Quantum Griffiths Singularities Research Articles

Quantum Griffiths Singularity in Ordered Artificial Superconducting-Islands-Array on Graphene.

Quantum Griffiths phase (QGP) is a novel quantum phenomenon of quantum phase transition in two-dimensional (2D) superconductors, and the emergence of inhomogeneous superconducting rare regions immersed in a metallic matrix is theoretically related to the quantum Griffiths singularity (QGS). However, the theoretical proposal of superconducting rare regions still lacks intuitive experimental verification. Here, we construct an artificial ordered superconducting-islands-array on monolayer graphene with the aid of an anodic aluminum oxide (AAO) membrane. The QGS under both in-plane and out-of-plane magnetic fields is evidenced by the divergent dynamical critical exponent and is in compliance with the direct activated scaling behavior. The phase diagram clearly shows that the QGP is indeed bred in the rare superconducting regions within isolated superconducting islands with a vanished quantum coherence. Our results reveal the universal features of QGP in artificial heterostructured systems and provide a visualized platform for the theoretical proposal of QGS.

Quantum Griffiths singularity in two-dimensional superconducting 4Ha-TaSe2 nanodevices

Quantum Griffiths singularity in two-dimensional superconducting 4Ha-TaSe2 nanodevices

The activated scaling behavior of quantum Griffiths singularity in two-dimensional superconductors

Quantum Griffiths singularity (QGS) is characterized by the divergence of the dynamical critical exponent with the activated scaling law and has been widely observed in various two-dimensional superconductors. Recently, the direct activated scaling analysis with the irrelevant correction was proposed and successfully used to analyze the experimental data of crystalline PdTe2 and polycrystalline -W films, which provides new evidence of QGS. Here we show that the direct activated scaling analysis is applicable to the experimental data in different superconducting films, including tri-layer Ga films and LaAlO3/SrTiO3 interface superconductors. When taking the irrelevant correction into account, we calculate the corrected sheet resistance at ultralow temperatures. The scaling behavior of the corrected resistance in a comparably large temperature regime and the theoretical fitting of the phase boundary give unambiguous evidence of QGS. Compared to previous methods based on finite size scaling, the direct activated scaling analysis represents a more direct and precise way to analyze the experimental data of QGS in diverse two-dimensional superconductors.

Quantum phase transition in NbN superconducting thin films

We systematically investigated the low-temperature transport properties of a series of NbN epitaxial films with thickness $t$ ranging from $\sim$2.0 to $\sim$4.0 nm. The films undergo a superconductor-insulator transition (SIT) with decreasing film thickness, and the critical sheet resistance for the SIT is close to the quantum resistance of Cooper pairs $h/4e^2$ (6.45 k$\Omega$). Besides the Berezinski-Koterlitz-Thouless transition, a magnetic-field-driven SIT is observed in those two-dimensional (2D) superconducting films (2.6 nm $\lesssim t \lesssim 4.0$ nm). Interestingly, it is found that the low-temperature magnetoresistance isotherms do not cross at a single fixed point but at a well-distinguished region for these superconducting films. The dynamical critical exponent obtained by analyzing these magnetoresistance isotherms is divergent as the quantum critical point is being approached. The behavior of the dynamical critical exponent, originating from quenched disorder at ultralow temperatures, provides direct evidence for the occurrence of quantum Griffiths singularity in the quantum phase transition process of the films. The field-driven anomalous metal (quantum metal) state does not appear in these films. Our results suggest that the quantum Griffiths singularity not only occurs in the highly crystalline 2D superconductors with superconductor-metal transition but also in those with SIT.

Robust quantum Griffiths singularity above 1.5 K in nitride thin films

Quantum Griffiths singularity (QGS), which is closely correlated with the quenched disorder, is characterized by the divergence of the dynamical critical exponent and the presence of activated scaling behavior. Typically such a quantum phenomenon is rather rare and only observed in extremely low temperatures. Here we report the experimental observation of a robust QGS in nitride thin films, NbN, which survives in a rather high temperature range. The electrical transport propertied were measured under the magnetic field up to 12 T. The field induced superconductor-metal transitions were observed with the continuously changed transition points with the decrease of temperature. The dynamical critical exponent based on the conventional power-law scaling reveals a divergent trend when approaching the the low temperature limit. Moreover, the temperature and field dependence of sheet resistance can be described by the activated scaling analysis in the temperature region up to 1.6 K $\leq T \leq$ 4.0 K. We argue that the robustness of QGS in the present system originates from the Pauli paramagnetic effect due to the strong coupling between the magnetic field and the spin degree of freedom.

Correlation between Nanoscale Domain Structures and Superconducting Phase Transitions in Highly Crystalline 2D Superconductors

AbstractThe domains and domain boundaries in 2D materials are known to play essential roles in investigating intriguing physical properties and have potential applications in nanoscale devices. Understanding the influence of individual domains on the superconducting properties of ultrathin 2D superconductors is of crucial importance for fundamental studies on mesoscopic superconductivity as well as applications in superconducting nanoelectronics. Here, low‐temperature electronic transport measurements of high quality ultrathin Mo2C crystals are presented that show clear evidence for the presence of multiple superconducting phase induced by the nanoscale domain structures. In particular, the observation of an anomalous resistance peak in the vicinity of the onset of the superconducting transition is reported. This resistive anomaly is interpreted as a consequence of nonequilibrium charge imbalance near the domain boundaries, which could induce effective normal‐superconducting interfaces in 2D Mo2C crystals. Moreover, the magnetic field‐tuned superconductor‐metal transition for ultrathin Mo2C crystals is examined. The observed scaling behavior is consistent with the appearance of quantum Griffiths singularity in 2D superconducting systems. This study sheds light on the understanding of the domain boundaries and their role on the transport properties of highly crystalline 2D superconductors, which may open potential application of domain structure in functional superconducting nanodevices.

Observation of In-Plane Quantum Griffiths Singularity in Two-Dimensional Crystalline Superconductors.

Quantum Griffiths singularity (QGS) reveals the profound influence of quenched disorder on the quantum phase transitions, characterized by the divergence of the dynamical critical exponent at the boundary of the vortex glasslike phase, named as quantum Griffiths phase. However, in the absence of vortices, whether the QGS can exist under a parallel magnetic field remains a puzzle. Here, we study the magnetic field induced superconductor-metal transition in ultrathin crystalline PdTe_{2} films grown by molecular beam epitaxy. Remarkably, the QGS emerges under both perpendicular and parallel magnetic field in four-monolayer PdTe_{2} films. The direct activated scaling analysis with a new irrelevant correction has been proposed, providing important evidence of QGS. With increasing film thickness to six monolayers, the QGS disappears under perpendicular field but persists under parallel field, and this discordance may originate from the differences in microscopic processes. Our work demonstrates the universality of parallel field induced QGS and can stimulate further investigations on novel quantum phase transitions under parallel magnetic field.

Observation of thickness-tuned universality class in superconducting [formula omitted] thin films

The interplay between quenched disorder and critical behavior in quantum phase transitions is conceptually fascinating and of fundamental importance for understanding phase transitions. However, it is still unclear whether or not the quenched disorder influences the universality class of quantum phase transitions. More crucially, the absence of superconducting-metal transitions under in-plane magnetic fields in 2D superconductors imposes constraints on the universality of quantum criticality. Here, we observe the thickness-tuned universality class of superconductor-metal transition by changing the disorder strength in β-W films with varying thickness. The finite-size scaling uncovers the switch of universality class: quantum Griffiths singularity to multiple quantum criticality at a critical thickness of tc⊥1~8nm and then from multiple quantum criticality to single criticality at tc⊥2~16nm. Moreover, the superconducting-metal transition is observed for the first time under in-plane magnetic fields and the universality class is changed at tc‖~8nm. The observation of thickness-tuned universality class under both out-of-plane and in-plane magnetic fields provides broad information for the disorder effect on superconducting-metal transitions and quantum criticality.

Size dependent nature of the magnetic-field driven superconductor-to-insulator quantum-phase transitions

The nature of the magnetic-field driven superconductor-to-insulator quantum-phase transition in two-dimensional systems at zero temperature has been under debate since the 1980s, and became even more controversial after the observation of a quantum-Griffiths singularity. Whether it is induced by quantum fluctuations of the superconducting phase and the localization of Cooper pairs, or is directly driven by depairing of these pairs, remains an open question. We herein experimentally demonstrate that in weakly-pinning systems and in the limit of infinitely wide films, a sequential superconductor-to-Bose insulator-to-Fermi insulator quantum-phase transition takes place. By limiting their size to smaller than the effective penetration depth, however, the vortex interaction alters, and the superconducting state re-enters the Bose-insulating state. As a consequence, one observes a direct superconductor-to-Fermi insulator in the zero-temperature limit. In narrow films, the associated critical-exponent products diverge along the corresponding phase boundaries with increasing magnetic field, which is a hallmark of the quantum-Griffiths singularity.

Quantum Griffiths Singularity in a Layered Superconducting Organic–Inorganic Hybrid Superlattice

Quantum Griffiths singularity (QGS) is among the remarkable phenomena induced by disorder in quantum phase transitions (QPTs). In recent years, experimental progresses have been made in ultrathin s...

Superconductor-Metal Quantum Transition at the EuO/KTaO3 Interface* *Supported by the National Key R&D Program of China (Grant Nos. 2019YFA0308401 and 2017YFA0303301), the National Natural Science Foundation of China (Grant Nos. 11974025, 11674009, and 11934016), the Beijing Natural Science Foundation (Grant No. 1192009), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB28000000).

We report the experimental investigation of the superconductor-metal quantum phase transition of the EuO/KTaO3 interface. Around the transition, a divergence of the dynamical critical exponent is observed, which supports the quantum Griffiths singularity in the EuO/KTaO3 interface. The quantum Griffiths singularity could be attributed to large rare superconducting regions and quenched disorders at the interface. Our results could pave the way for studying the exotic superconducting properties at the EuO/KTaO3 interface.

Disorder-Induced Quantum Griffiths Singularity Revealed in an Artificial 2D Superconducting System.

Disorder‐induced Griffiths singularity of quantum phase transition (QPT) is a crucial issue in 2D superconductors (2DSC). In a superconducting system, the strength of disorder is found to be associated with the vortex pinning energy, which is closely related to the quantum Griffiths singularity; however, a direct study to elucidate the role of vortex pinning energy on the quantum Griffiths singularity in 2DSC remains to be undertaken. Here, an artificial 2DSC system is designed by randomly depositing superconducting nanoislands on 2Delectron gas (2DEG). Quantum Griffiths singularity is present in a graphene/Pb‐islands‐array hybrid, where the superconducting behavior transits to weakly localized metallic behavior induced by the vertical magnetic field and exhibits critical behavior with a diverging dynamical critical exponent approaching zero temperature. Compared to the study of graphene/Sn‐islands‐array hybrid where the sharp QPT is observed, the vortex pinning energy acquired from the Arrhenius plot analysis is greater in graphene/Pb‐islands‐array hybrid, which may contribute to the presence of the quantum Griffiths singularity. This work may provide a comprehensive interpretation of the QPT in 2DSC.

Quantum Griffiths singularities in TiO superconducting thin films with insulating normal states

A superconductor–metal transition (SMT) with an unconventional diverging dynamic critical exponent was recently discovered, and it drew tremendous attention because this signature of a quantum Griffiths singularity (QGS) was thought to be a common characteristic of low-disorder crystalline superconductors. However, because the QGS was observed only in limited materials with metallic normal states, the question of whether the QGS exists in other superconducting systems is still unanswered. In this paper, a superconductor–insulator transition (SIT) is observed in TiO thin films with insulating normal states, which offers a more universal platform for investigating the QGS. A thickness-tuned SIT is obtained when the magnetic field is zero. Importantly, a magnetic field-tuned SIT with a diverging dynamic critical exponent, which is direct evidence of a QGS, is observed in TiO thin films with different thicknesses. By constructing a comprehensive phase diagram, it is demonstrated that the critical magnetic field Hc tends to saturate as the temperature approaches 0 K, which is different from the upturn trend of Hc observed in SMT systems and probably due to the weaker Josephson coupling of the locally ordered superconducting islands (rare regions) in a weakly insulating normal state background. The results extend the QGS scenario from only SMT systems to SIT systems, and they provide vital evidence that QGSs are common in crystalline superconducting thin films, which has possible applications in quantum-computing devices.

Anomalous quantum Griffiths singularity in ultrathin crystalline lead films

Superconductor-insulator/metal transition (SIT/SMT) represents a prototype of quantum phase transition, where quantum fluctuation plays a dominant role and dramatically changes the physical properties of low-dimensional superconducting systems. Recent observation of quantum Griffiths singularity (QGS) offers an essential perspective to understand the subtleties of quantum phase transition in two-dimensional superconductors. Here we study the magnetic field induced SMT in ultrathin crystalline Pb films down to ultralow temperatures. The divergent critical exponent is observed when approaching zero temperature quantum critical point, indicating QGS. Distinctively, the anomalous phase boundary of SMT that the onset critical field decreases with decreasing temperatures in low temperature regime distinguishes our observation from previous reports of QGS in various two-dimensional superconductors. We demonstrate that the anomalous phase boundary originates from the superconducting fluctuations in ultrathin Pb films with pronounced spin-orbit interaction. Our findings reveal a novel aspect of QGS of SMT in two-dimensional superconductors with anomalous phase boundary.

Signature of quantum Griffiths singularity state in a layered quasi-one-dimensional superconductor

Quantum Griffiths singularity was theoretically proposed to interpret the phenomenon of divergent dynamical exponent in quantum phase transitions. It has been discovered experimentally in three-dimensional (3D) magnetic metal systems and two-dimensional (2D) superconductors. But, whether this state exists in lower dimensional systems remains elusive. Here, we report the signature of quantum Griffiths singularity state in quasi-one-dimensional (1D) Ta2PdS5 nanowires. The superconducting critical field shows a strong anisotropic behavior and a violation of the Pauli limit in a parallel magnetic field configuration. Current-voltage measurements exhibit hysteresis loops and a series of multiple voltage steps in transition to the normal state, indicating a quasi-1D nature of the superconductivity. Surprisingly, the nanowire undergoes a superconductor-metal transition when the magnetic field increases. Upon approaching the zero-temperature quantum critical point, the system uncovers the signature of the quantum Griffiths singularity state arising from enhanced quenched disorders, where the dynamical critical exponent becomes diverging rather than being constant.

High-temperature superconductivity and quantum Griffith singularity in two-dimensional crystal

Superconductors have become one of the most important directions in condensed matter physics and materials science due to their unique properties incuding zero-resistance and perfect diamagnetism. With the development of the fabrication technique of two-dimensional (2D) single crystals, 2D superconductors have recently come to be a new research frontier, in which novel physics phenomena, such as high-temperature superconductivity and quantum phase transitions, have emerged and received wide attention. In this artcle, we first briefly review the research background and basic properties of 2D superconductors. Then, focusing on two important classes of phenomena—high-temperature superconductivity and quantum phase transitions, the article is organized into two parts. In the first part, we introduce a typical example of high-temperature superconductivity in 2D systems, the ultrathin FeSe films grown on SrTiO3 (STO) substrate, including the experimental properties and mechanism discussions. In the second part, as an example of quantum phase transitions in 2D systems, an overview of the theories and experiments of the newly-discovered quantum Griffiths singularity in 2D crystalline superconductors is given. In the end, we summary the high-temperature superconductivity and quantum Griffiths singularity in 2D crystals and provide an outlook of the future development in the relevant frontiers.

Ising Superconductivity and Quantum Phase Transition in Macro-Size Monolayer NbSe2

Two-dimensional (2D) transition metal dichalcogenides (TMDs) have a range of unique physics properties and could be used in the development of electronics, photonics, spintronics, and quantum computing devices. The mechanical exfoliation technique of microsize TMD flakes has attracted particular interest due to its simplicity and cost effectiveness. However, for most applications, large-area and high-quality films are preferred. Furthermore, when the thickness of crystalline films is down to the 2D limit (monolayer), exotic properties can be expected due to the quantum confinement and symmetry breaking. In this paper, we have successfully prepared macro-size atomically flat monolayer NbSe2 films on bilayer graphene terminated surface of 6H-SiC(0001) substrates by a molecular beam epitaxy (MBE) method. The films exhibit an onset superconducting critical transition temperature (Tconset) above 6 K and the zero resistance superconducting critical transition temperature (Tczero) up to 2.40 K. Simultaneously, the transport measurements at high magnetic fields and low temperatures reveal that the parallel characteristic field Bc//(T = 0) is above 5 times of the paramagnetic limiting field, consistent with Zeeman-protected Ising superconductivity mechanism. Besides, by ultralow temperature electrical transport measurements, the monolayer NbSe2 film shows the signature of quantum Griffiths singularity (QGS) when approaching the zero-temperature quantum critical point.

Griffiths singularities in the random quantum Ising antiferromagnet: A tree tensor network renormalization group study

The antiferromagnetic Ising chain in both transverse and longitudinal magnetic fields is one of the paradigmatic models of a quantum phase transition. The antiferromagnetic system exhibits a zero-temperature critical line separating an antiferromagnetic phase and a paramagnetic phase; the critical line connects an integrable quantum critical point at zero longitudinal field and a classical first-order transition point at zero transverse field. Using a strong-disorder renormalization group method formulated as a tree tensor network, we study the zero-temperature phase of the quantum Ising chain with bond randomness. We introduce a new matrix product operator representation of high-order moments, which provides an efficient and accurate tool for determining quantum phase transitions via the Binder cumulant of the order parameter. Our results demonstrate an infinite-randomness quantum critical point in zero longitudinal field accompanied by pronounced quantum Griffiths singularities, arising from rare ordered regions with anomalously slow fluctuations inside the paramagnetic phase. The strong Griffiths effects are signaled by a large dynamical exponent $z>1$, which characterizes a power-law density of low-energy states of the localized rare regions and becomes infinite at the quantum critical point. Upon application of a longitudinal field, the quantum phase transition between the paramagnetic phase and the antiferromagnetic phase is completely destroyed. Furthermore, quantum Griffiths effects are suppressed, showing $z<1$, when the dynamics of the rare regions is hampered by the longitudinal field.

The discovery of a quantum Griffiths singularity in superconducting films

The discovery of a quantum Griffiths singularity in superconducting films

Observation of quantum Griffiths singularity and ferromagnetism at the superconducting LaAlO3/SrTiO3(110) interface

Diverse phenomena emerge at the interface between band insulators LaAlO3 and SrTiO3, such as superconductivity and ferromagnetism, showing an opportunity for potential applications as well as bringing fundamental research interests. Particularly, the two-dimensional electron gas formed at LaAlO3/SrTiO3 interface offers an appealing platform for quantum phase transition from a superconductor to a weakly localized metal. Here we report the superconductor-metal transition in superconducting two-dimensional electron gas formed at LaAlO3/SrTiO3(110) interface driven by a perpendicular magnetic field. Interestingly, when approaching the quantum critical point, the dynamic critical exponent is not a constant but a diverging value, which is a direct evidence of quantum Griffiths singularity raised from quenched disorder at ultralow temperatures. Furthermore, the hysteretic property of magnetoresistance was firstly observed at LaAlO3/SrTiO3(110) interfaces, which suggests potential coexistence of superconductivity and ferromagnetism.