Unique quantum states induced by disorders can be characterized by quantum phase transitions in many-body systems. In this study, we experimentally observed a sharp resistance peak near the superconducting transition in superconductor/ferroelectric TiN/Hf0.5Zr0.5O2 heterostructures. The peak is attributed to the disorder introduced by ferroelectric fluctuations within the empirical model of metal–boson insulator–superconductor transitions. By modulating the quantum phase transitions in superconductivity and competing with the disorder through ferroelectric polarization, we provide a versatile platform for investigating the influence of ferroelectric materials on superconducting states.
Superconductivity and Anderson localization exhibit opposite conductivity extremes, both stemming from subtle quantum effects. In the superconducting phase, Cooper pairs are generated via electron–phonon coupling and collapse into macroscopic quantum states that display a zero-resistance phenomenon. In contrast, if the disorder affects the quantum phase of the electron wave functions, a metal–insulator transition occurs, showing a divergent resistance. By exploring the unique quantum state associated with the disorder near the superconducting transition, insights can be obtained into the typical quantum phase transition triggered by disorder in many-body systems.1–3 This is a crucial issue in various quantum systems, including amorphous superconductors,4 superconducting nanowires,5 high-temperature superconductors,6 and supercooled atomic gases.7
Notably, the temperature-dependent resistance curve presents an anomalous resistance peak near the superconducting Tc in a few one-, two-, and even three-dimensional systems.8–12 A more general explanation is that the disorder causes significant quantum fluctuations near the quantum critical point, leading to a new quantum state called the Bose insulating state.11 Other theoretical models, including those related to charge balance, vortex dynamics, and Josephson coupling in layered systems,7–10 have also been proposed to explain this phenomenon. These quantum states are sensitive to an applied external field, similar to the electronic properties of superconducting thin films. Investigating the manipulation of quantum states by an external field can reveal the underlying physics.12 Alternatively, ferroelectric (FE) materials with large spontaneous electric polarization can generate a strong local electric field and modify the carrier densities of adjacent materials, thus leading to a greater tunability.13–15 Moreover, a ferroelectric gate can potentially tune the charge accumulation/depletion at the ferroelectric–superconductor interface in a nonvolatile manner, which can considerably change the superconductor transition temperature or superconducting gap.16–20 These unique features of ferroelectric materials provide a compelling impetus for the integration of ferroelectrics and superconductors, which may result in exotic quantum phenomena and functionalities.
In this study, we present the modulation of superconductivity via ferroelectric polarization in a heterostructure composed of TiN and Hf0.5Zr0.5O2 (HZO) thin films. TiN, an amorphous superconducting material, is well known for its disordered features, which cause inhomogeneity of the superconducting state close to the superconductor–insulator transition.21–23 The HZO thin film is a newly developed ferroelectric material that exhibits substantial residual polarization even at reduced thicknesses24–26 and is widely used in the research on ferroelectric heterojunctions.27–29 Transport measurements revealed that ferroelectric polarization in HZO can remarkably regulate the carrier concentration in the normal state of the TiN thin film. Reversible switching of the superconductor between the normal and zero-resistance conducting states was achieved by reversing the polarization of the HZO. In particular, a highly sharp peak, with a temperature width of only 0.2 K, in the vicinity of critical superconductivity was observed within the R–T curve in certain polarization states. In addition, the intensity of this peak was tunable by both the magnetic field and current, suggesting that a new quantum state emerges close to the superconducting transition, which can be modulated by proximate ferroelectricity. Further investigation and analysis demonstrated that such a quantum state can be ascribed to the bosonic insulating state intricately linked to the disorder, originating from nonuniform ferroelectric fluctuations. This superconductor/ferroelectric heterostructure offers a research platform for exploring fundamental physics and future applications.
The experimental TiN/HZO heterojunction was fabricated by selectively etching the upper TiN layer from the initially formed TiN/HZO/TiN heterojunction. The TiN/HZO/TiN heterojunction was prepared on a SiO2/Si substrate, with a 20-nm-thick TiN film deposited using ion beam sputtering and the HZO film grown through atomic layer deposition at a temperature of 280 °C. The resulting TiN/HZO/TiN heterojunction was annealed in a nitrogen atmosphere at 500 °C for 30 s to crystallize the HZO. The primary objective of the upper TiN layer was to stabilize the ferroelectric phase during annealing, thereby ensuring the quality of the heterojunction. Subsequently, this layer was removed via wet etching (NH4OH:H2O2:H2O = 1:1:5) after annealing. To facilitate precise electrical measurements, the TiN/HZO heterojunction was subjected to electron-beam-etching-assisted ultraviolet lithography, creating the desired Hall bar structure for testing, with multi-layer graphene serving as the upper electrode for polarization. During the measurements, the heterojunction was subjected to various voltages using a Keithley 2400, and the resulting electrical characteristic curve was obtained through four-probe resistance measurements using a physical property measurement system (PPMS-9T).
Figure 1(a) shows the grazing incidence x-ray diffraction (GIXRD) patterns of the HZO and TiN bilayers on Si(111) substrates, revealing their polycrystalline structures. The appearance of a relatively intense peak at approximately 30.5° indicates the ferroelectric phase associated with the orthorhombic structure of HZO. Additionally, the x-ray photoelectron spectroscopy (XPS) data shown in Fig. 1(b) reveal that there is a nearly 1:1 ratio of Hf to Zr atoms on the surface, which agrees with the nominal composition of the as-grown Hf0.5Zr0.5O2. As illustrated in Fig. 1(c), a characteristic ferroelectric polarization hysteresis loop is observed in HZO, with the full saturation polarization achieved at an applied voltage of 5.2 V and a residual polarization of approximately 14.47 μC/cm2. In addition, the piezoresponse force microscopy (PFM) further confirmed the reversible switching of HZO [Fig. 1(d)]. The PFM images shown in Fig. 1(d) reveal that the phase and amplitude of the ferroelectric phase can be effectively reversed after the polarization at +5 and −5 V. The cycle test showed good retention of ferroelectric reversal.29–31
To measure the superconductivity of TiN and the influence of the ferroelectric polarization of HZO on TiN, 100-μm long and 30-μm wide Hall bar electrodes were prepared through photolithography and etching, as shown in Fig. 2(a). A 10-nm-thick multi-layer graphene, which was used as the upper electrode for polarization, was deposited on the HZO/TiN bilayer using a two-dimensional (2D) transfer platform. Figure 2(b) shows a series of R–T curves under specific voltage polarization where the current during the test was set to 2 mA, demonstrating a clear superconducting transition for the TiN film at Tc = 3.64 K and a normal resistance of approximately 16 Ω/◻ when no polarization voltage is applied. The overall trend of the R–T curve, including the normal resistance, remained stable under negative voltage, whereas the positive polarization voltage caused significant changes in the R–T curve near Tc. A polarization voltage of 1 V caused minimal overall change, whereas a voltage of 2 V led to a sharp resistance peak of approximately 0.2-K width near Tc, accompanied by a drop in normal resistance to 0.1 Ω/◻. At 3 V, the peak remained with a smaller amplitude, and the normal resistance increased to 0.2 Ω/◻. However, when the voltage was increased to 4 or 5 V, the resistance peak decreased, and the resistance in the plateau regime increased to 0.38 and 0.4 Ω/◻. The results revealed a robust relationship between the ferroelectric polarization of the HZO layer and the anomalous resistance peak as well as the change in the normal resistance. A thorough examination of the variation in the superconducting transition temperature revealed that Tc gradually moves toward the high-temperature regime for positive polarization, whereas it shifts toward the low-temperature regime for negative polarization. In Fig. 2(c), P+ and P− denote the R–T curves when +5 V and −5 V are applied correspondingly. For comparison, P+ is magnified 40 times in the figure. A complete switch from the normal state to a zero-resistance superconducting state is observed upon the reversal of the HZO polarization direction in the temperature range of 3.65–3.85 K. This phenomenon can be attributed to the electron-dominated superconducting nature of polycrystalline TiN films. When the HZO polarization faces downwards (positive polarization), the charge carriers move toward TiN, resulting in an increase in Tc. Conversely, when the polarization faces upward (negative polarization), it depletes the TiN film carriers, thus decreasing Tc. This switching effect is highly useful for designing nanoscale electronic devices.16,30 The change in the superconducting state was closely linked to the normal carrier concentration, which was examined at 5 K (fitted by measuring the Rxy–B curve) under different polarization voltages, as shown in Fig. 2(d). The shift in the carrier concentration was on the order of magnitude between 1014 and 1015 cm−2. Under negative polarization, the transformation in the carrier concentration was minute, possibly due to the upward spontaneous polarization of HZO, which had little effect on the TiN film. Remarkably, there was a significant abnormal increase in the carrier concentration at a positive polarization of 2 V, which subsequently decreased and stabilized with an increase in the polarization voltage, in contrast to the anomalous peak detected in the R–T curve.
Next, we performed a thorough examination of the anomalous resistance peak in the incomplete positive polarized states of 2 V (P-State) and unpolarized states (U-State), employing R–T, I–V, R–B⊥, and R–B∥ measurements, as shown in Fig. 3 and extended data in Fig. 1. The temperature-dependent resistance characteristics of the two states under a zero magnetic field were examined, revealing a gradual increase in the resistance with a decreasing temperature, followed by a subsequent decline. This suggests that the grown TiN thin films possess the properties of a dirty metallic material, and the transition to the zero-resistance state occurs near the disordered modulation superconducting insulation transition. The P-State state exhibits a notable electron locality effect near the superconducting transition, leading to the formation of a sharp resistance peak. This distinct feature was observed in both the I–V and R–B curves of the P-State. The response of these peaks to external factors, including temperature, magnetic field, and current, indicates the emergence of a potentially novel state in the superconducting regime. Previous studies have reported anomalous increases in resistance in ultrathin (5-nm-thick) TiN films near superconductivity.21 However, the normal resistance observed in such films is likely due to the disorder inherent in ultrathin samples. In contrast, the thicker TiN film (10-nm-thick) exhibited a smaller normal resistance and a sharper peak. This peak was caused by ferroelectric polarization, owing to a distinct generation mechanism. Figure 3(b) shows the I–V curves of the P-State at different temperatures. An anomalous peak was observed in the I–V curves, and the height of the peak was suppressed at lower currents. Figures 3(c) and 3(d) illustrate the dependence of the P-State on the parallel and vertical magnetic fields, respectively. An anomalous resistance peak was observed in the R–B curve of the P-State under a stronger magnetic field at lower temperatures. Furthermore, the presence of the peak had little effect on the critical magnetic field in contrast to the magnetoresistance between the U-State and the P-State (as shown in the extended data of Fig. 2). This can be proven in detail using the statistics of the upper critical magnetic field with both parallel and vertical magnetic fields (extended data of Fig. 3). Notably, the TiN thin film exhibited an incongruous response to the two types of magnetic fields, suggesting that our samples were in the 2D regime. The strict linear dependence of the upper critical magnetic field of the vertical magnetic field on the temperature and the square dependence of the upper critical magnetic field of the parallel magnetic field, regarded as characteristics of 2D superconducting systems, can also prove the same. As temperature decreased and superconductivity emerges, the I–V curve gradually shifted from a regular Ohmic state ( ) to a power law relationship ( ) (as shown in the extended data, Fig. 4).31–33 This transformation is attributed to the Berezinskii–Kosterlitz–Thouless (BKT) transition in 2D superconductivity.
To gain further insight into the emergence and disappearance of anomalous resistance peaks under ferroelectric regulation, we adopted a two-channel model to elucidate our experimental observations.11,34 The two-channel model, illustrated in Fig. 4(b), provides a framework to describe the superconducting transformation process manifesting in the electric transport from the Fermion channel (orange region) to the Bose channel (blue region). In the normal state, the resistance is governed by the Fermi channel and conforms to a single quasiparticle model. However, upon lowering the temperature to Tc, a single quasiparticle exits the Fermi channel and pairs with another particle to form a Cooper pair, thus forming the boson channel and leading to superconductivity. In the absence of ferroelectric polarization, the carrier concentration is low, and the intrinsic disorder of the sample is negligible. Consequently, individual quasiparticles can migrate swiftly to regions characterized by low potential energies. In the case of complete positive polarization, the carrier concentration increases moderately; however, individual quasiparticles can still move quickly to regions of low potential energy owing to uniform polarization and small-size particle disorder. In both scenarios, the transformation from the Fermi-to-Bose channel proceeds with minimal impedance. As the temperature decreases, the TiN film undergoes a rapid transition from the normal state to the superconducting state. However, in the case of incomplete positive polarization, we infer that polarization non-uniformity leads to higher ferroelectric fluctuations, resulting in greater disorder. As the temperature decreases to Tc(local), some single quasiparticles enter regions of lower potential energy and aggregate to form boson islands, whereas others remain in high-potential energy regions and cannot pair with another particle to form Cooper pairs because of their high energy. The localized bosons absorb fermions near the Fermi level EF, thereby reducing the conductivity of single quasiparticles and inducing a sharp increase in resistance from the Fermi channel, giving rise to a Bose insulation state. As the temperature further decreases, Cooper pairs continue to form near the boson islands that have already emerged, leading to the development and coupling of more boson islands. At Tc(global), global phase coherence emerges between these continuous boson islands, enabling the boson channel to fully control the electrical transport and form a macroscopic superconducting state.
|.||Tc(global) (K) .||Tc(local) (K) .||ρM (Ω/□) .||ρ0 (Ω/□) .||Δ0 (meV) .||η .|
|5 V||3.61||3.89||1.347||50 696||7.55||3.89|
|0 V||3.46||3.725||16.49||2 281 211||7.46||4.4|
|.||Tc(global) (K) .||Tc(local) (K) .||ρM (Ω/□) .||ρ0 (Ω/□) .||Δ0 (meV) .||η .|
|5 V||3.61||3.89||1.347||50 696||7.55||3.89|
|0 V||3.46||3.725||16.49||2 281 211||7.46||4.4|
We manipulated the superconductivity of amorphous TiN using a ferroelectric thin film Hf0.5Zr0.5O2. By manipulating the direction of ferroelectric polarization, we could switch from the normal state to a zero-resistance superconducting state. Notably, strong ferroelectric fluctuations resulted in increased disorder in the superconducting film, leading to the emergence of a Bose insulation state near Tc. Further theoretical investigations are necessary to fully comprehend the intricate interplay between ferroelectric fluctuations and disorder, and their effects on superconductivity. Our findings provide special avenues for the development of next-generation superconducting devices with enhanced functionality and performance.
See the supplementary material for additional descriptions of (1) detailed transport measurement of transport in the unpolarized states, (2) contrast of magnetoresistance between U-State and P-State, (3) statistics of upper critical magnetic field with both parallel and vertical magnetic fields between U-State and P-State, (4) I–V curves of the U-State and P-State at different temperatures, respectively, near V ∝ I 3, and (5) characterization of inhomogeneity in HZO film's surface.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11974099 and 11405045), the Plan for Leading Talent of Fundamental Research of the Central China in 2020, and the Intelligence Introduction Plan of Henan Province in 2021 (No. CXJD2021008).
Conflict of Interest
The authors have no conflicts to disclose.
Qilin Han: Data curation (equal); Formal analysis (equal); Writing – original draft (equal). Chao-Yang Kang: Conceptualization (equal); Data curation (equal); Writing – review & editing (equal). Xuegang Chen: Methodology (supporting). Kai Wang: Data curation (supporting). Weifeng Zhang: Funding acquisition (lead); Writing – review & editing (equal).
The data that support the findings of this study are available from the corresponding author upon reasonable request.