Superconductivity

Mesoscopic Superconductors

On the microscopic level superconductivity is caused by the entangling of electrons into Cooper pairs. This naturally occurring pairing offers the opportunity to investigate quantum coherence and nonlocality in solid-state devices.

Our recent research has focused on the phenomenon of Crossed Andreev Reflection (CAR) wherein the the two electrons of a Cooper pair in a superconductor can be probed by spatially separated normal metal probes. As the effective size of a Cooper pair in a conventional superconductor such as Aluminum is a few hundred nanometers, the separate normal probes can be fabricated by conventional e-beam lithography.

Above is an annotated scanning electron micrograph of a sample used to detect the nonlocal effect of entangled Cooper pairs consisting of a vertical Aluminum wire crossed by seven normal Gold leads separated by 200 nanometers. A current is sent from the bottom Gold lead into the lower section of the Aluminum and the other leads out of the current path are used to measure the nonlocal resistance at different distances from the current path.

Below is the nonlocal resistance of the four closest leads as a function of temperature. Above the transition temperature of 0.6 K the Aluminum is normal and there is no nonlocal signal, below the transition there is a large spike in the nonlocal resistance which decreases with distance. These spikes are not primarily due to coherent effects, but rather the nonequilibrium effect of Charge Imbalance (CI), the creation of an excess of "hole-like" quasiparticles in the superconductor. However, as the sample is cooled to close to zero temperature the quasiparticle creation is frozen out, and the remaining nonlocal signal is due to effects of coherently entangled electrons in which one electron is part of the current path and the other enters the nonlocal leads and to the related coherent effect of Elastic Cotunneling (EC). As the Cooper pairs only span a few hundred nanometers the nonlocal signal disappears by the third nonlocal lead.

    For other work on CAR and EC see investigations by the groups of Beckmann and Morpurgo.

Using cross-correlation measurements to probe quantum coherence

For a three-terminal device with two normal-metal wires separated by a superconducting wire, it is interesting to know whether the electrons in the two normal-metal wires are in a quantum entangled state induced by the adjacent superconducting wire if the separation between them in the superconductor is small enough.

One possible microscopic process that can induce the entangled state is called Crossed Andreev Reflection (CAR), discussed above. The physical picture of CAR process can be thought of as follows: near the two normal-metal/superconducting interfaces, one  electron from each of the two normal-metal leads is converted simultaneously to (or is emitted from) a Cooper pair in the superconducting wire. Since the electrons disappear from the normal-metal wires at the same time, they are positively correlated and the currents flowing through the NS interfaces should also be positively correlated. One the other hand, it is also possible that the  electron can tunnel from one normal-metal wire to the other without being converted to Cooper pair, a process called Elastic Cotunneling (EC). In this case, due to the Pauli principle, electrons will tunnel one by one and this leads to negative correlation.

A simple transport measurement can not identify whether the correlation is positive or negative since it only gives the average value of the current. In contrast, a measurement of the current-current correlation is capable of separating the contribution from CAR and EC, thus determining whether or not there is an entangled state. The magnitude of the correlation is determined by the ratio of the separation distance between normal-metal wires over the superconducting coherence length.

With our nanofabrication capabilities and the ability to measure cross-correlations, we can investigate this cross-correlation with varying separations between normal-metal wires. In addition, replacing one or both normal-metal wires with a ferromagnetic wire can be used for probing spin entanglement.

Thermal transport in normal-metal superconductor structures

At temperatures below the superconducting transition temperature, the properties of normal metals (N) in contact with superconductors are governed by the penetration of the superconducting correlations from the superconductor, the well-known proximity effect. The resistance of a mesoscopic normal metal in proximity with a superconductor decreases as it is cooled below the transition temperature of the superconductor, but then is expected to regain its normal state resistance at zero temperature, which is the so-called reentrant behavior. In an effort to understand the physics underlying this effect, we have investigated the transport properties of devices containing NS interfaces, in particular, Andreev interferometers, or small micron size loops with one arm fabricated from a normal metal, and the other arm from a superconductor. These experiments involve measuring the temperature dependent resistance, magnetoresistance and differential resistance of these devices at low temperatures. We have been able to observe reentrant behavior in these devices in all these measurements. And also, we have investigated in detail the length dependence of the proximity effect in 1D wires. Detailed investigations of the magnetoresistance of these wires indicate that the length scale relevant for interference in proximity devices is not the thermal diffusion length in the normal metal, but a combination of the electron phase coherence length and the coherence length in the superconducting contact.

Using the techniques developed to measure thermoelectric effects in mesoscopic spin-glass wires, we are also investigating the thermopower of such Andreev interferometers at low temperatures. To achieve this, we have developed techniques to measure the local electronic temperature on a size scale of about 100 nm (see figure above).  The thermopower of Andreev interferometers is predicted to be periodic in magnetic field with a fundamental period corresponding to one superconducting flux quantum through the superconducting loop. We have been able to observe this periodicity in experiments on different types of Andreev interferometers. The oscillations of the thermopower in different types of interferometers can be either symmetric or antisymmetric with respect to the magnetic field (see figure below), even though the magnetoresistance for all interferometers is symmetric. The symmetry of the thermopower appears to depend on the topology of the Andreev interferometers. In addition, the amplitude of the thermopower oscillations shows a non-monotonic temperature dependence, which might be associated with reentrant behavior, but appears at a higher temperature.

                 Thermopower oscillations of Andreev interferometers

Ferromagnetic/superconductor heterostructures

We are also interested in the transport properties of ferromagnetic/superconductor heterostructures. Conventionally, one does not expect a strong superconducting proximity effect in a ferromagnet because of the exchange field in the ferromagnet which is expected to rapidly destroy superconducting correlations. However, there have been recent reports of a strong proximity effect in hybrid ferromagnet/superconductor structures. In order to test the proximity effect, we have fabricated hybrid ferromagnet/superconductor/normal metal heterostructures.

The design of the devices is based on our experience measuring the magnetoresistance of single ferromagnetic particles. An example of one of the samples fabricated by e-beam lithography is shown below (left). They consist of a single (typically elliptical) Ni particle fabricated such that the magnetization lies along the major axis of the ellipse. The particle is contacted by Au contacts (bright lines) to ensure that the magnetic structure of particle is not disturbed. Superconducting Al (dark lines) is then deposited on one end of the Ni particle. With this design, we can measure the Ni particle, the Al film and the Al/Ni interface separately, allowing us to determine the origin of any signal we observe.

Measurements on structures similar to this showed that the Ni particle showed essentially no superconducting proximity effect. The FS interface, however, showed a large temperature and voltage dependent resistance, which could be fit reasonably well with a modified BTK model which takes into account the spin-polarization of the conduction electrons in the ferromagnet.

SEM images of ferromagnetic/superconductor heterostructures. (a) consists of an elliptical Ni particle in contact with a superconducting Al film. The image is scaled to 1µm x 1µm. (b) is a simple FS cross.

A direct four-terminal differential resistance measurement of the FS interface (Py/Al interface) shows two dips at |Idc|=2~4 µA before approaching the normal state resistance at higher values of Idc. The dips in dV/dI are asymmetric, in that the amplitude of the dips is different. As theapplied external field H is increased, the features become sharper, and more symmetric. At larger values of H (not shown), the positions of the peaks and dips move down to lower values of |Idc|. Comparing the simulation results from the modified BTK model to the experimental data, we find that there are some similiarities, but substantial differences in even the qualitative behavior. We are attempting to understand this behavior.

Differential resistance of a Py/Al interface as a function of dc current at an external magnetic field (along the Py wire) of (a) H=0, and (b) H=0.1002 T. T=290 mK.