The quantum mechanical character of electronic transport is manifest in mesoscopic

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1 Mesoscopic transport in hybrid normal-superconductor nanostructures The quantum mechanical character of electronic transport is manifest in mesoscopic systems at low temperatures, typically below 1 K. Hybrid mesoscopic structures, characterized by small sizes in the range of a few nanometers to micrometers, are fabricated by putting into contact materials whose transport properties are different in nature. Superconductors, in particular, are characterized by the macroscopic phase coherence of the order parameter and by the supercurrent flow. Normal (metallic or semiconducting)-superconductor (NS) nanostructures show peculiar transport properties due to the presence of the superconducting gap. In these systems electronic transport is mediated by Andreev reflection, which is a scattering process occurring at the NS interface. It consists of the coherent evolution of an electron into a retro-reflected hole and describes the injection of a Cooper pair into the superconducting condensate. Our efforts in this field are both on the experimental and theoretical sides, and comprise different aspects. Here we summarize results obtained in the following topics: i) Andreev reflection in hybrid ferromagnet-superconductor structures; ii) out-of-equilibrium transport; iii) influence of quantizing magnetic fields and magnetic barriers on the Andreev reflection. Francesco Giazotto Fabio Taddei Carlo Castellana Michele Governale Diego Frustaglia Rosario Fazio Fabio Beltram The first topic concerns ferromagnetsuperconductor (FS) hybrid systems. These are an attractive subject of investigation because of the competition between the spin asymmetry characteristic of a ferromagnet (due to the spin splitting induced by the molecular exchange field) and the correlations (occurring among electrons belonging to opposite spin species) induced by superconductivity. For nonuniform magnetizations (magnetic textures) interference effects are expected due to the presence of additional spinrelated phases of geometric origin, usually referred to as Berry phases [ 1]. Berry phases arise when the carriers spin adiabatically follow the magnetic texture and stay (anti)aligned with it during transport. They manifest as an effective spin-dependent magnetic flux of geometric origin (geometric flux) and their magnitude is proportional to the corresponding solid angle accumulated by the spins. We have brought together these two distinct physical phenomena (Andreev reflection and Berry phases) by studying the Andreev conductance of a hybrid one-dimensional mesoscopic ring in the presence of a magnetic texture (Fig. 1) [2]. The proposed setup permits us to identify the signatures of magnetic and geometric phases in the energy spectrum of hybrid ring geometries. Our work can be considered an alternative proposal for the detection of Berry phases: Andreev reflection has the advantage of including particle-hole phase correlations that allow for a larger signal contrast and a high sensitivity to the magnetic/geometric Fig. 1 Hybrid magneticsuperconducting ring setup. The ring is subject to a magnetic texture h(a) that couples to the carriers spin. The coupling points of the ring (denoted by small filled circles) are attached to a normal lead (on the lefthand side) and to a superconducting lead (on the right-hand side). Andreev reflection is the only contribution to the subgap conductance G MS. 49 Nest Scientific Report

2 Fig. 2 Sketch of the FSF spin-valve. A thin superconducting film is sandwiched between two identical ferromagnetic layers whose magnetizations (yellow arrows) can be aligned both in the parallel (P) and antiparallel (AP) configuration. An electric current (white dashed arrows) is allowed to flow through the system parallel to the layers. The schematic representation of the spin-valve effect for half-metallic ferromagnets, showing the diagrams of the superconducting density of states, is displayed in (a) and (b). (a) In the P alignment, the lack of quasiparticles with opposite spin hinders the condensation of two electrons injected from the ferromagnets in a Cooper pair in S. As a consequence, the electric transport is confined within the F layers. (b) In the AP configuration, two electrons with opposite spin injected from the F layers can form a Cooper pair within the superconductor thanks to crossed Andreev reflection, thus "shunting" the current through the whole structure. flux-dependent splitting of quasi-bound This spin-valve consists of a thin states. Unlike the case of normal systems, superconducting film sandwiched between this is true even for ensemble-averaged two ferromagnetic layers whose quantities. Non adiabatic Aharonov- magnetization is allowed to be either Anadan phases are now under parallelly or antiparallelly aligned (see Fig. investigation. 2). The conductance dependence on S Very interesting is also the issue of layer thickness is shown in Fig. 3(a). The magnetoresistance in hybrid FS systems. resulting MR ratio, defined as the Even in the absence of superconductivity, maximum relative change in resistance ferromagnetic systems present a resistance arising from applying the external which strongly depends on the applied magnetic field, is shown in Fig. 3(b) and magnetic field. In particular, multilayered exhibits very large negative values around - FN structures show a magnetoresistance 70% for ts 3.5 xand 0 about -25% for ts (MR), for a number of layers of the order of 6.5 x(xbeing 0 0 the superconducting , which is typically around 10% coherence length). For a suitable choice of when the currents flows parallel to the structure parameters and nearly fully spinplanes [3]. We have showed that very large p o l a r i z e d f e r r o m a g n e t s t h e and negative values of magnetoresistance magnetoresistance can exceed -80%. can be obtained in magnetic trilayers in a current-in-plane geometry owing to the The second topic concerns the interplay existence of crossed Andreev reflection [4]. between out-of-equilibrium transport and Fig. 3 (a) Conductance in the P (black circles) and AP (red triangles) configurations versus t S with t F = 5 lattice constants. (b) Resulting MR ratio. Data were obtained assuming L = 150 lattice constants and 100% ferromagnet polarization. In (a) the error bars correspond to the standard error over all disorder configurations. Lines are guides to the eye. 50 Nest Scientific Report

3 Fig. 4 Heat current P out from S 2 by a S1IS2IS 1 line vs control voltage V C at T e1=t e2=t bath=0.4t c1 for several D/Dratios. 2 1 The dash-dotted line represents P when S 2 is in the normal state. Inset: scheme of the Josephson device. The bias V C across the S1IS2IS1 line allows to control the supercurrent I J (along the dashed line) increasing or suppressing its amplitude with respect to equilibrium. A and B represent tunnel contacts used to inject and measure the supercurrent. distribution in the N region through current injection. On the other hand, as recently p r o p o s e d a n d e x p e r i m e n t a l l y demonstrated, a superconductor- insulator-normal metal-insulator- superconductor (SINIS) control line (where I is a tunnel barrier) is particularly suitable for tuning the Josephson current, allowing both enhancement and suppression with respect to equilibrium. Operation of these devices is based on the modification of the superconductivity [5]. This was recently successfully exploited in a number of systems in order to implement Josephson transistors [6-9], p-junctions [10], and electron microrefrigerators [11,12]. A d e v e l o p m e n t i n m e s o s c o p i c superconductivity is indeed represented by controllable superconductor-normal metal-superconductor (SNS) metallic weak links [13], where supercurrent suppression is achieved by altering the quasiparticle Fig. 5 (a) Supercurrent I J vs control voltage V C calculated at different bath temperatures T bath for T c2 = 0.3T c1 (corresponding roughly to the Ti/Al combination) and T cj = T c1. Note the sharp I J suppression at ev C = 2[D(T 1 bath)+ D(T 2 e2)]. (b) Supercurrent vs V C calculated for several T cj/t c1 ratios at T bath = 0.8T c2 and for T c2 = 0.3T c1. 51 Nest Scientific Report

4 Fig. 6 Scheme of the structure investigated. An in-plane static magnetic field H is applied across the whole SINIS system [(a), (a)-type setup] or localized at the S electrodes [(b), (b)-type setup]. A finite voltage bias V C drives the normal metal out of equilibrium allowing to control its magnetization. The N wire is assumed quasi-one-dimensional. quasiparticle distribution function in the N region of the junction. We have proposed an all-superconducting tunnel junction device in which transistor effect is obtained by driving the electron distribution far from equilibrium in the superconductor [14]. This is performed by voltage biasing a superconductor-insulator-superconductor (SISIS) line (see Fig. 4) where the inter- electrode is one of the two terminals belonging to the Josephson junction. Compared to other hybrid devices, the present one benefits from the sharp characteristics due to the presence of superconductors with unequal energy g a p s. B o t h l a r g e s u p e r c u r r e n t enhancement and fast quenching can be achieved with respect to equilibrium by varying quasiparticle injection for proper temperature regimes and suitable superconductor combinations (see Fig. 5). Combined with large power gain, this makes the device attractive for applications where reduced noise and low-power dissipation are required. We are currently studying the behavior of this structure in the regime of strong nonequilibrium. We have further explored the potential of out-of-equilibrium transport in the area of magnetism and spintronics and presented a novel approach to control the magnetization and spin-dependent properties of a mesoscopic normal conductor [15]. To this end we have analyzed a hybrid superconductor normal metal superconductor system (see Fig. 6) and showed that the magnetization of the normal mesoscopic conductor can be electrostatically controlled (Fig. 7). This effect stems from the interplay between the non-equilibrium condition in the normal region and the Zeeman splitting of the Fig. 7 (a) Magnetization density M vs bias voltage V C at T = 0.1T c for different magnetic fields (H) for (a)-type setup [see Fig. 6(a)]. Inset: M vs V C for different temperatures at H = 0.2D/m. B (b) The same as in (a) for (b)-type setup. (a') Schematic diagrams of the N region density of states and quasiparticle occupation both at equilibrium (left) and nonequilibrium (right) for (a)-type setup. (b') The same as in (a') for (b)-type setup. c) Contour plot of the normalized magnetic susceptibility c/cvs Pauli V C and H at T = 0.1T c for (b)- type setup. 52 Nest Scientific Report

5 Fig. 8 (a) Scheme of the FS-I-N-I- SF spin valve. Ferromagnetic layers (F) induce in each superconductor through proximity effect an exchange field whose relative orientation is controlled by an externally applied magnetic field. t F (t S) labels the F (S) layer thickness and a voltage V is applied across the structure. (b) The F exchange fields (h 1,2) are confined to the y-z plane, and are misaligned by an angle f. quasiparticle density of states of the [see Fig. 8(a)] considered is a multilayer superconductor subjected to a static in- consisting of two identical FS bilayers (FS 1,2) plane magnetic field. Unexpected spin- symmetrically connected to a tn-thick dependent effects such as magnetization normal metal region (N) through insulating suppression, diamagnetic-like response of barriers (I) of resistance R t. Under the susceptibility, as well as spin-polarized appropriate conditions [17], the current generation are the most ferromagnet induces in S a homogeneous remarkable features found. The impact of * effective exchange field h and modifies the scattering events was evaluated and let us * superconducting gap (D). As a result, the show that this effect is compatible with superconducting DOS will be BCS-like, but realistic material properties and shifted by the effective exchange energy fabrication techniques. We are now (equivalent to that of a Zeeman-split considering the quasi-equilibrium situation superconductor in a magnetic field [18]). (where an effective temperature can be At finite bias V and in the limit of negligible defined) in the presence of non-collinear inelastic scattering, the steady-state fields in the superconductors to show the nonequilibrium distribution functions in the possibility of exploiting the system as a N layer, which control the electronic spin-valve. transport, are spin dependent. Figure 9 Along the same line, we have proposed a displays the absolute value of the TMR vs hybrid superconducting spin valve that can bias voltage V calculated for several angles yield huge tunnel magnetoresistance * * fat T = 0.1T c and h = 0.4 D. TMR turns 6 (TMR) values as high as several 10 % [16]. out to be only marginally affected by the Operation is based on the interplay presence of electron-electron relaxation. between out-of-equilibrium quasiparticle This leads to a fully-tunable structure which dynamics and proximity-induced exchange shows high potential for application in coupling in superconductors. The system spintronics. Fig. 9 Nonequilibrium tunnel magnetoresistance ratio TMR vs V calculated for several angles fat T = * * 0.1T c and h = 0.4 D. Gray regions correspond to voltage intervals of very large TMR. 53 Nest Scientific Report

6 Fig. 10 (a) Schematic view of the proposed device. The superconductor-2deg junction conductance is controlled by the fringe field generated by a ferromagnetic strip placed on top of the structure. The strength of the magnetic barrier in the twodimensional electron gas can be varied by changing the orientation of the magnetization (M). (b) Spatial profile of the B z - component of the magnetic fringe field for z 0 = 185 nm, h = 300 nm, and d = 1.5 m. The transport direction is x. Finally, we have investigated Andreev reflection at the interface between a superconductor and a two-dimensional electron system (2DES) in the presence of quantizing or localized magnetic fields. In the first case, an external magnetic field is applied such that cyclotron motion is important in the 2DES [19]. A finite Zeeman splitting in the 2DES and the presence of diamagnetic screening currents in the superconductor are incorporated into a microscopic theory of Andreev edge states, which is based on the Bogoliubov-de Gennes formalism. The Andreev-reflection contribution to the interface conductance is calculated. The effect of Zeeman splitting is most visible as a double-step feature in the conductance through clean interfaces. Due to a screening current, conductance steps are shifted to larger filling factors and the formation of Andreev edge states is suppressed below a critical filling factor. We are now considering the interplay between Josephson effect and Andreev edge states. In the second case, we have proposed a hybrid superconductor-semiconductor device whose sub-gap conductance can be controlled by changing the strength of a magnetic barrier induced by a ferromagnetic strip [20]. A sketch of our device is shown in Fig. 10(a). It consists of a superconductor/two-dimensional electron gas (2DEG) ballistic junction, where transport occurs along the x axis. On top of the junction a ferromagnetic strip of width d and thickness h is deposited. Electron transport in the 2DEG is affected by the perpendicular magnetic field generated by the x-component of the magnetization Fig. 11 (a) Semiclassical picture of the Andreev reflection suppression mechanism caused by a magnetic barrier. e and h represent electron- and hole-like quasiparticles, respectively. (b) Normalized zero-bias differential conductance RNG 0 vs cos fat T = 0 and mimi= T. 54 Nest Scientific Report

7 M =IMIcos f[fig. 10(b)]. The presence of the magnetic barrier can suppress Andreev at T = 0 and mimi=1.8 0 T. By reducing the reflection, and hence the sub-gap magnetization angle, G 0 is suppressed by conductance. The physical origin of this many orders of magnitudes with respect to -1 suppression can be easily understood R N. We are now working on the heat within a semiclassical picture [see Fig. transport properties of this system. 11(a)]. By controlling the intensity of the magnetic barrier it is possible to have Some of the works presented here result access to different transport regimes in the from collaborations with J. P. Pekola (HUT, same structure. The full switching behavior Helsinki, Finland) and U. Zülicke (Massey of the junction is shown in Fig. 11(b), which University, Palmerston, New Zealand). displays the normalized zero-bias -1 x differential conductance (RNG 0) vs cos f References [1] M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984). [2] D. Frustaglia, F. Taddei, and Rosario Fazio, Phys. Rev. B 72, (2005). [3] M. N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988). [4] F. Giazotto, F. Taddei, F. Beltram, and Rosario Fazio, Phys. Rev. Lett. 97, (2006). [5] Theory of Nonequilibrium Superconductivity, edited by N. B. Kopnin (Clarendon, Oxford, 2001). [6] A. A. Golubov, M. Yu. Kupriyanov, and E. Il'ichev, Rev. Mod. Phys. 76, 411 (2004). [7] A. F. Morpurgo, T. M. Klapwijk, and B. J. van Wees, Appl. Phys. Lett. 72, 966 (1998). [8] A. M. Savin et al., Appl. Phys. Lett. 84, 4179 (2004). [9] F. Giazotto et al., Appl. Phys. Lett. 83, 2877 (2003). [10] J. J. A. Baselmans, A. F. Morpurgo, B. J. van Wees, and T. M. Klapwijk, Nature (London) 397, 43 (1999). [11] See, e.g., J. P. Pekola, R. Schoelkopf, and J. Ullom, Phys. Today 57, No. 5, 41 (2004), and references therein. [12 J. P. Pekola et al., Phys. Rev. Lett. 92, (2004). [13] F. K. Wilhelm, G. Schön, and A. D. Zaikin, Phys. Rev. Lett. 81, 1682 (1998). [14] F. Giazotto and J. P. Pekola. J. Appl. Phys. 97, (2005). [15] F. Giazotto, F. Taddei, Rosario Fazio, and F. Beltram, Phys. Rev. Lett. 95, (2005). [16] F. Giazotto, F. Taddei, Rosario Fazio, and F. Beltram, Appl. Phys. Lett. 89, (2006). [17] F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Phys. Rev. Lett. 86, 3140 (2001). [18] R. Meservey and P. M. Tedrow, Phys. Rep. 238, 173 (1994). [19] F. Giazotto, M. Governale, U. Zülicke, and F. Beltram, Phys. Rev. B 72, (2005). [20] C. Castellana, F. Giazotto, M. Governale, F. Taddei, and F. Beltram, Appl. Phys. Lett. 88, (2006). 55 Nest Scientific Report