Restoring Superconductivity in the Quantum Metal Phase of NbSe2

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Restoring superconductivity in the quantum metal phase of NbSe using dissipative coupling 2

Abhishek Banerjee, Abhinab Mohapatra, Rajamanickam Ganesan, and P.S. Anil Kumar Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b04538 • Publication Date (Web): 08 Feb 2019 Downloaded from http://pubs.acs.org on February 8, 2019

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Restoring superconductivity in the quantum metal phase of NbSe2 using dissipative coupling Abhishek Banerjee1 , Abhinab Mohapatra1 , R. Ganesan1 and P. S. Anil Kumar1∗ 1 Department

of Physics, Indian Institute of Science, Bengaluru 560012, India

E-mail: [email protected] Abstract Localization arguments forbid the appearance of a metallic ground state in two dimensions. Yet, a large variety of disordered superconductors are known to manifest an anomalous metal phase in the zero temperature limit. While previous observations were confined to non-crystalline ‘dirty’ superconductors, the recent observation of the so-called Bose metal phase in crystalline thin flakes of NbSe2 has sparked off intense debate. While the exact nature of this phase remains unknown, it is thought that quantum fluctuations play a decisive role in Bose metal physics. In this work, we study the response of the anomalous metal phase in thin flakes of NbSe2 to dissipative coupling. We evince a drammatic quenching of the Bose metal phase when dissipative coupling is strong, fully restoring a zero resistance superconducting state in the entire region of the magnetic field (H)-temperature (T) phase diagram where the Bose metal phase is otherwise observed. The suppression of the Bose metal phase by dissipative coupling is possible only in a quantum system where dissipation can directly affect system thermodynamics. Our observation of a dissipative phase transition in twodimensional NbSe2 firmly establishes the quantum nature of the anomalous metal phase in this class of ‘clean’ superconductors. Keywords: Bose metal, two dimensional superconductor, dissipative phase transition, transition metal dichalcogenide, quantum transport

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Introduction Two dimensional systems are not expected to be metals at zero temperature due to Anderson localization. Yet, several examples of a zero temperature metallic state in two dimensions have been observed in diverse physical systems including disordered superconducting thin films

1–9

and arrays of Josephson junctions . 10,11 Of particular interest is the case of two-

dimensional superconducting systems where disorder in the form of crystalline defects or vortices induced by a magnetic field has been shown to produce an anomalous metal phase where the sample resistivity saturates to a finite value in the zero temperature limit. 1–9 In superconductors, where electrical current is carried by Bosonic excitations, namely Cooper pairs, such a metallic phase is unexpected. Conventional wisdom demands that Bosons can exist as eigenstates of either the phase or number operator, that is, they can either condense into a superfluid phase or be insulating. A metallic phase of Bosons is therefore completely anomalous and has been a subject of intense theoretical discussion. 12–20 While various theoretical models have been used to describe a Bose metal, there is no clear consensus yet, especially since all known models have been shown to fail to explain important aspects of the experimental data. 21 Nonetheless, it is thought that the general principle underlying the formation of a Bose metal state involves disorder/magnetic field driven quantum phase fluctuations that destroy global phase coherence leading to diffusive motion of Cooper pairs in a disordered electrostatic environment, culminating in a metallic state. The fact that Cooper pairs fail to condense even in the zero temperature limit points to the role of quantum fluctuations, rather than thermal fluctuations, that are, for example, responsible for finite resistance due to vortex-antivortex unbinding at finite temperatures, making this a purely quantum mechanical phenomena. Experimentally however, the role of quantum fluctuations in Bose metals remains poorly understood. In fact, in our opinion, there is no direct experiment that proves that the Bose metal phase is of purely quantum mechanical origin. It has been suggested that the role of quantum fluctuations may be detected by coupling 2


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Vxx

Zs h-BN

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Figure 1: (a) Optical micrograph of a representative h-BN capped NbSe2 device Scale bar=10µm (b) Equivalent circuit of the device measurement configuration. The series impedance Zs is used to control the effective dissipation of the circuit. (c) Resistance(R) versus temperature(T) at B = 0 showing a superconducting transition at Tc = 6.4K. Inset: log(R) vs T showing a zero resistance state at T < Tc (d) Current versus Voltage characteristics at different temperatures showing different power laws V ∝ I α . Inset: α vs T . Dashed line corresponds to α ' 3 at TBKT = 6.1K

the system in study to a dissipative bath. 22–27 Such a dissipative bath will damp quantum phase fluctuations, and has been shown to drive prototypical superconductor-insulator transitions in Josephson junction arrays, 28,29 granular superconductors and superconducting nanowires. 30–33 Experimentally, dissipative coupling is most easily achieved by introducing an external dissipative element such as a resistor in the path of the measurement circuit. The resistor provides a thermal bath that can be treated as a collection of L-C oscillators. This enters the Hamiltonian of the system as a drag term that can damp phase fluctuations, with the dissipation factor η ∝ 1/Zs , where Zs is the external environmental impedance. 27 3


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Although, the role of dissipative coupling has been recognized in previous works on Bose metals, 34 a complete suppression of the Bose metal phase and the consequent revival of a zero resistance superconducting state in response to dissipation has never been observed before. In this work, we exploit such a strategy to study the effect of dissipative coupling in thin flakes of NbSe2 , where the anomalous metal phase has been recently observed. 8 The observation of the Bose metal in such clean crystalline superconductors has been understood as an indication that the underlying phase is not an artifact of sample granularity or crystalline disorder. We study electrical transport in thin flakes of NbSe2 , where the Bose metal phase is clearly observed when coupled to a non-dissipative bath. On the other hand, when the same device is coupled to a dissipative environment, the Bose metal phase completely disappears and superconductivity is fully restored. Our experiment not only proves the quantum mechanical origin of the Bose metal phase in NbSe2 where quantum phase fluctuations drive the superconductor-metal transition, but also allows us to extract the exact resistance of the Bose metal within the H-T phase diagram.

Device fabrication and experimental setup Experiments are performed on flakes obtained by micromechanical exfoliation of NbSe2 single crystals. Details pertaining to growth and characterization of single crystals can be found in supplementary material section A. In Fig. 1(a), we show the optical micrograph of a typical NbSe2 device. Electrical connections to the sample are made through coaxial cables that are properly shielded and connected to a low impedance ground. To simulate the effect of an external source of dissipative coupling, in the spirit of Ref. 27 we adopt a measurement configuration with an equivalent electrical circuit as depicted in Fig. 1(b). In the first case(Config 1), ‘zero’ dissipation is obtained by using a Keithley 6221 current source with a very large output impedance Zs ' 1014 Ω. This configuration provides an ultra-low dissipation environment (η ∝ 1/Zs ) to the sample and is ideal to observe the Bose metal phase. For the second 4


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case (Config 2), we use a 5V voltage source available with the SRS-830 lock in amplifier and attach a resistor of Rs = 106 Ω in series with the sample. Considering the output impedance of the voltage source to be negligible compared to Rs , we obtain Zs ' Rs ' 106 Ω. This configuration provides a large dissipative coupling, and is used to determine the effect of dissipation on the Bose metal phase. To measure the four-terminal voltage, we use either a Keithley 2182 Nanovoltmeter for DC voltage measurements or the SRS-830 Lock-In amplifier for AC measurements. For AC measurements, any choice of signal frequency in the range 1Hz to 1KHz shows no measurable difference to the data. AC versus DC measurements or DC measurements in the Delta mode also do not affect our results, ruling out any frequency dependent effects. Unless specified otherwise, all measurements employ a bias current of Ibias = 1µA, which is small enough to prevent any extraneous heating or non-linear effects, but large enough to enable a measurement of minimum resistance ' 10mΩ, given that our voltage measurment limit is ' 10nV. All resistances are corrected for the sample geometry and represent two-dimensional sheet resistances.

Results Fig. 1(c) depicts the four terminal sheet resistance as a function of temperature. The resistance in the normal state is RN ' 3Ω. The sample thickness is estimated to be 2-3 nm using a combination of atomic force microscopy and a meausurement of the superconducting transition temperature Tc (see supplementary material section B) corresponding to a ∼4-layer NbSe2 flake. The coherence length(ξ) is estimated from magnetoresistance measurements using the relation:

Hc2 =

φ0 (1 − T /Tc ) 2πξ(0)2

(1)

where Hc2 is the upper critical field in the perpendicular field configuration, φ0 is the flux quantum, and ξ(0) is the Landau-Ginzburg coherence length at zero temperature, T

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is the sample temperature and Tc represents the mean-field transition temperature. The Bardeen-Cooper-Schieffer (BCS) coherence length can be estimated as ξ0 = 1.35ξ(0). Using the approximation that ξ(0) ' ξ(2K), and Hc2 (2K) = 3.5T , we obtain ξ0 ' 13.5nm. This indicates that the sample is in the two dimensional limit with d < ξ0 , d ' 2 − 3nm being the sample thickness. This is further confirmed by performing current(I) vs voltage(V) measurements shown in Fig. 1(d) that indicate the transition to the superconducting state to be of the Berezinskii-Kosterlitz-Thouless (BKT) type. 35–39 Such a transition is characterized by a non linear I-V relationship with V ∝ I α indicating voltage generation due to dissipation created by current induced vortex-antivortex unbinding. The BKT transition temperature is obtained when V ∝ I 3 , that is, α = 3. From the inset of Fig. 1(c), we obtain TBKT = 6.1, which is only slightly lower than the mean-field transition temperature Tc = 6.4. The proximity of TBKT to Tc is expected for a two-dimensional superconductor in the ultra-clean limit such as ours. Having established that our sample exhibits characteristics of a true two dimensional superconductor, we explore the response of our sample to a finite magnetic field. When the sample is connected to a low dissipation environment (Config 1), we obtain four terminal resistance as a function of temperature (T) as shown in Fig. 2(a) for different magnetic fields. At small magnetic fields (H > 0.1T ), that are significantly smaller than the upper critical Hc2 = 3.5T , the sample fails to manifest a true superconducting state with zero resistance. Instead the sample resistance appears to saturate in the zero temperature limit. As shown in the 2D color plot of Fig. 2(a), a zero resistance superconducting state is obtained only for H ≤ 0.1T , in the zero temperature limit. For H ≥ 0.1T , the resistance becomes finite and ⊥ increases monotonically until H ' Hc2 , where the sample crosses over to the normal state.

To obtain a clearer picture, in Fig. 2(c) we depict an Arrhenius plot of sample resistance versus temperature obtained for different magnetic fields. While the 0T curve indeed shows a true zero resistance state measured to the limit of our instrument resolution, increasing the magnetic field results in the dramatic appearance of a finite resistance state that persists

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Figure 2: Electrical transport measurements in low-dissipation configuration, Config-1 with Zs = 1014 Ω (a) Resistance (R) versus temperature (T) measurements at different magnetic fields (b) 2D color plot of sample resistance as a function of magnetic field (H) and Temperature(T) (c) Arhenius plots showing log(R) vs. 1/T at different magnetic fields. Solid black lines indicate linear fits, indicating thermal fluctuation induced motion of vortices. The saturation of resistance at lower temperatures indicates the onset of the Bose metal phase (d) Energy barrier U (K) to vortex motion as a function of magnetic field (H). The solid line indicates a linear fit to the depicted empirical form.

to the zero temperature limit. Approaching from the normal resistance state, where all curves overlap, the sample enters into a flux flow regime where resistance arises due to dissipation caused by thermal motion of vortices. 40 In a clean superconductor such as NbSe2 , this regime is characterized by an

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activated form of resistance where the activation energy for vortex-antivortex unbinding is provided by thermal fluctuations. In Fig. 2(b), these activation profiles are depicted as straight line fits and are used to determine the energy barrier U to the creation of a vortexantivortex pair. The dependence of U on the applied magnetic field is shown in Fig. 2(d), which is consistent with the form U = U0 ln(H0 /H), where U0 is the characteristic vortex unbinding energy and H0 ' Hc2 for a clean superconductor. We estimate U0 = 16.4 ± 0.9K and H0 = 1.9±0.1T , which are in close agreement with previous measurements on thin flakes of NbSe2 in the Bose metal phase. 8 However, we note that H0 ' 1.9T deviates significantly from Hc2 ' 3.5T . While such a large deviation has been observed previously as well in the Bose metal phase of NbSe2 , 8 it is not expected in a clean superconductor. When the sample temperature is decreased further, a clear deviation from an activated form is observed. In fact, the resistance appears to saturate beyond this point. The fact that the resistance saturation appears at lower temperatures for smaller magnetic fields (that correspond to lower values of the saturated resistance) indicates that our observations are not experimental artifacts due to sample overheating. The saturation of resistance as T → 0 when an external parameter controlling disorder (magnetic field in this case) is turned on is the hallmark of the Bose metal phase. In sharp contrast, measurements performed in the high dissipation environment (Config2) produce dramatically different behavior. In contrast to the low dissipation experiment (Config-1) where the sample fails to become superconducting at small magnetic fields (H > 0.1T ), in Config-2, the sample obtains a perfect zero resistance state to magnetic fields as large as the upper critical fields Hc2 = 3.5T as shown in Fig. 3(a). In Fig. 3(b), we depict the sample resistance as a function of both H and T, indicating complete restoration of the zero resistance superconducting state in the same range of the H-T phase diagram that was originally occupied by the Bose metal state. To capture the transition to the finite resistance state, we depict Arhenius plots of the sample resistance in Fig. 3(a). Even with a magnetic field as high as H = 1T , the sample

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Zs=106

Figure 3: (a) Electrical transport measurements in high-dissipation configuration, Config2 with Zs = 106 Ω (a) Resistance (R) versus temperature (T) measurements at different magnetic fields (b) 2D color plot of sample resistance as a function of magnetic field (H) and Temperature(T) (c) Arhenius plot showing log(R) vs. 1/T at different magnetic fields. Solid black line indicates linear fits. Beyond the linear regime, the sample immediately obtains a zero resistance state (d) Energy barrier U (K) to vortex motion as a function of magnetic field (H). The solid line indicates a linear fit to the depicted empirical form.

obtains perfect superconductivity as T → 0. The finite resistance part of log(R) vs 1/T curve can be entirely fitted with a straight line indicating perfectly activated behavior as expected for thermally driven vortex motion. Beyond the linear regime, the sample resistance becomes zero to the limit of our instrument resolution. The extracted values of vortex-antivortex unbinding energy U as a function of magnetic field is shown in Fig. 3(a), and is seen to

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TAFF

Bose metal 2D SC H(T)

Figure 4: (a) R vs H for the two measurement configurations. Bose metal resistance RBM is obtained by subtracting the high impedance resistance from low impedance resistance (b) Color plot showing RBM as a function of T and H (c) Magnetoresistance of the Bose metal phase at different temperatures (d) Full H-T phase diagram of the device. follow the empirical relation U = U0 ln(H0 /H), with U0 = 50.6 ± 1.0K and H0 = 3.6 ± 0.1T . First, we observe that U appears to diverge in the zero magnetic field limit as expected for a defect free superconductor. Next, we notice that U0 obtained here is considerably larger than obtained in the low-dissipation experiment. Finally, H0 is equal to Hc2 = 3.5T within limits set by experimental uncertainty, just as expected for a clean superconductor. These observations, combined with the observation of a perfect zero resistance state, indicate that the Bose metal phase has been fully quenched by dissipative coupling in our sample. We can now compare the resistances measured in the two configurations to obtain the 10


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true character of the Bose metal phase. In Fig. 4(a), we superimpose the resistance versus magnetic field (R-vs-H) curves obtained at T = 2K for both the high impedance and low impedance measurements. For H < HSM , where HSM represents the superconductor-metal transition, both configurations show a zero resistance state. Upon increasing H > HSM , the high impedance (Zs = 1014 Ω) measurement shows a monotonically increasing sample resistance indicative of the Bose metal phase, while the low impedance measurement (Zs = 106 Ω) shows a fully superconducting state. This continues till a cross-over field where the the magnetic field becomes sufficient strong to unbind vortex anti-vortex pairs and drive a superconductor to normal transiton. This phase is dominated by vortex motion due to thermal fluctuations and is known as the thermally assisted flux flow (TAFF) regime where both measurement configurations produce a finite resistance state. This persists until the normal state is achieved at H = Hc2 where resistances obtained from both measurement configurations match. To obtain only the Bose metal resistance RBM , we appeal to a Matthiessen’s-rule type argument. Since the Bose metal phase represents an additional dissipative mechanism that lends a finite resistance to the sample, we may treat RBM as arising from an additional scattering term that can be obtained by subtracting the resistances measured in the two configurations, that is RBM = R1014 Ω − R106 Ω . As show in Fig. 4(a), RBM sharply rises at H = HSM following a power law behavior with RBM ∝ (H − HSM )3.6 (see supplementary material section D). The strong power-law turn on is a unique signature of the Bose metal phase, and cannot originate from other effects such as quantum tunneling of macroscopic vortices. 8,12–16 Similar power-law turn-on of the Bose metal resistance has also been reported in the previous experiment on NbSe2 by Tsen et. al. 8 Upon increasing the magnetic field further, the Bose metal resistance appears to saturate with a sub-linear power law dependence RBM ∝ (H − HSM )0.66 (see supplementary material section D), a regime which is again predicted by Phillips 16 but not observed before. RBM finally obtains a peak at a field roughly coinciding with the onset of thermal flux flow, before sharply dropping to zero at

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the the critical field Hc2 . The Bose metal resistance is plotted as a 2D color plot as a function of both magnetic field and temperature in Fig. 4(b). For clarity, we also present in Fig. 4(c) several curves representing the magnetoresistance of the Bose metal phase at different temperatures. As evident from Figs. 4((b) and (c)), the Bose metal phase exists in a larger region of the H-T phase diagram than previously thought. In fact, the Bose metal resistance remains finite right until the mean field critical temperature and mean field critical magnetic field are reached. Using the peak of RBM as the cut-off between the Bose metal and thermally assisted flux flow (TAFF) state, we obtain the phase diagram as indicated in Fig. 4(d). In sharp contrast to a similar phase diagram obtained before , 8 the Bose metal phase in our experiment can be seen to persist upto Tc and occupy a larger region of H-T space.

Discussions The quenching of the Bose metal state in the presence of a low impedance dissipative environment is a striking manifestation of its purely quantum mechanical origin. The finite resistance of the Bose metal is a direct consequence of diffusive motion of Cooper pairs in a strongly disordered energy landscape created by quantum phase fluctuations. Strong dissipation coupled by a low impedance environment suppresses quantum phase fluctuations and thereby destroys the Bose metal state. Dissipation plays a crucial role in all known models that explain the Bose metal phase. 12–16 Specifically, in the theory of Phillips 14–16 where glassy dynamics is shown to be responsible for the zero temperature metallic state, ~ 3m4 where m is the inverse correlathe resistivity of the Bose metal state is given as ρ = 2 4e qη tion length, q is the effective strength of Josephson coupling between neighboring domains, and most importantly, η is the effective dissipation factor. When η diverges, the Bose metal state transforms into a zero resistance superconductor phase, exactly as shown in our experiment. We specifically highlight this model since our experiments satisfy several power law behaviors predicted by this theory, 14,16 as discussed in the previous section and section D of 12


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the supplementary material. Heuristically, the suppression of the Bose metal phase by an external dissipative bath can be understood as follows: quantum fluctuations of phase give rise to voltages across the sample that are proportional to the time derivative of the quantum mechanical phase variable φ, with hV i ∝ dφ/dt. In a voltage biased configuration depicted in Fig. 1(b), Kirchoff’s law dictates that the same fluctuation (with opposite sign) must appear across the bias impedance Zs . Since Zs is a resistive element, it dissipates power P ∝ hV i2 /Zs . A lower value of Zs results in larger power dissipation, resulting in strong damping of quantum phase fluctuations. Previous works have shown that these induced voltages are in the microwave regime and couple not only to the source impedance but also to the general electromagnetic environment of the measurement setup. 27 If the setup allows for the system to release this electromagnetic energy into a low impedance node, quantum phase fluctuations must be generically suppressed. In our experiments, we use this property to couple our sample to two different environments with vastly different dissipative couplings. In the regime of low dissipation, a clear Bose metal phase is observed, whereas, in a high dissipation regime, the Bose metal phase is entirely quenched and a zero resistance superconducting state is fully restored. In a recent experiment by Tamir et al., 41 the authors observe a similar quenching of the Bose metal phase in thin flakes of NbSe2 and full restoration of the superconducting phase when a low pass filter is used in the path of the measurement circuit. This is in perfect agreement with our experiment: the low pass filter acts as a high dissipation environment for the device, suppressing quantum phase fluctuations and naturally leading to a transition to a fully superconducting phase. However, the authors interpret this as a signature that external noise coupling into the device leads to a sample temperature that is much larger than the cryostat temperature, leading to a saturation of the device resistance at low temperatures and the apparent Bose metal phase. Removing the external noise through a low pass filter leads to proper cooling of the sample, thereby producing a fully superconducting phase.

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This interpretation is however at odds with our experiment where no additional filters have been used in the measurement circuit. In both the high impedance and low impedance configurations, our device is exposed to the same amount of external noise, yet we are able to clearly tune between the Bose metal and the superconductor phase simply by tuning the external impedance of the device (see also section D of the supplementary material) . Although the issue of sample heating due to external noise is pertinent and has been previously addressed in experiments on the Bose metal phase , 21 we believe that the relatively high measurement temperatures ('1.8K and above) used in our experiments preclude the possibility of overheating of the sample due to externally coupled noise. In conclusion, we show that coupling to a low impedance dissipative environment can fully suppress the anomalous metal phase observed in the crystalline superconductor NbSe2 , and restore a true two dimensional superconducting state. Such an observation proves, for the first time, the quantum mechanical origin of the Bose metal phase. Additionally, our work provides important clues towards understanding the role of quantum phase fluctuations in such systems and puts constraints on various theoretical models that have been proposed to explain this anomalous metal phase. This will inspire similar experiments on a large body of other two dimensional superconductors where similar metallic phases have been observed. Supporting Information Available Supporting information contains details of single crystal preparation and characterization of NbSe2 , details of device fabrication, additional electrical transport experiments and data analysis. Acknowledgements A.B. thanks MHRD, Govt. of India for support. A.M. thanks KVPY, Govt. of India for support. P.S.A.K. acknowledges support form Nanomission, DST, Govt. of India. All authors thank MNCF and NNCF, CeNSE, IISc Bangalore for nanofabrication and characterization facilities.

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Bose metal

Superconductor TOC graphic

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Restoring Superconductivity in the Quantum Metal Phase of NbSe2

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