin-nematic phase in the frustrated chain material LiCuVO4 in high magnetic fields . I also discuss a relation to the longitudinally modulated phase at intermediate fields found in the same material.