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Ising Superconductivity and Quantum Phase Transition in Macro-Size Monolayer NbSe2 Ying Xing, Kun Zhao, Pujia Shan, Feipeng Zheng, Yangwei Zhang, Hai-Long Fu, Yi Liu, Mingliang Tian, Chuanying Xi, Haiwen Liu, Ji Feng, Xi Lin, Shuai-Hua Ji, Xi Chen, Qi-Kun Xue, and Jian Wang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b03026 • Publication Date (Web): 02 Oct 2017 Downloaded from http://pubs.acs.org on October 3, 2017
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Ising Superconductivity and Quantum Phase Transition in Macro-Size Monolayer NbSe2 Ying Xing,†,∥,∆ Kun Zhao,‡,#,∆ Pujia Shan,†,# Feipeng Zheng,†,# Yangwei Zhang,†,# Hailong Fu,†,# Yi Liu,†,# Mingliang Tian,§ Chuanying Xi,§ Haiwen Liu,⊥ Ji Feng, †,# Xi Lin, †,# Shuaihua Ji, ‡,#,* Xi Chen, ‡,# Qi-Kun Xue, ‡,# Jian Wang†,‡,#,* †
International Center for Quantum Materials, School of Physics, Peking University, Beijing
100871, China ‡
State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua
University, Beijing 100084, China §
High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China
∥Beijing
Key Laboratory of Optical Detection Technology for Oil and Gas, China University of
Petroleum, Beijing 102249, China ⊥
Department of Physics, Beijing Normal University, Beijing 100875, China
#Collaborative
Innovation Center of Quantum Matter, Beijing 100084, China
ABSTRACT
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
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and quantum computing devices. The mechanical exfoliation technique of micro-size 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 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.
TABLE OF CONTENTS GRAPHIC
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KEYWORDS: NbSe2, transition-metal dichalcogenides, macro-size monolayer film, ultralow temperature and high magnetic field electrical transport, Ising superconductivity, quantum phase transition (QPT)
TEXT
Quasi-2D superconductors such as ultrathin films with thickness down to monolayer 1-7 and composites interfaces8-10, have remained an active topic in recent years due to fundamental research interests and potential applications. Nevertheless, just a few monolayer crystalline superconductors can be prepared successfully on special substrates since fluctuations can destroy the long range correlation of superconductivity in 2D systems. Recently, TMDs as natural layered materials have provided a new platform to study superconductivity due to the tunable nature of the superconducting properties coexistent with other collective electronic excitations, as well as strong intrinsic spin-orbit coupling (SOC). The bulk crystals of TMDs are formed of monolayers bound to each other by Van-der-Waals attraction, which makes it feasible to experimentally study monolayer TMDs.
2H-NbSe2, one kind of TMDs, is found to be superconducting even in its freestanding monolayer.11-14 More interestingly, Zeeman-protected Ising superconductivity is expected in monolayer NbSe2 due to the non-centrosymmetric structure with in-plane inversion symmetry breaking and strong SOC. Very recently, Ising superconductivity with the anomalous large inplane critical magnetic field has become one important direction in crystalline 2D superconductors7. In recent experiments on exfoliated micron-size NbSe2 monolayers11, 12, 14, the coexistence of charge density wave (CDW) and the superconducting phase was observed down
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to the monolayer limit but the superconducting critical transition temperature of monolayer NbSe2 got significantly suppressed (Tc ~ 3.0 K) compared with its bulk value (7.2 K).
Superconductor-insulator (metal) transition (SIT/SMT), a paradigm of QPT, is an important topic in condensed matter physics.15-21 Despite of efforts over last few decades, there still remain many open issues, such as different critical exponents signifying different universality classes and various values of critical points found in different materials.22 Recent observations of the QGS in thin Ga films23 and LaAlO3/SrTiO3(110) (LAO/STO) interface24 shed a new light on SIT/SMT22 and have turned to one important topic in 2D superconductors7. Verifying QGS in Ising superconductors would not only demonstrate the universal property of QGS, but also help to understand the underlying mechanism of the 2D superconductors where Ising superconductivity and QGS coexist.
In this paper we successfully prepared atomically flat monolayer NbSe2 films (~ 0.6 nm thick) on bilayer graphene terminated surface of 6H-SiC (0001) substrates by MBE method. The high quality films are uniform and macro-size large (mm2). Here, monolayer means one Se-NbSe sequence and each unit cell of NbSe2 consists of two Se-Nb-Se sequences. By low temperature
and
high
magnetic
field
electrical
transport
measurements,
the
Ising
superconductivity is found in NbSe2 monolayers, with Tconset above 6 K (Tczero is up to 2.40 K defined at the temperature showing zero resistance within instrumental resolution) and Bc// (T = 0) up to 32.43 T. The observed superconductivity anisotropy and Berezinski-Kosterlitz-Thouless (BKT)-like transition reveal the 2D nature of NbSe2 films. Through systematic ultralow temperature transport measurements, the monolayer NbSe2 films manifest magnetic field induced SMT and the critical exponent of SMT diverges as T approaching zero, indicating QGS.
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Figure 1(a) shows the typical atomic-resolved scanning tunneling microscope (STM) image (18 nm × 18 nm) on NbSe2 monolayer, from which a 3 × 3 CDW superlattice can be clearly seen at 80 mK. Large-scale (1.9 µm × 1.9 µm) STM topographic image with atomically flat surface and regular steps originating from the SiC (0001) surface is shown in Figure 1(b). Very similar morphology images of NbSe2 are observed by STM in different regions, which implies the uniformity of NbSe2 films in macro-size. The flat terraces are monolayer 2H-NbSe2 inheriting from SiC substrate and the small islands are bilayer NbSe2 with random orientation (not 2H phase) and in-plane size less than 100 nm, which could suppress the superconductivity in the islands. Furthermore, the ratio of small triangular islands in the whole film is only 3.14%. Therefore, the superconducting features from ex situ transport measurement are mainly from monolayer NbSe2. The monolayer NbSe2, bilayer graphene and SiC (0001) substrate are all Van der Waals coupling between each other. Due to this weak coupling, the monolayer Se-Nb-Se is more like freestanding state. Before being transferred out of MBE high vacuum chamber, an amorphous Se capping layer with the thickness of 20 nm was deposited on the monolayer NbSe2 at 80 K to protect the film from degrading in ambient atmosphere. These formed Se/NbSe2/bilayer graphene/SiC heterostructure. The high quality nature of the macro-size NbSe2 monolayer protected by the capping layer guarantees the observation of superconductivity with zero resistance at relatively high temperature by ex situ transport measurements, which could extend the investigation to a previously unexplored regime for the 2D limit NbSe2 monolayer in macro-size.
Figure 2(a) exhibits temperature dependence of sheet resistance (Rs) of sample 1 at zero magnetic field. With the temperature decreasing, the Rs of monolayer NbSe2 rapidly increases at 120 K, saturates around 50 K, then begins to decrease at 6.61 K (Tconset), and drops to zero within
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the instrumental resolution at 2.40 K (Tczero) (Figure 2(b)). Tcmiddle determined at the temperature where the resistance drop reaches 50% of resistance at 8 K is 3.50 K. In the rest part of the paper, we use Tc as the Tcmiddle. The superconductivity is better than that of mechanical exfoliated monolayer NbSe2 flakes (Tc onset is ~ 4.2 K, Tc ~ 3.0 K)11 and MBE grown monolayer NbSe2 films (Tconset ~ 1.9 K, Tc ~ 0.65 K, Tczero ~ 0.46 K)13 in previous reports. The inset of Figure 2(a) schematically depicts the diagram for transport measurements. The similar Rs(T) properties for sample 2 are displayed in Figure S1(a) with Tconset up to 6.95 K and Tczero~ 1.50 K. The Se/bilayer
graphene/SiC
heterostructure
under
the
growth
conditions
identical
to
Se/NbSe2/bilayer graphene/SiC heterostructure exhibits insulating behavior (Figure S1(b)). This confirms that the superconductivity only comes from the monolayer NbSe2. Theoretically, we investigate the electron-phonon coupling of freestanding monolayer NbSe2 without charge density wave modulation by density-functional theory and density-functional perturbation theory calculations within local density approximation. The critical temperature Tc calculated using McMillan formula25 falls in range between 3.8 and 4.1 K, which is close to our experimental result (Tconset ~ 6.61 K and Tczero ~ 2.40 K for sample 1). We also qualitatively investigated the influence of bilayer graphene on the electronic band structure of the monolayer NbSe2 and found that the graphene has little influence on the electronic band structure of the NbSe2. (Figure S4)
A magnetic field up to 15.50 T perpendicular to the film was applied (Figure 2(b)) and magnetoresistance isotherms (perpendicular magnetic field) were measured at temperature from 0.50 K to 10.00 K (Figure 2(c), full data shown in Figure S2(a)). It is clearly evident that the increasing magnetic field gradually destroys the superconductivity. When the magnetic field is parallel to the film (see Figure 2(d)), Bc(T) is apparently much higher than that in perpendicular field. 15 T can hardly destroy the superconductivity of monolayer NbSe2. To obtain Bc at lower
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temperatures, we further measured the magnetoresistance of the same sample by applying steady ultrahigh magnetic field up to 35 T. Due to the degradation in atmosphere, Tc decreased from 3.50 K to 2.69 K in ultrahigh magnetic field measurements. For T = 0.35 K, 35 T high magnetic field still cannot destroy the superconductivity of the monolayer NbSe2 completely (Figure 2(e)). We define the characteristic field Bc(T) at a given temperature at the 50% of normal resistance for both perpendicular and parallel magnetic fields, and summarize in Figure 2(f). With T/Tc down to 0.13, Bc(T) can be fitted by Bc⊥(T)∝1-T/Tc and Bc//(T)∝(1-T/Tc)1/2 respectively,26,
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which yield Bc⊥(0) = 2.16 T and Bc//(0) = 32.43 T. In the previous report on mechanical exfoliation fabricated micro-size monolayer NbSe2 flakes, T/Tc is down to 0.78.11 The anisotropic parameter ε = Bc//(0)/Bc⊥(0) is about 15 for NbSe2 monolayer but only 3.2 for bulk NbSe228. BKT-like transition has also been observed (Figure S3) in monolayer NbSe2. Such observations demonstrate the 2D nature of the superconductivity.
In the 2D limit regime, the orbital effect is restricted in parallel magnetic field. The Bc is only determined by Pauli-limiting field Bp, which originates from the Zeeman splitting. In general, the Pauli-limiting field is strong enough to break Cooper pairs and destroy superconductivity. Bp, is written as Bp = g-1/2∆/ µ B , where g is the Landé g-factor, µ B is the Bohr magneton, and ∆ is the superconducting gap. For BCS superconductors, Bp can be simply rewritten as Bp = 1.84 Tc when assuming a g-factor equals to 2. For our MBE grown monolayer NbSe2 films, Bp is estimated to be 4.95 T (Tc ~ 2.69 K) by using g ~ 2 in previous reports11. If we use g factor value of bulk NbSe2 (~ 1.2)29, then Bp should be 6.37 T. Surprisingly, as revealed in Bc-T/Tc phase diagram in the inset of Figure 2(f), the monolayer NbSe2 could withstand an applied parallel magnetic field as strong as 32.43 T (T = 0). Thus, Bc//(0) is 5.09 times of Bp by
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using g ~ 1.2 or 6.55 times of Bp by using g ~ 2. Similar phenomenon has ever been reported in gated MoS2 flakes30,
31
and mechanical exfoliation fabricated micro-size monolayer NbSe2
flakes11. In non-centrosymmetric monolayer NbSe2 with considerable spin-orbit interactions, the spin-orbit interaction split the spin states and manifest as a strong effective internal magnetic fields. The spin-orbit interaction experienced by a moving electron with momentum k is proportional to k × E ⋅ σ , where E is the electric field experienced by the electron and σ denoted the Pauli matrices. In monolayer NbSe2, the in-plane inversion symmetry is broken and the electrons can experience effective in-plane electric field. Hence, the spins of the pairing electrons are strongly locked to the out-of-plane orientation by an effective Zeeman field. Instead of damaging superconductivity, this special type of internal magnetic field due to strong spinorbit interaction is able to protect the superconducting electron pairs under high external magnetic fields. This kind of superconductor is called "Ising superconductor". Our measurement results at high magnetic fields up to 35 T and the low temperature down to 0.35 K as T/Tc down to 0.13 offers a more solid evidence of Ising superconductivity in macro-size monolayer NbSe2 approaching to lower temperature and higher magnetic field.
We note that the high critical magnetic field in low temperature regime has been observed in heavy Fermion superconductors32 and organic superconductors33. The mechanism was interpreted as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state34. For the FFLO phase to appear, the compounds must have a Maki parameter35 α =
2
Borb/Bp larger than 1.8 such that the upper
critical field can easily approach the Pauli paramagnetic limit Bp. Simultaneously, the system must be in the clean limit ξ
