Tunneling density of states measurements of disordered superconducting (SC) Al films in high Zeeman fields reveal a significant population of subgap states which cannot be explained by standard BCS theory. We provide a natural explanation of these excess states in terms of a novel disordered Larkin-Ovchinnikov (dLO) phase that occurs near the spin-paramagnetic transition at the Chandrasekhar-Clogston critical field. The dLO superconductor is characterized by a pairing amplitude that changes sign at domain walls. These domain walls carry magnetization and support Andreev bound states, which lead to distinct spectral signatures at low energy.
Superconductor insulator transition in transverse magnetic field is studied in the highly disordered MoC film with the product of the Fermi momentum and the mean free path $k_F*l$ close to unity. Surprisingly, the Zeeman paramagnetic effects dominate over orbital coupling on both sides of the transition. In superconducting state it is evidenced by a high upper critical magnetic field $B_{c2}$, by its square root dependence on temperature, as well as by the Zeeman splitting of the quasiparticle density of states (DOS) measured by scanning tunneling microscopy. At $B_{c2}$ a logarithmic anomaly …
We report spin-polarized tunneling density of states measurements of the proximity modulated superconductor-insulator transition in ultra thin Be-Al bilayers. The bilayer samples consisted of a Be film of varying thickness, $d_\mathrm{Be}=\,$0.8-4.5 nm, on which a 1 nm thick capping layer of Al was deposited. Detailed measurements of the Zeeman splitting of the BCS coherence peaks in samples with sheet resistances $R\sim h/4e^2$ revealed a super-linear Zeeman shift near the critical field. Our data suggests that critically disordered samples have a broad distribution of gap energies and that o…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is a superconducting state stabilized by a large Zeeman splitting between up- and down-spin electrons in a singlet superconductor. In the absence of disorder, the superconducting order parameter has a periodic spatial structure, with periodicity determined by the Zeeman splitting. Using the Bogoliubov-de Gennes (BdG) approach, we investigate the spatial profiles of the order parameters of FFLO states in a two-dimensional s-wave superconductors with nonmagnetic impurities. The FFLO state is found to survive under moderate disorder strength, and …
We report the non-equilibrium behavior of disordered superconducting Al films in high Zeeman fields. We have measured the tunneling density of states of the films through the first-order Zeeman critical field transition. We find that films with sheet resistances of a few hundred ohms exhibit large avalanche-like collapses of the condensate on the superheating branch of the critical field hysteresis loop. In contrast, the transition back into the superconducting phase (i.e., along the supercooling branch) is always continuous. The fact that the condensate follows an unstable trajectory to the n…
Zeeman fields can drive semiconductor quantum wires with strong spin-orbit coupling and in proximity to s-wave superconductors into a topological phase which supports end Majorana fermions and offers an attractive platform for realizing topological quantum information processing. Here, we investigate how potential disorder affects the topological phase by a combination of analytical and numerical approaches. Most prominently, we find that the robustness of the topological phase against disorder depends sensitively and non-monotonously on the Zeeman field applied to the wire.
The Zeeman interaction results in spontaneous current through a Josephson contact with a spin-orbit coupled normal metal, even in the absence of any voltage, or phase bias. In the case of the Rashba spin orbit coupling of electrons in a two-dimensional (2D) electron gas this effect takes place for the Zeeman field which is parallel to the 2D system and to superconducting contacts. At the same time, the spontaneous current is absent when this field is perpendicular to the contacts. It is shown that in the latter case it may manifest itself in oscillations of the critical Josephson current at th…
Starting from a random matrix model, we construct the low-energy effective field theory for the noninteracting gas of quasiparticles of a disordered superconductor in the mixed state. The theory is a nonlinear sigma model, with the order parameter field being a supermatrix whose form is determined solely on symmetry grounds. The weak localization correction to the field-axis thermal conductivity is computed for a dilute array of s-wave vortices near the lower critical field H_c1. We propose that weak localization effects, cut off at low temperatures by the Zeeman splitting, are responsible for…
It is shown that the spin-orbit and Zeeman interactions result in phase shifts of Andreev-reflected holes in disordered topological insulator, or normal Rashba spin-orbit-coupled wires, which are in a contact with an s-wave superconductor. Due to interference of the holes reflected through different paths in Andreev interferometer the electric current through the contact varies depending on the strength and direction of the Zeeman field. It also depends on mutual orientations of Zeeman fields in different shoulders of the interferometer. Such a nonlocal effect is a result of the long-range coh…
Layered singlet paired superconductors with disorder and broken time reversal symmetry are studied. The phase diagram demonstrates charge-spin separation in transport. In terms of the average intergrain transmission and the interlayer tunnelling we find quantum Hall phases with spin Hall coefficients of 0 and 2 separated by a spin metal phase. We identify a spin metal-insulator localization exponent as well as a spin conductivity exponent of ~0.9. In presence of a Zeeman term an additional phase with spin Hall coefficient of 1 appears.
Monolayer NbSe$_2$ is a nodal topological Ising superconductor at magnetic in-plane fields exceeding the Pauli limit, with nodal points strictly on high symmetry lines in the Brillouin zone. Here, we use a combined numerical and group-theoretical approach in real-space to characterize the unconventional superconducting state in monolayer transition metal dichalcogenides. Even with a conventional pairing interaction, the superconducting state is intrinsically parity-mixed and robust against on-site disorder. The interplay between the Zeeman magnetic field, strong spin-orbit interaction, and ele…
Using Bogoliubov-de Gennes (BdG) equations we numerically calculate the disorder averaged density of states of disordered semiconductor nanowires driven into a putative topological p-wave superconducting phase by spin-orbit coupling, Zeeman spin splitting and s-wave superconducting proximity effect induced by a nearby superconductor. Comparing with the corresponding theoretical self-consistent Born approximation (SCBA) results treating disorder effects, we comment on the topological phase diagram of the system in the presence of increasing disorder. Although disorder strongly suppresses the ze…
We consider DC supercurrents in SNS junctions. Spin-orbit coupling in combination with Zeeman fields can induce an effective vector potential in the normal conductor. As a consequence, an out-of-plane spin-density varying along the transverse direction causes a longitudinal phase difference between the superconducting terminals. The resulting equilibrium phase coherent supercurrent is analogue to the non-equilibrium inverse spin Hall effect in normal conductors. We explicitly compute the effect for the Rashba spin orbit coupling in a disordered two-dimensional electron gas with an inhomogeneou…
We study the transport in ultrathin disordered film near the quantum critical point induced by the Zeeman field. We calculate corrections to the normal state conductivity due to quantum pairing fluctuations. The fluctuation-induced transport is mediated by virtual rather than real quasi-particles. We find that at zero temperature, where the corrections come from purely quantum fluctuations, the Aslamazov-Larkin paraconductivity term, the Maki-Thompson interference contribution and the density of states effects are all of the same order. The total correction leads to the negative magnetoresista…
The existence of "superconducting islands" (i.e., locally confined regions with superconducting correlations) in amorphous superconducting thin films can account for numerous experimental findings. Such spatial fluctuations in the superconducting gap were indeed observed experimentally, and were shown to persist into the insulating side of the superconductor-insulator transition. In this work a detailed account on the formation and evolution of superconducting islands in disordered two-dimensional superconductors is presented, using a locally self-consistent numerical solution of the Bogoliubo…
We study the superconducting instability in disordered non-centrosymmetric monolayers with intrinsic Ising spin-orbit coupling (SOC) subjected to an in-plane Zeeman magnetic field. The pairing interaction contains the channels allowed by crystal symmetry, such that in general, the pairing state is a mixture of singlet and triplet Cooper pairs. The joint action of SOC and Zeeman field selects a specific in-plane $\mathbf{d}$-vector triplet component to couple with the singlets, which gains robustness against disorder through the coupling. The out-of-plane $\mathbf{d}$-vector component, that in …
Highly disordered magnetism confined to individual weakly interacting vortices is detected by muon spin rotation in two different families of high-transition-temperature superconductors, but only in samples on the low-doping side of the low-temperature normal state metal-to-insulator crossover (MIC). The results support an extended quantum phase transition (QPT) theory of competing magnetic and superconducting orders that incorporates the coupling between CuO2 planes. Contrary to what has been inferred from previous experiments, the static magnetism that coexists with superconductivity near th…
We report on novel superconducting characteristics of the heavy fermion (HF) superconductor CePt3Si without inversion symmetry through 195Pt-NMR study on a single crystal with T_c= 0.46 K that is lower than T_c= 0.75 K for polycrystals. We show that the intrinsic superconducting characteristics inherent to CePt3Si can be understood in terms of the unconventional strong-coupling state with a line-node gap below T_c= 0.46 K. The mystery about the sample dependence of T_c is explained by the fact that more or less polycrystals and single crystals inevitably contain some disordered domains, which …
We present results of numerical studies of spin quantum Hall transitions in disordered superconductors, in which the pairing order parameter breaks time-reversal symmetry. We focus mainly on p-wave superconductors in which one of the spin components is conserved. The transport properties of the system are studied by numerically diagonalizing pairing Hamiltonians on a lattice, and by calculating the Chern and Thouless numbers of the quasiparticle states. We find that in the presence of disorder, (spin-)current carrying states exist only at discrete critical energies in the thermodynamic limit, …
Exploring the conventional and anomalous Josephson effects at arbitrary disorder strength in systems with spin-dependent fields
University of Jyväskylä（于韦斯屈莱大学）；Centro de Física de Materiales (CFM-MPC) Centro Mixto CSIC-UPV/EHU（材料物理中心（CFM-MPC）CSIC-巴斯克国立理工大学混合中心）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）
