Visualizing the elongated vortices in $\gamma$-Ga nanostrips

7.9 MB·English

by  Hui-Min Zhang

Visualizing the elongated vortices in γ-Ga nanostrips
Hui-Min Zhang,1,2 Zi-Xiang Li,3 Jun-Ping Peng,2 Can-Li Song,1,4,∗ Jia-Qi Guan,2 Zhi Li,2 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 Xue1,4
1State Key Laboratory of Low-Dimensional Quantum Physics,
Department of Physics, Tsinghua University, Beijing 100084, China
2Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
3Institute for Advanced Study, Tsinghua University, Beijing 100084, China
4Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
(Dated: April 5, 2016)
6 Westudythemagneticresponseofsuperconductingγ-Gavialowtemperaturescanningtunneling
1 microscopyandspectroscopy. ThemagneticvortexcoresrelysubstantiallyontheGageometry,and
0 exhibit an unexpectedly-large axial elongation with aspect ratio up to 40 in rectangular Ga nano-
2
strips(widthl<100nm). Thisisinstarkcontrastwiththeisotropiccircularvortexcoreinalarger

r round-shapedGaisland. WesuggestthattheunusualelongatedvorticesinGananostripsoriginate
p fromgeometricconfinementeffectprobablyviathestrongrepulsiveinteractionbetweenthevortices
A
andMeissnerscreeningcurrentsatthesampleedge. Ourfindingprovidesnovelconceptualinsights
intothegeometricalconfinementeffectonmagneticvorticesandformsthebasisforthetechnological
3
applications of superconductors.

]
n PACSnumbers: 68.37.Ef,74.25.Op,74.78.Na,74.25.Ha
o
c
- Magnetic vortices in mesoscopic superconductors, in- the model applies for the extremely narrow supercon-
r
p cluding symmetric disks, triangles, squares and rectan- ducting nanostrips remains unjustified.
u gles [1–4], have recently stimulated tremendous interest Herein we report the direct visualization of unexpect-
s due to their fundamental importance in controlling su- edly elongated vortex cores in superconducting γ-Ga
.
t perconductingenergydissipation,asignificantfeaturefor nanostrips by STM, and show that they are caused by
a
m superconductor-based nanotechnologies. When a super- thestrongrepulsiveinteractionbetweenthevorticesand
conductor is shrunk to nanoscale, exotic vortex shapes Meissner screening currents at the sample edge. All ex-
-
d (i.e. giant vortex and antivortex-vortex molecule) and periments were conducted in a Unisoku ultrahigh vac-
n configurationsmayoccur,butsofarmostlyinferredfrom uum STM system equipped with molecular beam epi-
o
indirectmeasurements[5]. Directrealspacevisualization taxy (MBE) for in-situ sample preparation. The MBE
c
of vortices in nanostructured superconductors remains growth of superconducting Ga nanoislands has been de-
[
challenging and rarely explored. A few scanning tunnel- scribed in detail elsewhere [1], and in the Supplemental
3
ing microscopy (STM) studies present the preliminary Material [17]. The measurements were carried out at 4.4
v
evidence of giant vortex in Pb islands [6–8], but the ill- K unless otherwise noted. A magnetic field up to 7 T
7
6 definedgeometryofthesamplesinvestigatedrendersthe can be applied perpendicular to the sample surface. The
0 issue quite complicatedand difficult fora direct compar- differential conductance dI/dV spectra and maps were
5 ison with theory. measured by disrupting the feedback circuit at the set-
0
Amongallthesesuperconductingnanostructures,rect- point of V = 10 mV and I = 100 pA, sweeping the
. s
1 angular nanostrips or nanowires are especially appealing sample voltage V , and extracting the conductance using
s
0 forsuperconductingelectricalcircuitandquantuminter- a standard lock-in technique with a bias modulation of
5
ferencedevice. Regularoscillationsofresistanceandcrit- 0.3 mV at 987.5 Hz.
1
ical current as a function of magnetic field have been re- Figure 1(a) shows the constant-current topographic
:
v spectivelyreportedinsuperconductingInOandAlstrips image of a rectangular Ga nanostrip, which has a length
i
X [9,10],whichcanbeaccountedforbytheso-calledWeber l∼440nmandawidthw ∼64nm. Notethatthenanos-
r blockadetheory[11]. Hereeachoscillationineithermag- tripexhibitsanalmostperfectrectangle,whichcaneasily
a netoresistance or critical current corresponds to adding be modeled in theory. The atomically resolved STM im-
asinglevortexintothestrip, inanalogywithsingleelec- age on the nanostrip, shown in Fig. 1(b), reveals defect-
tron transport through quantum dots in the Coulomb free surface. The unit cell, marked by the blue rhombus,
blockade regime. Furthermore, the penetrating vortices consists of two bright spots with a periodicity of a =
0
areanticipatedtoconfigureintoaone-dimensionalchain 0.86 nm and an intersection angle of 76o, which are con-
at the center of strip [10–12], because of the lower vor- sistent with γ-Ga(001) plane [Fig. 1(c)] [18]. Figure 1(d)
tex potential energy there. Upon increasing field, the plots a series of differential conductance dI/dV spectra
vortex chain may split into two or more buckled parallel acquired on the Ga nanostrip at various temperatures,
rows [13–15]. However, so far as we know, such vortex normalized to the normal-state one above T (10 K). A
c
chains have little been directly visualized, and whether superconducting gap with clear coherence peaks is visi-
2
(a) (b) (d) 5 7.0 K diately noticed. The first phenomenon, which is also the
6.8 K
4 6.6 K more interesting and unexpected one, is that the mag-
malized dI/dV23 45566.....25804 KKKKK n(naeatnaiocxsivtsro)irpat,enxrdecssophreoecrsttieevrxepl(yba,nardexgiasan)rddsilcdeosemssopofrfettshhseeafirloeecnldtga.ntThgehuillsaorncogGnear-
Nor 3.0 K sequentlyleadstotheanisotropicvortexcoreswithgreat
1 2.5 K
1 nm
axial elongation. The elongation ratio η is estimated to
6.36nm
0
(c) -10 -5 0 5 10 be15at0.435T,andincreasesfurtherwiththemagnetic
(e) Sample bias (mV)
1.5 field. At1.0T,manyvorticesmergetogetherandthesu-
perconductivity is almost completely killed, pushing the
0 ba 30 nm meV)1 Data whole island into the normal state. Figure 2(b) reveals
m)6 76o Δ (0.5 BCS theory the field-dependent ZBC profiles across the vortex cores.
Height (n0240 4P0ositio8n0 (nm12)0 160 bca 00 Tc=2T6.e8m0 Kpera4ture (K)6 8 AevleornygZtBheCbparxofiisl,etehxeceluxdisetsenrecaesoofnoanbllyy othnee pexotsrseibmiluitmy ionf
vortex chain for a single individual yellow stripe. On the
FIG. 1. (color online) (a) STM topography of a rectangular
other hand, ZBC oscillates along the a axis, with each
Ga nanostrip with a height of 5.85 nm (45 ML) (V = 3.5 V,
s peaked region representing single or multiple (e.g. giant
I = 50 pA, 483 nm × 161 nm). Line profile taken along the
vortex) of the magnetic flux quantum Φ . The number
red curve characterizes the height and width w of Ga nanos- 0
trip. Bothlabelsa andb denoterespectivelytheorientations of peaks invariably appears smaller than, but tends to
of the short and long side of the rectangular strips through- close the applied flux Φ/Φ0 as the field increases. Above
out this paper. Dotted rectangle marks the region where all 0.7 T (Φ/Φ = 10.1), the ratio between them becomes
0
ZBC maps are taken in Fig. 2(a). (b) Atomic resolution im- greaterthan0.5,rulingoutthepossibilityofgiantvortex.
age (V = 20 mV, I = 50 pA, 10 nm × 10 nm) of the Ga
s We therefore suggest that each peak (or yellow stripe)
nanostrip. The bright spots correspond to the Ga atoms in
actually denotes a single flux quantum Φ , namely the
thetoplayer. (c)Schematiccrystalstructureofγ-Ga. Along 0
vorticity L = 1 [Fig. S1].
the c(001) axis, each unit cell consists of four atomic layers.
For clarity, the spheres in each layer are coded in different Secondly, we find that the magnetic vortex first pen-
opacity. The brightest Ga spheres at the top layer form a etrates into the Ga nanostrip in a rather high filed, i.e.
dimmer-likestructure,consistentwiththeSTMimagein(b). 0.435 T in Fig. 2(a). This is caused by the finite en-
(d) Temperature-dependent dI/dV spectra on Ga nanostrip ergy barrier for vortex entry, consisting of the geometric
(blackdots)andtheirbestfitstotheDynes’sexpression(red
[28]andBean-Livingston(BL)surfacebarrier[29]. Both
curves), with the broadening parameter Γ of 0.1 ∼ 0.2 meV.
barriers conspire to preclude the penetration of vortices
(e)Theextractedgapmagnitude∆versustemperature(black
at low field. The first vortex penetration occurs only
squares). The red line shows the fit to BCS gap function.
when the surface superconducting currents exceed the
pair-breakingcurrent,locallyweakeningsuperconductiv-
ble at 2.5 K. At elevated temperature, the gap gradually ity and then allowing the nucleation of a vortex.
reduces and both the coherence peaks are suppressed, as The anisotropic internal vortex structure constitutes
expected. Thesuperconductinggapscanbefittedbyus- the major finding in this study: their large elonga-
ing Dynes’s expression [19], as illustrated in Fig. 1(d). tion and the mechanism behind are unprecedented. For
Figure 1(e) plots the extracted superconducting energy anisotropic vortex cores, such as sixfold star-shape [20],
gap ∆ at various temperatures. Fitting the data to BCS fourfold [23–25] and twofold symmetry [26, 27, 30], to
gap function yields T = 6.80 K and ∆(0) = 1.28 meV. name a few, seen previously in certain unconventional
c
Having identified the lattice structure and supercon- superconductors, the anisotropy in either the Fermi sur-
ductivity, we then focus on the magnetic response of faceorthesuperconductinggaphasbeensuggestedtobe
γ-Ga nanostrip. To visualize the magnetic vortices in the primary cause. However, this is not the case here: in
real space, we map the spatial variation of zero bias con- γ-Ga the superconducting gap can be well fitted by the
ductance (ZBC) on the dotted rectangle in Fig. 1(a), a isotropic BCS theory [Fig. 1(e)], and no gap anisotropy
common approach for STM imaging of vortices [6–8, 20– isinvolved. Toshedmoreinsightintothepossiblemech-
27]. ThistechniquetakesadvantageoftheZBCcontrast anism behind, we have investigated the vortices in more
within and outside the magnetic vortex cores, and has a Ga nanostructures, and find that the vortices invariably
higher spatial resolution (∼ξ). Here, the suppressed su- elongate onceif thewidth ofGa nanostrips is reducedto
perconductivitywithinthevortexcoresleadstoahigher below∼100nm. Incontrast,usualisotropiccircularvor-
ZBC value, leaving superconductivity only outside the ticesdevelopinaroughlyround-shapedGaislandwitha
vortex cores with lower ZBC. Thus the regions with en- largerlateraldimension[Fig.3(a)],whichalthoughshows
hancedZBCindicatetheemergenceofmagneticvortices. the same lattice structure and superconductivity as Ga
Figure2(a)illustratessuchmapsatvariousfieldsranging nanostrips. ShowninFigs.3(b-i)aretheisotropicvortex
from0.3Tto1T.Twointriguingphenomenaareimme- cores, which bear strong similarities with those observed
3
(a) 0.3 T 0.435 T 0.44 T 0.45 T 0.5 T 0.6 T 0.7 T 0.8 T 0.9 T 1.0 T (b) a b
L Φ/Φ0
14.4
8
13
7
11.6
6
10.1
1.0
4
8.7
C
B
Z 3 7.2
2 6.5
0.42
2 6.4
1 6.3
0 4.4
ba 0 10 20 30 40 50 0 100 200 300
Position (nm) Position (nm)
FIG. 2. (color online) (a) Normalized ZBC maps at various magnetic fields, acquired in a field of view of 380 nm × 51 nm on
theGananostripofFig.1(a). Thenormalizationwasperformedbydividingthesemapsbythenormal-stateZBCvalueatthe
vortex 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 critical
state justly before the penetration for the second vortex. (b) ZBC profiles across vortex centers in (a). The ZBC presents
oscillationsalongthea axis,whileitshowsasingleextremumalongtheb axis. HereΦ/Φ andLdenotetheappliedmagnetic
0
flux and total vorticity in the strip, respectively.
(a) (b) (c) (d) (e) (f)
70 nm
0.12 T 0.25 T 0.3 T 0.35 T 0.4 T
(g) (h) (i) (j) 1 (k) 0.8 l/w
Normalized σ000...864 σ(r)=σ0+(1−σ0)(1−tanh(r/2ξ)) hanced ZBC (arb. units)000...246 6281...915
n
0.45 T 0.5 T 0.8 T E 0
0 20 40 60 80 100 0 2 4 6 8
0.3 1.0 Radial distance r (nm) Voticity L
FIG. 3. (color online) (a) STM topography (V = 3.0 V, I = 50 pA) of a larger Ga island (350 nm × 280 nm) with a height
s
of3.39nm(26ML).ThedottedsquaremarkstheregionoverwhichallZBCmapsin(b-i)areacquired. (b-i)MagneticField
dependence of ZBC maps, acquired in a field of view of 140 nm × 140 nm in (a). The isotropic vortex cores are unchanged
respective of the fields. (b) ZBC map (140 nm × 140 nm) taken on a round shaped Ga island with a height of 3.39 nm (26
ML), showing a highly isotropic vortex core. (j) Radial dependence of σ(r) across the isotropic vortex, which are color-coded
to match ZBC map in (b). Here σ(r) has been normalized to optimize their fit to the inserted expression by minimizing the
residual, as shown by the red curve. (k) Magnetic vortex-induced ZBC enhancement on various Ga nanostructures.
in conventional superconductors such as Pb [22]. This expression for the superconducting order parameter ∆
completelyexcludestheanisotropyinintrinsicelectronic near the interface between a superconductor and a nor-
structure of γ-Ga as a possible cause for the elongated mal metal, the radial ZBC profile across the vortex core
vortices. Instead, the vortex elongates mainly via a geo- should obey [21]
metrical confinement effect. √
σ(r)=σ +(1−σ )(1−tanh(−r/ 2ξ)), (1)
∞ ∞
Figure 3(j) plots the radial dependence of vortex-
induced ZBC [or σ(r)]. Based on the Ginzburg-Landau
4
(a) (b) core cannot be ignored. Moreover, the nanostrip thick-
Je Je 40 ness (several nanometers) is considerably smaller than
B the penetration depth λ, vortices are of the Pearl rather
Js minEinmeirzgayt ion Js pect ratio η2300 l/8w.5 tthhaenMAeibsrsinkeorsosvcretyenpieng[32cu].rrTenhtesvaotrttehxe isnatmerpalcetieodngsew(Jiteh)
As10 62..91 becomes long ranged and prominent. In terms of the
1 counterpropagationbetweenJ andthescreeningcurrent
0 e
b J encirclingthevortex(leftpanelinFig.4(a)),theinter-
a 0.3 0.4 0.5 0.6 0.7 0.8 s
B (T) actions are dominantly repulsive and pronounced along
the a axis. To minimize this repulsive interaction, the
FIG. 4. (color online) (a) Schematic of vortex axial elonga-
vortex current J will deform or more specifically elon-
tion. J and J denote the Meissner screening currents at s
e s gate along the b axis until they are fully exploring the
the sample edge and around the vortex, respectively. Black
thickarrowslabeltherepulsiveforcebetweenthevortexand sample geometry (right panel in Fig. 4(a), less energeti-
Meissner screening currents Je. (b) Magnetic field and γ-Ga cally costly), where the Je-Js repulsive interaction along
geometrydependenceofvortexelongationη. Theextractedη the b axis gets stronger as well. Consequently, an equi-
for l/w = 1.0, 2.1, 6.9 and 8.5 are coded magenta, red, black librium with the strong deformation in J and thus ZBC
s
and blue, respectively.
or vortex cores is reached, as observed.
FromconsideringJ -J repulsiveinteractions,onemay
e s
where σ(r) is the normalized ZBC away from the vortex further argue that vortex elongation η could enhance as
core and r is the radial distance from the vortex center. theratiol/w andmagneticfieldincreases,becauseJ in-
e
A best fit of ZBC profile σ(r) to Eq. (1) yields a super- creaseswithincreasingfield. Inaddition,onceifmultiple
conducting coherence length ξ = 24.6 ± 1.1 nm at 4.4 vortices enter into the nanostrips, the strong interaction
K. Figure 3(k) further qualifies the vortex-induced ZBC between vortices will not only compress a certain vortex
enhancementasafunctionofthevorticityLintheround along the a axis as well and contributes to enhance η,
Ga island and rectangular Ga nanostrips, seen more vi- but also configure all vortices parallel to the b axis, as
sually in Fig. S2. The linear relationship between them, observed. Figure 4(b) summarizes the vortex elongation
guided by the dashed line, indicates the equivalence (ex- η as function of the field B and l/w of the γ-Ga nanos-
ceptfortheshape)amongallobservedmagneticvortices, tructrues. Clearly, η increases abruptly with B and l/w.
regardless of the geometry. For example, in the Ga nanostrip with the aspect ratio
We now consider possible explanations for the elon- l/w of 8.5, η is as high as 40.5 at 0.7 T. Therefore, even
gatedvorticesintheGananostrips. Firstly,asthewidth though further detailed theoretical investigations will be
w of Ga nanostrips is comparable to their Fermi wave needed to understand the vortex elongation in a quanti-
length λ , quantum confinement will become important tativeway,ourexperimentalfindingssupportthatthere-
F
and might lead to sizable spatial modulation in ∆ across pulsiveinteractionbetweenthevorticesandsampleedge
the width of nanostrips[3], forming a single or a multi- screening current is a reasonable explanation of the vor-
ple of weak superconducting thin slices normal to the a tex elongation in Ga nanostrips.
axis. As a result, vortices, as locally quenched supercon-
ductivity, will most probably reside inside the weak su- To summarize, our real space visualization of unusu-
perconducting slices (more energetically favorable), and ally elongated vortices in γ-Ga nanostrips sheds light on
may enormously elongate along the slices [27, 31]. How- Pearl vortex dynamics in the extremely thin and narrow
ever, our Bogoliubov de-Gennues (BdG) self-consistent superconductingnanostrips(w <4ξ),wherethegeomet-
calculations show that this explanation from the quan- rical confinement effect may deform the internal vortex
tum confinement effect is applicable only if the Fermi core structure and then configure vortices in a brand-
wave length λF is larger than about eight times of the new way. The elongated vortices observed here provide
lattice constant. In a usual metal, however λF is com- anovelplatformtostudyexoticvorticesinnanoscalesu-
monlycomparabletoitslatticeconstant(e.g.λF ∼0.4a0 perconductor. Fromtheviewpointofsuperconductorap-
inγ-Ga)[1],asindicatedbyconsideringfreeelectronap- plications, the strong geometrical confinement could im-
proximation. Therefore, the quantum confinement effect posedeeppotentialwellforthevortextransversemotion
might not play the primary role in the vortex elongation andimmobilizethevortices,providingapromisingstrat-
observed here. egytodesignnanoscalesuperconductingdevicesworking
Alternatively,anotherpossibleoriginofelongatedvor- at high magnetic field, a long-standing dream of super-
tices is from the geometric confinement effect imposed conducting research.
by narrowness of the rectangular Ga nanostrips. In the
Ga nanostrips studied here whose widths are of the or- ThisworkwassupportedbyNationalScienceFounda-
der of ξ (e.g. w ∼2.5ξ in Fig. 2), the finite size of vortex tion and Ministry of Science and Technology of China.
5
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6
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∗ [email protected]
such features accommodate the magnetic flux of 1.18Φ
0 † [email protected]
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Soci. Jpn. 76, 082001 (2007).
from Φ most possibly originates from an overestimate
0 [3] G.Stan,S.B.Field, andJ.M.Martinis,Phys.Rev.Lett.
of the effective island area A for nanoscale superconduc-
92, 097003 (2004).
tors. Compared to Nb strips previously reported [3], B
m
appears larger in Ga strips we studied here, due to their
extremely small dimensions.
(a) (b)
35 35
30 30
dI/dV (arb. units)221505 dI/dV (arb. units)221505
10 10
5 5
0 0
-10 -5 0 5 10 -10 -5 0 5 10
Sample bias (mV) Sample bias (mV)
FIG. S2. Differential conductance dI/dV spectra straddling
(a) a round magnetic vortex core (Fig. 3, 0.15 T) and (b) an
elongatedvortexcore(Fig.2,0.435T),respectively. Inserted
are the two vortices, with the dashed lines indicting where
the dI/dV spectra are acquired. As anticipated, the super-
conductivity is significantly suppressed with enhanced ZBC
when approaching the vortex cores, regardless of their inter-
nal core structure.The small E -near conductance reduction
F
in (b) is primarily caused by a large (∼ 12 nm) spatial in-
terval between the neighboring dI/dV spectra, which fails to
acquire the spectrum justly at the vortex core center.