Abstract
We have performed detailed transport measurements on a 3 nm thick (as-grown) Al film on GaAs prepared by molecular beam epitaxy (MBE). Such an epitaxial film grown on a GaAs substrate shows the Berezinskii-Kosterlitz-Thouless (BKT) transition, a topological transition in two dimensions. Our experimental data shows that the MBE-grown Al nanofilm is an ideal system for probing interesting physical phenomena such as the BKT transition and superconductivity. The increased superconductor transition temperature (~2.4 K) compared to that of bulk Al (1.2 K), together with the ultrathin film quality, may be advantageous for future superconductor-based quantum devices and quantum information technology.
1. Introduction
The ideas of mathematical topology play an important role in many aspects of quantum physics—from phase transitions to topological insulators [1–4]. In particular, an interesting example of this is the Berezinskii-Kosterlitz-Thouless (BKT) transition—a topological transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and antivortices at the critical temperature [5, 6]. This elegant model developed by BKT [5, 6] can be used to explain the seemingly forbidden superconducting (ferromagnetic) transition in two dimensions. For a superconducting, topological transition (BKT transition) in two dimensions, at the critical temperature , , where and are the measured voltage drop between two voltage probes and the driving current flowing between the source and drain contacts, respectively [7]. The BKT transition has been observed in various ultrathin films such as Pb atomic films [8], Ga thin films [9], monolayer NbSe2 [10], and one-atom-layer Tl-Pb compound on Si (111) [11].
Aluminum (Al) is the most abundant metal on the Earth’s crust, and it has already found wide applications in interconnects, coating on graphene, plasmonic devices, and so on [12–14]. Recent advances in sample preparation have made it possible to prepare large-area, high-quality Al films [14, 15]. In particular, large-area Al films with an atomically smooth surface grown by molecular beam epitaxy (MBE) on a GaAs substrate can be readily accessible [15]. Such a high-quality two-dimensional (2D) metallic film is an ideal system for probing 2D physics. Interestingly, the critical temperature of the studied MBE-grown Al nanofilms (~2.4 K) [15] can be significantly higher than that of bulk Al (1.2 K). In order to obtain a thorough understanding of the physics and the nature of the observed superconductivity in Al nanofilms, we perform detailed transport measurements on a 3 nm thick (as-grown) Al nanofilm. Here, we report experimental evidence for the BKT transition in such a MBE-grown sample. The measured when is approximately the critical temperature determined by the BCS model, unequivocally showing that the observed superconductor transition is a topological transition in two dimensions. Although superconductivity in Al thin films has been studied in depth [16], our Al nanofilms are grown on GaAs; therefore, it is possible for one to combine superconducting devices with GaAs-based transistors and high-frequency devices on the same substrate. Such an advantage may be useful for future quantum information processing and computation technology.
2. Experimental Section
The 3 nm thick Al film reported in this paper was prepared in a Varian Gen-II solid-source MBE system [15]. The experimental details can be found in the supplementary information (S1). The quality of the sample in this work is similar to those reported in Ref. [15]. In our earlier work, for a MBE-grown film deposited at room temperature with an intended thickness of 3 nm, the average roughness of the film is about 4.9 nm which is thicker than the deposited thickness and is possibly caused by the Al oxidation after the exposure to air [17]. In contrast, the surface roughness of the current Al nanofilm grown below 0°C is more than an order of magnitude lower (see Figure 1(a)). Therefore, we believe that the substrate temperature is the key issue for preparing a high-quality MBE-grown Al nanofilm: the lower the substrate temperature, the higher the sample quality (the lower the surface roughness).
(a)
(b)
We chose to study a 3 nm thick Al film as this is the thinnest conducting sample which we can prepare. If the as-grown thickness is below 3 nm, for example, say 2.5 nm, the film becomes nonconducting even at room temperature, suggesting that the thin film may be discontinuous. For the current experiments, the sample was processed into a Hall bar geometry (see Supplementary Information S2).
3. Results and Discussion
Figure 1(a) shows a atomic force microscope (AFM) top-view image of the 3 nm thick Al film in air. The root mean square (RMS) roughness is about 0.29 nm. This low RMS surface roughness demonstrates that our film is of high quality. The black regions may correspond to voids in the Al nanofilm which are not conducting and should not affect the transport properties and superconductivity in our Al nanofilm.
Figure 1(b) shows a cross-sectional transmission electron microscope (TEM) image. A nearly defect-free Al film of thickness of ~1 nm can be observed. According to the TEM data shown in Figure 1(b), although the as-grown thickness of our Al film is 3 nm, the actual conducting layer is about 1 nm thick due to the formation of the ~2 nm thick AlOx layer on top of the aluminum film. Such an AlOx layer can prevent the Al nanofilm from further oxidation. An AlOx overlaying layer may introduce strain to the Al nanofilm, though this layer is present in most Al films in the literature.
The MBE-grown Al nanofilm was processed into Hall bars, and standard dc four-terminal resistance measurements were performed on our Al samples (please see Supplementary Information S3). Figure 2(a) shows the square resistance measurements as a function of magnetic field of a 3 nm thick Al device at various temperatures . The magnetic field is applied perpendicular to the plane of the Al film. At the lowest temperature of 0.25 K, is zero when . For , starts to increase and reaches saturation (the normal state where is about 1650 Ω) at around 3 T. When is half of the normal state value , we can determine the critical magnetic field to be 1.47 T. By repeating this procedure for various temperatures, can be measured, and such results are shown in Figure 2(b). There is a good fit based on the Gorter-Casimir theory [18] which is strongly related to the BCS model [19] to the data. According to the fit to our experimental data, we can determine the critical magnetic field and critical temperature to be 1.51 T and 2.40 K, respectively. We note that in the normal state in the high magnetic field regime, tends to decrease slightly with increasing temperature , showing weak semiconductor-like behavior [20–22]. Similar results have been observed in monolayer NbSe2 [10], ultrathin crystalline lead films [23], and a two-atom layer of hexagonal Ga film grown on semiconducting GaN(0001) [24]. A possible reason for these results is that the sample shows a weak localization effect when increasing the measurement temperature.
(a)
(b)
(c)
In order to further study the observed superconducting transition, over a wider range of temperature is shown in Figure 2(c). We are now able to fit out data to the following equations based on the Aslamazov-Larkin- (AL-) Maki-Thompson (MT) correction as described in Ref. [25]:
Here, and are given by where is the phase-breaking parameter. According to the red curve which corresponds to the fit to Equations (1), (2) and (3), and of our 3 nm thick Al film are measured to be 2.21 K and 0.775. The estimated is close to that predicted (0.993) in Ref. [26].
Figure 3 shows the four-terminal - characteristics of the 3 nm thick Al nanofilm at different temperatures. At , a dissipationless current, i.e., a supercurrent, can be observed. There is a superconductor-metal transition at around , where we observe an abrupt increase in the measured voltage. With increasing temperature, the supercurrent is decreased. At , there exists a low supercurrent, showing that the device is still superconducting. Such an elevated transition temperature is highly useful for our superconducting devices grown on GaAs as we can integrate superconductor-based devices with GaAs-based high-electron mobility transistors (HEMTs) and high-frequency transistors on the same GaAs substrate.
In order to further probe the superconductor transition, we perform detailed measurements at various temperatures. Figure 4 shows such results on a log-log scale. The red lines correspond to fits to experimental data at various temperatures. The black line corresponds to when the BKT transition occurs. The measured exponent as a function of temperature is shown in Figure 5. By interpolation, we can determine the topological transition temperature to be 2.29 K at , which is in close agreement with the measured and the critical temperature based on the Aslamazov-Larkin-Maki-Thompson correction in the linear regime. Our experimental results clearly show that the observed superconductor transition in our Al nanofilm is a topological transition in two dimensions, and our data can be described by both the Gorter-Casimir theory related to the BCS model and the Aslamazov-Larkin-Maki-Thompson correction.
Normally, the superconducting transition temperature of a thin film is lower than that of a bulk sample. We note that the opposite trend (increased measured in thin films compared to those of bulk samples) has been observed in double-atomic-layer Ga films on GaN [24], FeSe monolayer films on SrTiO3 [27], and FeSe on TiO2 [28]. These interesting results, together with the present work on the MBE-grown Al nanofilm, may suggest that the interface effects play a significant role in the enhanced superconductor transition temperature in a thin film over that of its bulk counterpart [29].
4. Conclusion
In conclusion, we have performed extensive transport measurements on a 3 nm thick (as-grown) Al film grown on a GaAs substrate by MBE. Such a MBE-grown Al nanofilm is of high quality as demonstrated by both AFM and TEM measurements. Importantly, we have observed the BKT transition in two dimensions as evidenced by in the nonlinear - regime. The measured topological transition temperature is close to the critical temperature as determined by the Gorter-Casimir theory strongly related to the BCS model as well as the transition temperature based on the Aslamazov-Larkin-Maki-Thompson correction . The higher transition temperature compared to that of bulk Al (1.2 K) is highly desirable for possible future superconductor-based quantum computation scheme and quantum devices. Moreover, our high-quality Al film is fully compatible with the existing GaAs-based HEMT technology; thus, our experimental results may open the way for combination of superconducting devices and HEMT devices.
Data Availability
The data used to support the findings of this study are available from the corresponding authors upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Authors’ Contributions
Ankit Kumar and Guan-Ming Su contributed equally to this work.
Acknowledgments
The authors acknowledge the technical support from the Center of Nano Science and Technology and the Center of Nano Facility at National Chiao Tung University, Integrated Service Technology Co. Ltd., and National Device Laboratory. This work was financially supported by the Ministry of Education (MOE) ATU program, National Taiwan University (NTU) (grant numbers 107L892101 and 108L892101), and the Ministry of Science and Technology (MOST) (grant numbers MOST 105-2112-M-002-005-MY3, MOST 108-2112-M-002-014-MY2, and MOST 108-2622-8-002-016), Taiwan. L.C. acknowledges the hospitality of the Physics Department of NTU during his sabbatical stay at NTU. The work of A.K. at NTU was made possible by arrangement with Prof. E. S. Kannan at BITS-Pilani, India. A.K. was supported by the TEEP@India Program provided by the MOE, Taiwan (grant number 106M4102-7).
Supplementary Materials
S1: MBE growth of Al nanofilm. S2: device geometry and stability. S3: low-temperature resistance measurements. (Supplementary Materials)