Nonvolatile voltage-tunable ferroelectric-superconducting quantum interference memory devices

Superconductivity serves as a unique solid-state platform for electron interference at a device-relevant lengthscale, which is essential for quantum information and sensing technologies. As opposed to semiconducting transistors that are operated by voltage biasing at the nanometer scale, superconductive quantum devices cannot sustain voltage and are operated with magnetic fields, which impose a large device footprint, hindering miniaturization and scalability. Here we introduce a system of superconducting materials and devices that have a common interface with a ferroelectric layer. An amorphous superconductor was chosen for reducing substrate-induced misfit strain and for allowing low-temperature growth. The common quantum pseudowavefunction of the superconducting electrons was controlled by the non-volatile switchable polarization of the ferroelectric by means of voltage biasing. A controllable change of 21% in the critical temperature was demonstrated for a continuous film geometry. Moreover, a controllable change of 54% in the switching current of a superconducting quantum interference device (SQUID) was demonstrated. The ability to voltage bias superconducting devices together with the non-volatile nature of this system paves the way to quantum-based memory devices.

Superconducting quantum interference devices (SQUIDs) are basic building blocks for quantum technologies. The macroscopic quantum characteristic of SQUIDs is advantageous for magnetic sensing, 1,2 , whereas these devices are a major player in the recent race for quantuminformation technologies. [3][4][5] While the perfect conductance of superconductors is advantageous for low power consumption. [6][7][8] following Ohm's low, the absence of resistance also hinders energy efficient voltage biasing. Thus, superconducting quantum devices lack the convenient gating platform that semiconducting transistors have. There has been therefore a continuous effort to introduce tunability to superconductive quantum devices, 9 including by ionic liquid 10,11 , as well as by voltage-tunable −SQUIDs. 12 A prominent example is integration of ferromagnetic components. Ferromagnets retain magnetic polarization, which is switchable with an external magnetic field, allowing non-volatile tunability. 13,14 Yet, magnetic controllability is more cumbersome than the semiconducting transistor electric-field tunability, especially for miniaturized devices.
Electric tunability of the quantum state of superconductive devices has been demonstrated successfully by introducing a ballistic or very clean semiconductor in proximity to the superconducting device. 15 In several such devices, the gating mechanism is based on voltagedriven charge injection of holes or electrons from the semiconductor either directly or by means of a field effect. The resultant change in the superconductor charge-carrier density ( s ) is accompanied by direct voltage control of the common quantum pseudo-wavefunction of the superconducting electrons: s = |ψ| 2 . Hence, the superconducting energy gap (Δ) is also voltage depended: ψ = Δ θ (θ is the common phase of the superconductive electrons) as well as material parameters, such as critical temperature ( c ): 16 Here, B is Boltzmann's constant and this relationship is valid for finite temperatures ≈ c , whereas it is reduced to a simpler form: Δ = 1.752 B c for → 0 K. Likewise, following Ambegaokar and Baratoff, 17 device properties, such as the critical current, are also tunable: where e is the electron charge and N is the device's normal-state resistance.
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0061160
Charge injection with a semiconductor requires constant voltage application and the effect is limited by the charge carrier of the semiconductor. It has been proposed that ferroelectrics offer a potential answer to these two hurdles already from the pioneering work by Ahn et al. in 1999. 18 Ferroelectrics are high-dielectric materials that retain electric polarization, which is switchable with an external bias. The internal polarization in ferroelectrics is compensated with a surface charge that is available for direct charge injection 19,20 as well as induces an electric field. 21 Here, a layer within the superconductor as thin as the Thomas-Fermi screening length screens the bound charge of the ferroelectric. [22][23][24] The bound charge in the ferroelectric depends on the remanent polarization, which in turn is switchable by an external electric field and is unchanged even upon the field removal due to the hysteretic nature of the ferroelectric polarization. Hence, the superconductor charge density and related parameters change with the polarization switching, giving rise to an effective non-volatile memory effect of the superconducting properties (see Figure   1A-B).
Despite the great potential of ferroelectric-superconductive quantum devices, to date, only a handful number of successful attempts have been demonstrated. 25,26 Similar to ferromagnetic and semiconducting tunability, the main challenge in realizing competitive ferroelectricsuperconducting quantum devices is the limited capability of presenting an electronically transparent interface between the two materials. That is, the existence of chemical, electric, and magnetic impurities as well as strain at the interface impinges charge control in the superconductor, suppressing the voltage tunability. Thus far, to overcome these limitations, the superconducting and ferroelectric materials were selected according to the match of their lattice parameters.
However, this approach is limited to highc superconductors 25,26 and superconductors with an extremely low c . Another approach uses 2D superconductors, where the material itself is the interface. 27 Nevertheless, contemporary quantum-information technologies are based on thin superconductors with a finite thickness and with c in the range of ~1-10 K. 28 This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0061160
An Mo80Si20 was deposited by means of magnetron sputtering on top of a lead zirconate titanate (PZT) ferroelectric film, which in turn was laid on a bottom electrode as illustrated schematically in Figure 1C (see methods for details regarding the material processing). Amorphous materials do not require lattice matching. 31,32 PZT was chosen because the associated bound charge (4.33•10 -3 charge carriers per unit cell 33 is much larger than the available charge in semiconducting material (1.8•10 -4 charge carriers per unit cell for highly doped silicon). 34 Using piezoresponse force microscopy, it was found that the polarization in the ferroelectric is reversible with a bias of 5-6 V ( Figure 1D). Thus, a higher voltage bias (10 V) was applied for 10 min to switch the ferroelectric polarization at the substrate sandwiched between the bottom electrode and the 80 20 films at the normal state ( =25 K). The resultant effect on the superconducting c was then measured by removing the bias and cooling down the polarized sample. The sample was then heated back to the normal state ( =25 K) and the polarization was switched with an opposite bias before c was measured again. This experimental procedure was performed repeatedly to verify the effect reproducibility. Here, c was determined by the temperature at which the resistance drops by 90% from its value at 20 K. This experimental protocol is demonstrated schematically in Figure   2A. To demonstrate the repeatability of the process, a sequential cycle was performed. Figure 2B shows that a negative polarization in the ferroelectric was accompanied by c = 6.8±0.1 K, whereas c = 5.8±0.1 K for positive polarization.
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

FIG. 2. Voltage-tunable superconductive-ferroelectric device. (A)
Schematics of the c measurement setup. The polarization was first set by biasing the ferroelectric with s that is larger than the coercive value with either positive or negative polarity. After removing the bias, c was extracted from a four-point measurement. The procedure was then repeated for the opposite polarity. (B) Cooling curves of Mo80Si20 on a ferroelectric substrate shows that the measured c at 90% drop of the resistance was 5.7 K for positive polarization (circles) and 6.9 K for negative polarization (squares) as well as the reproducibility of the effect for three sequencing cycles (black, blue and red curves).
To demonstrate the direct effect of polarization reversal on the behavior of a SQUID, a planar SQUID was fabricated as illustrated in Figure 3 (see Reference 35 for details related to device fabrication). Figure 4 shows that a negative polarization in the ferroelectric resulted in c = 4.0±0.03 A, and c = 2.6±0.03 A for positive polarization (measured at 3 K). These values correspond in a good agreement to the estimated change in c based on the measured change in c , following Equations 1-2. That is, the SQUID characteristics are voltage-tunable with a measurable change of 54%, whereas the effect is observed even after the voltage is removed.
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. Gray curves correspond to the best fit of a sine (see Table S1) (B) Current-voltage curves of the Mo80Si20 SQUID at zero magnetic field measured for negative and positive polarization of the ferroelectric, showing a significant change in both c (length of the horizontal segment) as well as the device's normal resistance (slope of the linear regime at the normal state). Results of two sequencing measurements are presented, demonstrating the reproducibility of the effect (the derivative resistance is depicted in Figure S3).

PLEASE CITE THIS ARTICLE AS
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0061160
To complement the device and material characterization, the device normal resistance and the superconducting charge-carrier density were also measured for negative and positive ferroelectric polarization. Table 1  The effect of polarization reversal on s can also be calculated. The surface charge due to ferroelectric remnant polarization ( r ) satisfies: surf = ∯ r • ,Where is surface area. Thus, the change in surface charge due to polarization reversal is given by: surf = 2 r . It is now possible to substitute = 6000 nm 2 for the weak links of the above SQUID ( Figure 3B) and r = 75 C cm -2 for the PZT (see Figure 1D) to obtain that the change in charge carrier density in the 15-nm thick Mo80Si20 film due to polarization reversal is: e ≈ 5 • 10 26 m -3 .
The Thomas-Fermi screening length of MoSi is about one tenth of the thickness of the films examined in this work. 36 Yet, the device thickness is comparable to the coherence length (< 3 ).
In this geometry, we expect the electron-phonon coupling and the density of states do not vary much between the screening layer and the bulk. 24 Hall-effect measurements of the Mo80Si20 film were performed for a negative and a positive polarized ferroelectric for extracting the corresponding change in charge carriers within the superconductor ( Figure S4). The Hall coefficient is extracted from the slope of the measured Hall resistivity (ρ ) with respective to magnetic field at the normal state. We obtained Hall coefficients of 4.2 and 9 10 -8 Ω •m T -1 and therefore charge-carrier density of 15 and 7 10 25 m -3 for the respective positive and negative polarizations. Thus, the change in charge-carrier density due to polarization reversal is 8•10 25 m -3 , which is in agreement with the expected charge that is required for polarization screening. [37][38][39] Table 1 shows that the extracted e is in agreement with the expected value, where it also presents the extracted coherence length = ℏ Δ

(with Fermi velocity
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.  Therefore, to conclude, the change in material and device parameters can be attributed directly to the polarization-induced charge injection as elucidated schematically in Figure 1A