Visualizing the elongated vortices in γ -Ga nanostrips
Hui-Min Zhang, Zi-Xiang Li, Jun-Ping Peng, Can-Li Song, Jia-Qi Guan, Zhi Li, Lili Wang, Ke He, Shuai-Hua Ji, Xi Chen, Hong Yao, Xu-Cun Ma, Qi-Kun Xue
VVisualizing the elongated vortices in γ -Ga nanostrips Hui-Min Zhang,
1, 2
Zi-Xiang Li, Jun-Ping Peng, Can-Li Song,
1, 4, ∗ Jia-Qi Guan, Zhi Li, Lili Wang,
1, 4
Ke He,
1, 4
Shuai-Hua Ji,
1, 4
Xi Chen,
1, 4
Hong Yao,
3, 4, † Xu-Cun Ma,
1, 2, 4, ‡ and Qi-Kun Xue
1, 4 State Key Laboratory of Low-Dimensional Quantum Physics,Department of Physics, Tsinghua University, Beijing 100084, China Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China Institute for Advanced Study, Tsinghua University, Beijing 100084, China Collaborative Innovation Center of Quantum Matter, Beijing 100084, China (Dated: September 27, 2018)We study the magnetic response of superconducting γ -Ga via low temperature scanning tunnelingmicroscopy and spectroscopy. The magnetic vortex cores rely substantially on the Ga geometry, andexhibit an unexpectedly-large axial elongation with aspect ratio up to 40 in rectangular Ga nano-strips (width l <
100 nm). This is in stark contrast with the isotropic circular vortex core in a largerround-shaped Ga island. We suggest that the unusual elongated vortices in Ga nanostrips originatefrom geometric confinement effect probably via the strong repulsive interaction between the vorticesand Meissner screening currents at the sample edge. Our finding provides novel conceptual insightsinto the geometrical confinement effect on magnetic vortices and forms the basis for the technologicalapplications of superconductors.
PACS numbers: 68.37.Ef, 74.25.Op, 74.78.Na, 74.25.Ha
Magnetic vortices in mesoscopic superconductors, in-cluding symmetric disks, triangles, squares and rectan-gles [1–4], have recently stimulated tremendous interestdue to their fundamental importance in controlling su-perconducting energy dissipation, a significant feature forsuperconductor-based nanotechnologies. When a super-conductor is shrunk to nanoscale, exotic vortex shapes(i.e. giant vortex and antivortex-vortex molecule) andconfigurations may occur, but so far mostly inferred fromindirect measurements [5]. Direct real space visualizationof vortices in nanostructured superconductors remainschallenging and rarely explored. A few scanning tunnel-ing microscopy (STM) studies present the preliminaryevidence of giant vortex in Pb islands [6–8], but the ill-defined geometry of the samples investigated renders theissue quite complicated and difficult for a direct compar-ison with theory.Among all these superconducting nanostructures, rect-angular nanostrips or nanowires are especially appealingfor superconducting electrical circuit and quantum inter-ference device. Regular oscillations of resistance and crit-ical current as a function of magnetic field have been re-spectively reported in superconducting InO and Al strips[9, 10], which can be accounted for by the so-called Weberblockade theory [11]. Here each oscillation in either mag-netoresistance or critical current corresponds to addinga single vortex into the strip, in analogy with single elec-tron transport through quantum dots in the Coulombblockade regime. Furthermore, the penetrating vorticesare anticipated to configure into a one-dimensional chainat the center of strip [10–12], because of the lower vor-tex potential energy there. Upon increasing field, thevortex chain may split into two or more buckled parallelrows [13–15]. However, so far as we know, such vortexchains have little been directly visualized, and whether the model applies for the extremely narrow supercon-ducting nanostrips remains unjustified.Herein we report the direct visualization of unexpect-edly elongated vortex cores in superconducting γ -Gananostrips by STM, and show that they are caused bythe strong repulsive interaction between the vortices andMeissner screening currents at the sample edge. All ex-periments were conducted in a Unisoku ultrahigh vac-uum STM system equipped with molecular beam epi-taxy (MBE) for in-situ sample preparation. The MBEgrowth of superconducting Ga nanoislands has been de-scribed in detail elsewhere [1], and in the SupplementalMaterial [17]. The measurements were carried out at 4.4K unless otherwise noted. A magnetic field up to 7 Tcan be applied perpendicular to the sample surface. Thedifferential conductance dI/dV spectra and maps weremeasured by disrupting the feedback circuit at the set-point of V s = 10 mV and I = 100 pA, sweeping thesample voltage V s , and extracting the conductance usinga standard lock-in technique with a bias modulation of0.3 mV at 987.5 Hz.Figure 1(a) shows the constant-current topographicimage of a rectangular Ga nanostrip, which has a length l ∼
440 nm and a width w ∼
64 nm. Note that the nanos-trip exhibits an almost perfect rectangle, which can easilybe modeled in theory. The atomically resolved STM im-age on the nanostrip, shown in Fig. 1(b), reveals defect-free surface. The unit cell, marked by the blue rhombus,consists of two bright spots with a periodicity of a =0.86 nm and an intersection angle of 76 o , which are con-sistent with γ -Ga(001) plane [Fig. 1(c)] [18]. Figure 1(d)plots a series of differential conductance dI/dV spectraacquired on the Ga nanostrip at various temperatures,normalized to the normal-state one above T c (10 K). Asuperconducting gap with clear coherence peaks is visi- a r X i v : . [ c ond - m a t . s up r- c on ] A p r N o r m a li ze d d I / d V (b) (d)(e) Δ ( m e V ) -10010 2 4 6 8 DataBCS theory T c =6.80 K
1 nm ab ab c o (a) (c)
30 nm H e i gh t ( n m ) Position (nm)
FIG. 1. (color online) (a) STM topography of a rectangularGa nanostrip with a height of 5.85 nm (45 ML) ( V s = 3.5 V, I = 50 pA, 483 nm ×
161 nm). Line profile taken along thered curve characterizes the height and width w of Ga nanos-trip. Both labels a and b denote respectively the orientationsof the short and long side of the rectangular strips through-out this paper. Dotted rectangle marks the region where allZBC maps are taken in Fig. 2(a). (b) Atomic resolution im-age ( V s = 20 mV, I = 50 pA, 10 nm ×
10 nm) of the Gananostrip. The bright spots correspond to the Ga atoms inthe top layer. (c) Schematic crystal structure of γ -Ga. Alongthe c (001) axis, each unit cell consists of four atomic layers.For clarity, the spheres in each layer are coded in differentopacity. The brightest Ga spheres at the top layer form adimmer-like structure, consistent with the STM image in (b).(d) Temperature-dependent dI/dV spectra on Ga nanostrip(black dots) and their best fits to the Dynes’s expression (redcurves), with the broadening parameter Γ of 0.1 ∼ ble at 2.5 K. At elevated temperature, the gap graduallyreduces and both the coherence peaks are suppressed, asexpected. The superconducting gaps can be fitted by us-ing Dynes’s expression [19], as illustrated in Fig. 1(d).Figure 1(e) plots the extracted superconducting energygap ∆ at various temperatures. Fitting the data to BCSgap function yields T c = 6.80 K and ∆(0) = 1.28 meV.Having identified the lattice structure and supercon-ductivity, we then focus on the magnetic response of γ -Ga nanostrip. To visualize the magnetic vortices inreal space, we map the spatial variation of zero bias con-ductance (ZBC) on the dotted rectangle in Fig. 1(a), acommon approach for STM imaging of vortices [6–8, 20–27]. This technique takes advantage of the ZBC contrastwithin and outside the magnetic vortex cores, and has ahigher spatial resolution ( ∼ ξ ). Here, the suppressed su-perconductivity within the vortex cores leads to a higherZBC value, leaving superconductivity only outside thevortex cores with lower ZBC. Thus the regions with en-hanced ZBC indicate the emergence of magnetic vortices.Figure 2(a) illustrates such maps at various fields rangingfrom 0.3 T to 1 T. Two intriguing phenomena are imme- diately noticed. The first phenomenon, which is also themore interesting and unexpected one, is that the mag-netic vortex cores expand and compress along the longer( a axis) and shorter ( b axis) sides of the rectangular Gananostrip, respectively, regardless of the field. This con-sequently leads to the anisotropic vortex cores with greataxial elongation. The elongation ratio η is estimated tobe 15 at 0.435 T, and increases further with the magneticfield. At 1.0 T, many vortices merge together and the su-perconductivity is almost completely killed, pushing thewhole island into the normal state. Figure 2(b) revealsthe field-dependent ZBC profiles across the vortex cores.Along the b axis, the existence of only one extremum inevery ZBC profile excludes reasonably the possibility ofvortex chain for a single individual yellow stripe. On theother hand, ZBC oscillates along the a axis, with eachpeaked region representing single or multiple (e.g. giantvortex) of the magnetic flux quantum Φ . The numberof peaks invariably appears smaller than, but tends toclose the applied flux Φ / Φ as the field increases. Above0.7 T (Φ / Φ = 10.1), the ratio between them becomesgreater than 0.5, ruling out the possibility of giant vortex.We therefore suggest that each peak (or yellow stripe)actually denotes a single flux quantum Φ , namely thevorticity L = 1 [Fig. S1].Secondly, we find that the magnetic vortex first pen-etrates into the Ga nanostrip in a rather high filed, i.e.0.435 T in Fig. 2(a). This is caused by the finite en-ergy barrier for vortex entry, consisting of the geometric[28] and Bean-Livingston (BL) surface barrier [29]. Bothbarriers conspire to preclude the penetration of vorticesat low field. The first vortex penetration occurs onlywhen the surface superconducting currents exceed thepair-breaking current, locally weakening superconductiv-ity and then allowing the nucleation of a vortex.The anisotropic internal vortex structure constitutesthe major finding in this study: their large elonga-tion and the mechanism behind are unprecedented. Foranisotropic vortex cores, such as sixfold star-shape [20],fourfold [23–25] and twofold symmetry [26, 27, 30], toname a few, seen previously in certain unconventionalsuperconductors, the anisotropy in either the Fermi sur-face or the superconducting gap has been suggested to bethe primary cause. However, this is not the case here: in γ -Ga the superconducting gap can be well fitted by theisotropic BCS theory [Fig. 1(e)], and no gap anisotropyis involved. To shed more insight into the possible mech-anism behind, we have investigated the vortices in moreGa nanostructures, and find that the vortices invariablyelongate once if the width of Ga nanostrips is reduced tobelow ∼
100 nm. In contrast, usual isotropic circular vor-tices develop in a roughly round-shaped Ga island with alarger lateral dimension [Fig. 3(a)], which although showsthe same lattice structure and superconductivity as Gananostrips. Shown in Figs. 3(b-i) are the isotropic vortexcores, which bear strong similarities with those observed (a) ab Z BC Φ/Φ L (b) a b FIG. 2. (color online) (a) Normalized ZBC maps at various magnetic fields, acquired in a field of view of 380 nm ×
51 nm onthe Ga nanostrip of Fig. 1(a). The normalization was performed by dividing these maps by the normal-state ZBC value at thevortex core. Yellow regions with enhanced ZBC correspond to the vortex cores, all showing enormous elongation along the b axis. The small ZBC enhancement on the right side Ga nanostrip at 0.435 T probably indicates that we are probing a criticalstate justly before the penetration for the second vortex. (b) ZBC profiles across vortex centers in (a). The ZBC presentsoscillations along the a axis, while it shows a single extremum along the b axis. Here Φ / Φ and L denote the applied magneticflux and total vorticity in the strip, respectively.
70 nm (a) (c) (b) (e) (f) (g) (d) (h) (i) N o r m a li ze d σ )) ξ /tanh(1)(1()( r σσ r σ −− += Radial distance r (nm) (j) l / w E nh a n ce d Z BC ( a r b . un it s ) Voticity L (k) FIG. 3. (color online) (a) STM topography ( V s = 3.0 V, I = 50 pA) of a larger Ga island (350 nm ×
280 nm) with a heightof 3.39 nm ( 26 ML). The dotted square marks the region over which all ZBC maps in (b-i) are acquired. (b-i) Magnetic Fielddependence of ZBC maps, acquired in a field of view of 140 nm ×
140 nm in (a). The isotropic vortex cores are unchangedrespective of the fields. (b) ZBC map (140 nm ×
140 nm) taken on a round shaped Ga island with a height of 3.39 nm (26ML), showing a highly isotropic vortex core. (j) Radial dependence of σ ( r ) across the isotropic vortex, which are color-codedto match ZBC map in (b). Here σ ( r ) has been normalized to optimize their fit to the inserted expression by minimizing theresidual, as shown by the red curve. (k) Magnetic vortex-induced ZBC enhancement on various Ga nanostructures. in conventional superconductors such as Pb [22]. Thiscompletely excludes the anisotropy in intrinsic electronicstructure of γ -Ga as a possible cause for the elongatedvortices. Instead, the vortex elongates mainly via a geo-metrical confinement effect.Figure 3(j) plots the radial dependence of vortex-induced ZBC [or σ ( r )]. Based on the Ginzburg-Landau expression for the superconducting order parameter ∆near the interface between a superconductor and a nor-mal metal, the radial ZBC profile across the vortex coreshould obey [21] σ ( r ) = σ ∞ + (1 − σ ∞ )(1 − tanh( − r/ √ ξ )) , (1) ab B (T)0.6 0.7 0.8 (b)(a) A s p ec t r a ti o η Energy minimization BJ e J e J s J s l / w FIG. 4. (color online) (a) Schematic of vortex axial elonga-tion. J e and J s denote the Meissner screening currents atthe sample edge and around the vortex, respectively. Blackthick arrows label the repulsive force between the vortex andMeissner screening currents J e . (b) Magnetic field and γ -Gageometry dependence of vortex elongation η . The extracted η for l/w = 1.0, 2.1, 6.9 and 8.5 are coded magenta, red, blackand blue, respectively. where σ ( r ) is the normalized ZBC away from the vortexcore and r is the radial distance from the vortex center.A best fit of ZBC profile σ ( r ) to Eq. (1) yields a super-conducting coherence length ξ = 24.6 ± L in the roundGa island and rectangular Ga nanostrips, seen more vi-sually in Fig. S2. The linear relationship between them,guided by the dashed line, indicates the equivalence (ex-cept for the shape) among all observed magnetic vortices,regardless of the geometry.We now consider possible explanations for the elon-gated vortices in the Ga nanostrips. Firstly, as the width w of Ga nanostrips is comparable to their Fermi wavelength λ F , quantum confinement will become importantand might lead to sizable spatial modulation in ∆ acrossthe width of nanostrips[3], forming a single or a multi-ple of weak superconducting thin slices normal to the a axis. As a result, vortices, as locally quenched supercon-ductivity, will most probably reside inside the weak su-perconducting slices (more energetically favorable), andmay enormously elongate along the slices [27, 31]. How-ever, our Bogoliubov de-Gennues (BdG) self-consistentcalculations show that this explanation from the quan-tum confinement effect is applicable only if the Fermiwave length λ F is larger than about eight times of thelattice constant. In a usual metal, however λ F is com-monly comparable to its lattice constant (e.g. λ F ∼ . a in γ -Ga) [1], as indicated by considering free electron ap-proximation. Therefore, the quantum confinement effectmight not play the primary role in the vortex elongationobserved here.Alternatively, another possible origin of elongated vor-tices is from the geometric confinement effect imposedby narrowness of the rectangular Ga nanostrips. In theGa nanostrips studied here whose widths are of the or-der of ξ (e.g. w ∼ . ξ in Fig. 2), the finite size of vortex core cannot be ignored. Moreover, the nanostrip thick-ness (several nanometers) is considerably smaller thanthe penetration depth λ , vortices are of the Pearl ratherthan Abrikosov type [32]. The vortex interactions withthe Meissner screening currents at the sample edge ( J e )becomes long ranged and prominent. In terms of thecounterpropagation between J e and the screening current J s encircling the vortex (left panel in Fig. 4(a)), the inter-actions are dominantly repulsive and pronounced alongthe a axis. To minimize this repulsive interaction, thevortex current J s will deform or more specifically elon-gate along the b axis until they are fully exploring thesample geometry (right panel in Fig. 4(a), less energeti-cally costly), where the J e - J s repulsive interaction alongthe b axis gets stronger as well. Consequently, an equi-librium with the strong deformation in J s and thus ZBCor vortex cores is reached, as observed.From considering J e - J s repulsive interactions, one mayfurther argue that vortex elongation η could enhance asthe ratio l/w and magnetic field increases, because J e in-creases with increasing field. In addition, once if multiplevortices enter into the nanostrips, the strong interactionbetween vortices will not only compress a certain vortexalong the a axis as well and contributes to enhance η ,but also configure all vortices parallel to the b axis, asobserved. Figure 4(b) summarizes the vortex elongation η as function of the field B and l/w of the γ -Ga nanos-tructrues. Clearly, η increases abruptly with B and l/w .For example, in the Ga nanostrip with the aspect ratio l/w of 8.5, η is as high as 40.5 at 0.7 T. Therefore, eventhough further detailed theoretical investigations will beneeded to understand the vortex elongation in a quanti-tative way, our experimental findings support that the re-pulsive interaction between the vortices and sample edgescreening current is a reasonable explanation of the vor-tex elongation in Ga nanostrips.To summarize, our real space visualization of unusu-ally elongated vortices in γ -Ga nanostrips sheds light onPearl vortex dynamics in the extremely thin and narrowsuperconducting nanostrips ( w < ξ ), where the geomet-rical confinement effect may deform the internal vortexcore structure and then configure vortices in a brand-new way. The elongated vortices observed here providea novel platform to study exotic vortices in nanoscale su-perconductor. From the viewpoint of superconductor ap-plications, the strong geometrical confinement could im-pose deep potential well for the vortex transverse motionand immobilize the vortices, providing a promising strat-egy to design nanoscale superconducting devices workingat high magnetic field, a long-standing dream of super-conducting research.This work was supported by National Science Founda-tion and Ministry of Science and Technology of China. ∗ [email protected] † [email protected] ‡ [email protected][1] B. J. Baelus and F. M. Peeters, Phys. Rev. B , 104515(2002).[2] R. Geurts, M. V. Miloˇsevi´c, and F. M. Peeters, Phys.Rev. Lett. , 137002 (2006).[3] L. F. Zhang, L. Covaci, M. V. Miloˇsevi´c, G. R. Berdiyorov,and F. M. Peeters, Phys. Rev. Lett. , 107001 (2012).[4] G. Teniers, L. F. Chibotaru, A. Ceulemans, and V. V.Moshchalkov, Europhys. Lett. , 296 (2003).[5] R. C´ordoba, T. I. Baturina, J. Ses´e, A. Y. Mironov,J. M. De Teresa, M. R. Ibarra, D. A. Nasimov, A. K.Gutakovskii, A. V. Latyshev, I. Guillam´on, H. Suderow,S. Vieira, M. R. Baklanov, J. J. Palacios, and V. M. Vi-nokur, Nat. Commun. , 1437 (2013).[6] T. Cren, D. Fokin, F. Debontridder, V. Dubost, andD. Roditchev, Phys. Rev. Lett. , 127005 (2009).[7] T. Cren, L. Serrier-Garcia, F. Debontridder, andD. Roditchev, Phys. Rev. Lett. , 097202 (2011).[8] T. Tominaga, T. Sakamoto, H. Kim, T. Nishio, T. Eguchi,and Y. Hasegawa, Phys. Rev. B , 195434 (2013).[9] A. Johansson, G. Sambandamurthy, D. Shahar, N. Jacob-son, and R. Tenne, Phys. Rev. Lett. , 116805 (2005).[10] T. Morgan-Wall, B. Leith, N. Hartman, A. Rahman, andN. Markovi´c, Phys. Rev. Lett. , 077002 (2015).[11] D. Pekker, G. Refael, and P. M. Goldbart, Phys. Rev.Lett. , 017002 (2011).[12] P. S´anchez-Lotero and J. J. Palacios, Phys. Rev. B ,214505 (2007).[13] E. Bronson, M. P. Gelfand, and S. B. Field, Phys. Rev.B , 144501 (2006).[14] J. J. Palacios, Phys. Rev. B , 10873 (1998).[15] R. B. G. Kramer, G. W. Ataklti, V. V. Moshchalkov,and A. V. Silhanek, Phys. Rev. B , 144508 (2010).[1] H. M. Zhang, J. P. Peng, J. Q. Guan, Z. Li, C. L. Song,L. Wang, K. He, X. C. Ma, and Q. K. Xue, Sci. China , 107402 (2015).[17] Materials and Method are available as supporting mate-rial.[18] L. Bosio, H. Curien, M. Dupont, and A. Rimsky, ActaCrystal. Sect. B , 367 (1973).[19] R. C. Dynes, V. Narayanamurti, and J. P. Garno, Phys.Rev. Lett. , 1509 (1978).[20] N. Hayashi, M. Ichioka, and K. Machida, Phys. Rev.Lett. , 4074 (1996).[21] N. Bergeal, V. Dubost, Y. Noat, W. Sacks, D. Roditchev,N. Emery, C. H´erold, J.-F. Marˆech´e, P. Lagrange, andG. Loupias, Phys. Rev. Lett. , 077003 (2006).[22] Y. X. Ning, C. L. Song, Z. L. Guan, X. C. Ma, X. Chen,J. F. Jia, and Q. K. Xue, Europhys. Lett. , 27004(2009).[23] H. Nishimori, K. Uchiyama, S. Kaneko, A. Tokura,H. Takeya, K. Hirata, and N. Nishida, J. Phys. Soc. Jpn. , 3247 (2004).[24] T. Hanaguri, K. Kitagawa, K. Matsubayashi, Y. Mazaki,Y. Uwatoko, and H. Takagi, Phys. Rev. B , 214505(2012).[25] B. B. Zhou, S. Misra, E. H. da Silva Neto, P. Aynajian,R. E. Baumbach, J. D. Thompson, E. D. Bauer, andA. Yazdani, Nat. Phys. , 474 (2013). [26] C. L. Song, Y. L. Wang, P. Cheng, Y. P. Jiang, W. Li,T. Zhang, Z. Li, K. He, L. L. Wang, J. F. Jia, H. H. Hung,C. J. Wu, X. C. Ma, X. Chen, and Q. K. Xue, Science , 1410 (2011).[27] C. L. Song, Y. L. Wang, Y. P. Jiang, L. Wang, K. He,X. Chen, J. E. Hoffman, X. C. Ma, and Q. K. Xue, Phys.Rev. Lett. , 137004 (2012).[28] E. H. Brandt, Phys. Rev. B , 3369 (1999).[29] C. P. Bean and J. D. Livingston, Phys. Rev. Lett. , 14(1964).[30] Z. Y. Du, D. L. Fang, Z. Y. Wang, Y. F. Li, G. Du,H. Yang, X. Y. Zhu, and H. H. Wen, Nat. Commun. ,9408 (2015).[31] C. Y. Liu, G. R. Berdiyorov, and M. V. Miloˇsevi´c, Phys.Rev. B , 104524 (2011).[32] J. Pearl, App. Phys. Lett. , 65 (1964). SUPPLEMENTAL MATERIAL
Commercially purchased Si(111) wafers with a resis-tivity of 0.01 Ω · cm were used as substrate, and the cleanSi(111)-7 × ∼ o C while keeping the vacuum better than 1 × − Torr. We then prepared Ga nanoislands by evap-orating Ga (99.999%) sources from a standard Knudsencell at a nominal beam flux of approximately 0.4 mono-layer (ML, ∼ × × ∼ V o r ti c it y L B (T) A= , nanostrip A= , Fig. 3(a) A= , Fig. 1(a) FIG. S1. Vorticity L plotted as a function of the appliedfield B for three Ga nanaoislands with varying geometry andlateral area A . Figure S1 depicts the evolution of vorticity L (the num-ber of individual isolated stripy or round yellow featuresin ZBC maps) with varying magnetic field B . Above athreshold field B m , depending on A or the width W ofsuperconducting strips, L increases almost linearly with B , as anticipated for the gradual penetration of mag-netic vortices into Ga islands [3]. By extracting the slope(dashed lines) and island area A , we estimate that each ofsuch features accommodate the magnetic flux of 1.18Φ (left triangle), 1.25Φ (upper triangle) and 1.47Φ (cir-cle), respectively, close to a single magnetic flux quantumΦ and never exceeding 2Φ . This strongly supports asingle magnetic vortex nature of the observed stripy orround features in Figs. 2 and 3. The small discrepancyfrom Φ most possibly originates from an overestimateof the effective island area A for nanoscale superconduc-tors. Compared to Nb strips previously reported [3], B m appears larger in Ga strips we studied here, due to theirextremely small dimensions. -10 -5 0 5 1003530252015105 03530252015105-10 -5 0 5 10 d I / d V ( a r b . un it s ) d I / d V ( a r b . un it s ) Sample bias (mV) Sample bias (mV) (a) (b)
FIG. S2. Differential conductance dI/dV spectra straddling(a) a round magnetic vortex core (Fig. 3, 0.15 T) and (b) anelongated vortex core (Fig. 2, 0.435 T), respectively. Insertedare the two vortices, with the dashed lines indicting wherethe dI/dV spectra are acquired. As anticipated, the super-conductivity is significantly suppressed with enhanced ZBCwhen approaching the vortex cores, regardless of their inter-nal core structure.The small E F -near conductance reductionin (b) is primarily caused by a large ( ∼
12 nm) spatial in-terval between the neighboring dI/dV spectra, which fails toacquire the spectrum justly at the vortex core center. ∗ [email protected] † [email protected] ‡ [email protected][1] H. M. Zhang, J. P. Peng, J. Q. Guan, Z. Li, C. L. Song,L. Wang, K. He, X. C. Ma, and Q. K. Xue, Sci. China , 107402 (2015).[2] J. F. Jia, S. C. Li, Y. F. Zhang, and Q. K. Xue, J. Phys.Soci. Jpn. , 082001 (2007).[3] G. Stan, S. B. Field, and J. M. Martinis, Phys. Rev. Lett.92