Abstract
The transitions from a superconductor to a resistive state in two dimensions provide a valuable platform for studying continuous quantum phase transitions and critical phenomena. Here we uncover anomalous quantum fluctuations and identify an unconventional superconducting quantum critical point in a gate-tuned excitonic quantum spin Hall insulator, the monolayer tungsten ditelluride. We do this by extending Nernst experiments down to millikelvin temperatures. The vortex Nernst effect that we observe reveals singular superconducting fluctuations in the resistive normal state induced by magnetic fields or temperature, even well above the transition. Near the doping-induced quantum critical point, the Nernst signal driven by quantum fluctuations is large in the millikelvin regime, an indication of the proliferation of vortices. Unexpectedly, the Nernst signal abruptly disappears when the doping falls below the critical value, in contrast with conventional expectations. This series of phenomena calls for careful examination of the mechanism of the quantum critical point in the monolayer.
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Data availability
The data that support the findings of this study are available from the Harvard Dataverse (https://doi.org/10.7910/DVN/UAJDHM) or from the corresponding author upon reasonable request. Source data are provided with this paper.
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Acknowledgements
We acknowledge helpful discussions with Z. Bi, T. Grover, F. D. M. Haldane, D. Huse, B. Lian, S. Ryu, S. Sondhi, A. Vishwanath, A. Yazdani and Y. Zhang. We especially thank L. Pfeiffer and M. Shayegen for their GaAs sample, which was used for calibrating the electron temperature of our dilution refrigerator. This work is mainly supported by Office of Naval Research through a Young Investigator Award (N00014-21-1-2804) to S.W. Measurement systems and data collection were partially supported by the National Science Foundation through a CAREER award (DMR-1942942) to S.W. The data analysis was partially supported by the Young Investigator programme of the Air Force Office of Scientific Research (FA9550-23-1-0140) to S.W. N.P.O. is supported by the US Department of Energy (DE-SC0017863). S.W. and L.M.S. acknowledge support from the Eric and Wendy Schmidt Transformative Technology Fund at Princeton. Materials synthesis and device fabrication were partially supported by the Materials Research Science and Engineering Center of the National Science Foundation (DMR-2011750) through support to R.J.C., L.M.S., N.P.O. and S.W. T.S. acknowledges support from the Princeton Physics Dicke Fellowship programme. A.J.U. acknowledges support from the Rothschild Foundation and the Zuckerman Foundation. K.W. and T.T. acknowledge support from the Japan Society for the Promotion of Science (KAKENHI Grant Nos. 19H05790, 20H00354 and 21H05233). L.M.S. and N.P.O. acknowledge support from the Gordon and Betty Moore Foundation through grant nos. GBMF9064 and GBMF9466, respectively. L.M.S. is also supported by the David and Lucile Packard Foundation and the Sloan Foundation.
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S.W. designed the project. T.S. fabricated the devices and performed the measurements, assisted by Y.J., Y.T., G.Y., P.W., A.J.U. and M.O. G.Y. and P.W. built the dilution refrigerator measurement system. T.S., S.W. and N.P.O. analysed the data. R.S., L.M.S., X.G. and R.J.C. grew and characterized the bulk WTe2 crystals. K.W. and T.T. provided the hBN crystals. S.W., T.S. and N.P.O. interpreted the results and wrote the paper with input from all authors.
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Extended data
Extended Data Fig. 1 Microscope and AFM images during the device 1 fabrication process.
a, Bottom gate and metal electrodes after AFM tip clean. b, Dark field optical image of the bottom part. c, Tapping-mode AFM image of the metal electrodes. d, Microscope image of monolayer WTe2 flake exfoliated in the glovebox. e, Microscope image of device 1 after transferring the top gate and monolayer WTe2. The monolayer WTe2 flake is outlined in red. Top and bottom graphite flakes are outlined in yellow and orange. f, Dark field optical image of device 1. No bubbles were observed.
Extended Data Fig. 2 Electron temperature calibration of the measurements in the dilution refrigerator.
The calibration was performed based on an ultra-high mobility GaAs device with a series of fractional quantum Hall states. The plot shows the longitudinal resistance (Rxx) in log scale versus the inverse fridge temperature (1/T), taken at the 14/9 fractional quantum Hall state. Error bar is defined as the measurement noise.
Extended Data Fig. 3 Temperature gradient estimation in device 1.
a, Microscope image of device 1 with the two-probe resistance measurement configuration. The monolayer WTe2 flake is outlined in red. b, Temperature gradient generated by Heater 1 and Heater 2. c and d, Two-probe resistance for Pair 2 and Pair 1, respectively, as a function of the Heater 2 current and the fridge temperature. The black dashed lines trace the same R2p, and extract T1 and T2.
Extended Data Fig. 4 High efficiency of microheaters fabricated on vdW heterostructures.
a, Microscope image of device 2 with three microheaters fabricated on hBN/graphite (Heater 1), only hBN (Heater 2), and only SiO2 (Heater 3), respectively. The monolayer WTe2 flake is outlined in red. Top and bottom graphite flakes are outlined in yellow and orange. The Nernst signal was measured from the same two probes labeled 1 and 2. b, Nernst signal as a function of B measured with Heater 1 (red), Heater 2 (blue), and Heater 3 (black), respectively, for the same Ph = 6.5 nW and ng = 15.39 × 1012 cm−2.
Extended Data Fig. 5 Raw resistance data taken on device 1.
a, Microscope image of device 1 with the four-probe resistance measurement configuration. The monolayer WTe2 flake is outlined in red. b, Four-probe resistance as a function of ng and temperature. The white dots represent TBKT. c, Temperature dependence of Rxx for various ng. d, The four-probe conductance (Gxx) calculated from Rxx as a function of ng at various temperatures. e, Normalized Rxx as a function of ng and B (the same data of Fig. 2b). For each ng, Rxx is normalized to its value at −95 mT to highlight its B dependence. The black dotted line represents BR,90%, at which Rxx drops to 90% of its saturated value at high B. f, Rxx as a function of B for ng = 13.56 × 1012 cm−2 showing a vertical line cut of e. The red dashed line indicates the identified BR,90%.
Extended Data Fig. 6 Extracting TBKT in device 1.
a, Characteristic nonlinear I-V curves on a logarithmic scale at various temperatures. The black dashed line shows a tentative fit to the Vxx ∝ IDC3 power law, which extracts TBKT to be 580 mK for ng = 22.84 × 1012 cm−2. b, The corresponding differential resistance (dVxx/dI) as a function of IDC and T. c, dRxx/dT as a function of ng and T (the same data of Fig. 1b, using two neighboring points for the temperature derivative). The black dots represent TBKT extracted by fitting to the Vxx ∝ IDC3 power law for various ng. d, B-dependence of Rxx as a function of T for ng = 22.84 × 1012 cm−2.
Extended Data Fig. 7 Nernst data taken on device 2.
a, Nernst signal as a function of ng and B. b, Nernst signal as a function of ng under very small B. The dual-heater power is 13 nW. The Nernst signal is recorded at the base temperature. The noise data (also seen in device 1) at low ng is not antisymmetric to B and hence not Nernst signal. They likely arise due to bad contact to Au in this regime. The results reproduce the findings in device 1 discussed in the main text.
Extended Data Fig. 8 Ruling out a first-order transition.
a, Rxx as a function of ng, swept back and forth, at base temperature. The green and orange curves correspond to decreasing and increasing ng, respectively. b, Nernst signal as a function of ng measured at 5 mT. The dual-heater power is 128 pW. No hysteresis in the sweeps, the characteristic of a first-order transition, is found for both resistance and Nernst signal. Note that data in a and b were taken from a new cooldown after about a year (stored in an Ar-filled glovebox) after the first cooldown, in which we took most of the data presented in the manuscript. The device and data remain of high quality with negligible changes. c, Rxx normalized to its value at 900 mK as a function of ng (red) or T (blue), along the two dashed lines shown in d. The data is extracted from Fig. 1b. Rxx(ng) and Rxx(T) display an excellent overlap under linear scaling which suggests that the two transitions share the same characteristic. Started from the same superconducting state, the T-induced transition is a continuous BKT transition in nature, whereas the ng-induced transition is also induced by the proliferation of vortices and antivortices (driven by quantum fluctuations). d, Nernst signal as a function of ng and T, taken at B = 2 mT and Ph = 46 pW (the same data from Fig. 4a). The ng-induced QPT manifests as the zero-temperature limit of the continuous BKT transition. All these observations speak against a first-order transition and demonstrate that indeed the ng-induced 2D superconducting transition is BKT-like, in terms of how the superconducting state is destroyed (the proliferation of vortices and antivortices). The sudden disappearance of the Nernst signal below the critical density (Fig. 2 & 3) is unexpected, raising intriguing questions regarding the behaviors of the vortices near the QPT.
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Song, T., Jia, Y., Yu, G. et al. Unconventional superconducting quantum criticality in monolayer WTe2. Nat. Phys. 20, 269–274 (2024). https://doi.org/10.1038/s41567-023-02291-1
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DOI: https://doi.org/10.1038/s41567-023-02291-1
