Evidence for chiral superconductivity on a silicon surface F. Ming1X. Wu2 3C. Chen2K. D. Wang2P. Mai4T. A. Maier4J. Strockoz5 6 J. W. F. Venderbos5 6C. Gonzalez7 8J. Ortega9S. Johnston10 11and H. H. Weitering10 11

2025-04-26 0 0 8.2MB 25 页 10玖币

侵权投诉

Evidence for chiral superconductivity on a silicon surface

F. Ming,1X. Wu,2, 3 C. Chen,2K. D. Wang,2P. Mai,4T. A. Maier,4J. Strockoz,5, 6

J. W. F. Venderbos,5, 6 C. Gonzalez,7, 8 J. Ortega,9S. Johnston,10, 11 and H. H. Weitering10, 11

1State Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology

and Guangdong Province Key Laboratory of Display Material, Sun Yat-sen University, Guangzhou 510275, China

2Department of Physics, Southern University of Science and Technology,

Shenzhen, Guangdong 518055, China

3School of Physical Sciences, Great Bay University, Dongguan, Guangdong 523000, China

4Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831-6494, USA

5Department of Physics, Drexel University, Philadelphia, PA 19104, USA

6Department of Materials Science and Engineering, Drexel University, Philadelphia, PA 19104, USA

7Departamento de Física de Materiales, Universidad Complutense de Madrid, 28040 Madrid, Spain

8Instituto de Magnetismo Aplicado UCM-ADIF, Vía de Servicio A-6,

900, E-28232 Las Rozas de Madrid, Spain

9Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC),

Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain

10Department of Physics and Astronomy,

The University of Tennessee, Knoxville, TN 37996, USA

11Institute of Advanced Materials and Manufacturing, The University of Tennessee, Knoxville, TN 37996, USA

Sn adatoms on a Si(111) substrate with 1/3 monolayer coverage form a two-dimensional trian-

gular adatom lattice with one unpaired electron per site and an antiferromagnetic Mott insulating

state. The Sn layers can be modulation hole-doped and metallized using heavily-doped p-type

Si(111) substrates, and become superconducting at low temperatures. While the pairing symme-

try of the superconducting state is currently unknown, the combination of repulsive interactions

and frustration inherent to the triangular adatom lattice opens up the possibility for a chiral or-

der parameter. Here, we study the superconducting state of Sn/Si(111) using scanning tunneling

microscopy/spectroscopy and quasi-particle interference imaging. We ﬁnd evidence for a doping-

dependent Tcwith a fully gapped order parameter, the presence of time-reversal symmetry breaking,

and a strong enhancement of the zero-bias conductance near the edges of the superconducting do-

mains. While each individual piece of evidence could have a more mundane interpretation, our

combined results suggest the tantalizing possibility that Sn/Si(111) is an unconventional chiral d-

wave superconductor.

Superconductivity – dissipationless electrical conduc-

tivity in conjunction with perfect diamagnetism – is a

profound manifestation of a macroscopic quantum phe-

nomenon. Microscopically, supercurrents are carried by

Cooper pairs whose pair wave functions become phase

locked as they condense, like bosons, into a coherent

macroscopic quantum state [1]. In conventional su-

perconductors, electron pairing is mediated by virtual

phonon exchange. In this case, the relatively slow motion

of the ions provides a time-retarded eﬀective attractive

interaction that allows the electrons to overcome their

mutual repulsion resulting in Cooper pairs with s-wave

symmetry, where the composite spin and orbital angu-

lar momenta of the electrons are zero. Higher angular

momentum states are typically driven by repulsive in-

teractions [2,3] as is the case for e.g. high-Tccuprate

superconductors [3,4]. Here, electron repulsion is min-

imized by imposing a nodal structure with correspond-

ing sign change in the superconducting wave function.

More recent emphasis on topological materials systems

have raised expectations for the discovery of novel multi-

component order parameters that are topologically dis-

tinct from those of ordinary Cooper pair condensates [5–

15]. Besides the microscopic nature of the pairing inter-

actions, the physics of these systems is dictated by bro-

ken symmetries such as crystal, spin rotation, and time-

reversal symmetries, though experimental validation of

intrinsically topological order parameters remains scant.

Superconductivity has recently been discovered in a

system comprised of one-third monolayer of Sn deposited

on degenerately doped p-type Si(111) substrates [17]. Its

pairing symmetry, however, remains undetermined. This

system is of particular interest because the undoped Sn

monolayer is an antiferromagnetic single-band Mott in-

sulator [16,18] that becomes superconducting upon hole

doping, drawing interesting comparisons with the high-

Tccuprates [3,19] with d-wave order parameters. The Sn

layer, however, has triangular lattice symmetry imposed

by the Si(111) substrate. This geometry naturally allows

for the existence of a chiral order parameter with topolog-

ical edge states [7,12,20], if repulsive interactions domi-

nate the pairing. The appearance of such an exotic order

parameter is expected to furthermore depend on the elec-

tron correlation strength, shape of the Fermi surface, and

the doping level [7,20,21]. In particular, recent renor-

malization group calculations for the Sn/Si(111) system

indicated a competition between chiral d- and f-wave and

triplet p-wave instabilities, depending on the doping level

arXiv:2210.06273v1 [cond-mat.supr-con] 12 Oct 2022

FIG. 1. Structure, topography and spectral properties of the superconducting (√3×√3)-Sn surface on Si(111).

a, Structure model with the three outermost surface layers and one Sn adatom per (√3×√3) unit cell. b, Noninteracting

dispersion of the dangling-bond surface state according to Ref. 16. The inset shows the Fermi surface in the hexagonal surface

Brillouin zone. The high symmetry points are indicated. The Γpoint is located at the center of the hexagon. c, Comparison of

diﬀerential conductance spectra of two Si(111)(√3×√3)-Sn surfaces. The spectrum for the undoped surface is from Ref. 17,

acquired at 77 K, showing the upper and lower Hubbard bands (UHB/LHB) and a small gap around the Fermi level; the other

spectrum is from a doped surface (p= 0.08) obtained at 0.5 K, showing an extra quasiparticle peak (QPP) near the Fermi level,

consistent with Ref. 17.d, Topographic STM image (Vs=−0.1V, It= 0.1nA) showing a near perfect Sn adatom lattice, along

with a substitutional Si defect, vacancy, and other defect, labelled with a triangle, square and a circle, respectively (p= 0.08).

e, Normalized STS spectra for three diﬀerent hole concentrations, revealing a clear doping dependence of the superconducting

gap. f, A set of raw dI/dV spectra taken at equidistant locations along the dotted line shown in panel d, starting on the left.

(p= 0.08). g, Normalized dI/dV spectra as a function of temperature (p= 0.08). The spectra in panels fand gare oﬀset

vertically for clarity.

and value of the nearest-neighbor Hubbard repulsion [21].

At the same time, electron-phonon interactions, partic-

ularly to interfacial Si modes [22], could drive a conven-

tional s-wave pairing [17].

Here we study the superconducting state of the

Sn/Si(111) interface using scanning tunneling microscopy

and spectroscopy (STM/STS) and quasiparticle interfer-

ence (QPI) imaging. Our observations reveal a strong

doping dependence of the superconducting Tc, a fully

gapped order parameter, the presence of time-reversal

symmetry breaking, and a strong enhancement of the

zero-bias conductance near the edges of the supercon-

ducting domains. While each of these observations may

have a mundane explanation, we discuss why we believe

that a chiral d-wave scenario oﬀers the most consistent

interpretation of the measurements and theoretical mod-

eling. Final conﬁrmation, however, awaits experimental

validation concerning the topological nature of the edge-

state conductance.

At 1/3 monolayer coverage, the Sn adatoms form

a (√3×√3) superlattice on the Si(111) surface with

one half-ﬁlled dangling-bond orbital per site and a Sn-

Sn distance of 6.65 Å; see Fig.1a. All other chemical

bonds in the system are passivated. The non-interacting

dangling-bond surface state has a bandwidth W≈0.5eV

(Fig. 1b), which is comparable to the on-site Hubbard in-

teraction U≈0.66 eV of the dangling bond orbitals [16].

As such, the system is a Mott insulator with an upper

and a lower Hubbard band (UHB/LHB) straddling the

Fermi level (Fig. 1c).

Figure 1dshows an STM image of the triangular Sn

adatom lattice. The Sn atoms are clearly resolved and

well ordered. The dark point defects correspond to sub-

stitutional Si adatoms (most prevalent) and Sn adatom

vacancies. Holes are introduced via modulation doping,

using boron-doped Si substrates with diﬀerent doping

levels [17,18]. (For a discussion on dopant segregation,

see Supplementary Note 1 and Supplementary Figure 1).

The hole concentration in the dangling-bond surface state

is estimated from the spectral weight transfer in the tun-

neling spectra, associated with the introduction of holes

and formation of a quasiparticle peak in the Mott gap

(see Fig. 1band Extended Data Fig. 1) [18].

Fig. 1eshows the normalized dI/dV tunneling spec-

tra for excess hole concentrations of p= 0.06,0.08, and

0.10, recorded at T= 0.5K. (The p= 0.10 data were

reported in Ref. 17.) These spectra are representative of

the superconducting density of states (DOS). Here, we

FIG. 2. Low-temperature diﬀerential conductance and

QPI spectra of the p= 0.08 (√3×√3)-Sn surface on

Si(111).a, Best ﬁts of the low-energy normalized dI/dV

spectra at T= 0.5K, for diﬀerent pairing symmetries. The

inset zooms in on the zero bias region. b,c, QPI images ac-

quired at Vs=±5mV, beyond the superconducting gap. d,

Real space conductance map g(r, V ), obtained at zero bias.

The bright six-leaf features are scattering features from sur-

face defects. e, Corresponding QPI spectrum g(q, V )ob-

tained from the conductance map in panel dvia Fourier trans-

formation. The six dark blue crosses in panels b,c, and ein-

dicate the Bragg peaks, while the colored contours highlight

characteristic features in each QPI image.

divided the raw tunneling spectra by the normal state

dI/dV spectrum obtained in a perpendicular 15 Tesla

magnetic ﬁeld. This ﬁeld is large enough to completely

suppress the superconductivity for the p= 0.08 and 0.10

samples, which have upper critical ﬁeld values of Hc2(0.5)

of 3 Tesla [17] and 13 Tesla, respectively (see Extended

Data Fig. 2). This procedure is a bit problematic for

the p= 0.06 sample, where the upper critical ﬁeld ex-

ceeds the magnetic-ﬁeld capability of our instrument (15

Tesla).

The Sn adatom lattice in Figure 1ais highly ordered,

while the boron dopants are located in the silicon bulk.

The superconducting DOS is, therefore, spatially uniform

away from localized point defects and the edges of the

(√3×√3) domains. Fig. 1fshows a series of spectra

recorded at T=0.5K along the line segment in Fig. 1d.

This level of homogeneity distinguishes the Sn on Si(111)

system from e.g. complex oxides, which exhibit consider-

able electronic inhomogeneity, often in conjunction with

various competing orders [23,24].

The normalized dI/dV spectra of the p= 0.08 sam-

ple are plotted as a function of temperature in Fig. 1g.

The gap feature persists up to about 8K. Detailed Dynes

ﬁts [25] of the spectra assuming s-wave and dx2−y2±idxy

order parameter symmetries, as well as zero bias con-

ductance measurements as a function of temperature,

consistently produce a Tcof about 7.6±0.2K with

some evidence of superconducting ﬂuctuations above Tc

(see Ref. 17, Extended Data Fig. 3, and Fig. 2a). A

similar procedure for the p= 0.10 sample produces Tc

= 4.7±0.3K [17], while the Tcof the p= 0.06 sample

was diﬃcult to ascertain because the spectra cannot be

properly normalized [Hc2(0.5 K) >15 T]. We conserva-

tively estimate its Tcto be around 9K (see Extended

Data Fig. 2).

Fitting the p= 0.08 dI/dV spectra with an s-wave

gap produces a reasonable ﬁt but with notable discrep-

ancies near zero-bias. Turning to potential chiral order

parameters, we ﬁnd that a chiral d-wave ﬁt also agrees

well with the data and even improves the ﬁt at low en-

ergies. A chiral p-wave gap clearly fails to describe the

spectra, particularly at low-energy (Fig. 2a). This fail-

ure occurs because any p-wave gap function must vanish

at the M-point by symmetry. This point corresponds

to the van Hove singularity and lays close to the Fermi

surface [17,18]. It therefore aﬀects the gap signiﬁcantly,

producing pronounced shoulders in the DOS that are not

observed experimentally. Other parameter symmetries

such as extended chiral p-wave and nematic d-wave sym-

metries (i.e., dx2−y2and dxy ) do not ﬁt the spectra either,

see Supplementary Note 2. (A multigap order parameter

can also be ruled out since this is a single-band system.)

Only s- and chiral d-wave symmetries produce good re-

sults and it is not possible to conclusively discriminate

between the two based on ﬁtting alone.

Important details about the Fermi surface and or-

der parameter symmetry can be obtained from spectro-

scopic STM imaging [26]. Here, one acquires a spatial

map of the diﬀerential tunneling conductance g(r, V ) =

dI(r, V )/dV . Such dI/dV maps typically reveal the

presence of electronic standing waves as quasi-particles

are scattered elastically by defects on the surface. The

power spectrum of the diﬀerential conductance map –

the QPI spectrum – then identiﬁes the dominant scatter-

ing processes contributing to the standing wave pattern.

In itinerant systems, these typically correspond to scat-

tering wavevectors connecting diﬀerent k-points on the

constant energy contours (corresponding to the imaging

bias) q= 2k±G, where Gis a reciprocal lattice vector

of the (√3×√3) adatom lattice.

Figs. 2b,cshow the T= 0.5K QPI spectra taken

at ±5meV bias (p= 0.08). Both spectra reveal the

FIG. 3. Comparison of the measured QPI spectra with

theory.a,b, Experimental QPI images g(q, V )obtained at

zero bias on the p= 0.10 surface above (panel a) and below

Tc(panel b). c,d, Simulated QPI images for a superconduc-

tor with a chiral d-wave (panel c) and s-wave (panel d) order

parameter, assuming non-magnetic defects. In each image,

the six dark blue crosses indicate the locations of the Bragg

points, while the colored contours highlight characteristic fea-

tures in each QPI spectrum.

warped hexagonal Fermi contour of the normal state

(G=0), highlighted in magenta, along with several

scattering replica’s (G6=0) as indicated by the light

blue dumbbell-shaped contours [18]. These spectra agree

very well with previous calculations for the spectra in

the normal state, and are fully consistent with the band

structure for the Sn surface state [18]. (The presence of

the quasiparticle band and its dispersion is inconsistent

with an interpretation in terms of impurity band physics;

see Supplementary Note 3.) Real space diﬀerential con-

ductance maps at zero bias (Fig. 2d), i.e. deep inside the

superconducting gap, reveal the existence of very strong

star-like scattering features centered at the various sur-

face defects. The corresponding Fourier map (Fig. 2e)

now reveals the presence of a ﬂower-like feature centered

at q=0and with six “petals” pointing towards the Bragg

points of the (√3×√3) lattice, as outlined by the red con-

tour. Meanwhile, the Fermi contour seen at ±5meV is

suppressed. This ﬂower feature appears to be intimately

related to the superconductivity; it only exists when the

sample is in the superconducting state (Fig. 3a,b) and

when the tunneling bias is within the superconducting

gap (Fig. 2b,c,e). Hence, they are unique features of

the superconducting state (see Extended Data Fig. 4for

additional QPI results).

To elucidate the origin of the ﬂower-like features, we

ﬁrst simulated the QPI patterns for the s-wave and chi-

ral d-wave order parameters using the T-matrix formal-

ism and assuming nonmagnetic scattering (see Meth-

ods). Fig. 3shows the experimental QPI spectra of the

p= 0.10 sample, along with the simulated spectra for

the dx2−y2±idxy and s-wave state. The experimental

pattern in Fig. 3bis well reproduced in the calculations

for the d-wave pairing channel (Fig. 3c). (The theoret-

ical features exhibit much more curvature because the

calculations are based on the non-interacting band dis-

persion whereas the experimental band dispersion has

correlation-driven band renormalizations [18].) Impor-

tantly, the ﬂower is absent for the s-wave pairing channel,

as shown in Fig. 3d.

Our simulations reveal that the ﬂower features only

appear when time reversal symmetry is broken. Such

would be the case for non-magnetic scattering in a chiral

superconductor, as simulated above, but it could also be

due to magnetic scattering in an s-wave superconductor

(see Extended Data Fig. 5). In particular, the star-like

scattering features in the real-space QPI maps are very

similar to those observed for magnetic point scatterers

in s-wave systems, and have been attributed to a focus-

ing eﬀect of magnetic bound states or Yu–Shiba–Rusinov

(YSR) states due to Fermi surface anisotropy [27–31]. To

discriminate between the s-wave and d-wave scenarios, it

is essential to establish the nature of the defects on the

surface.

The most prevalent scattering defect on the surface is

the substitutional Si adatom (replacing a Sn adatom). It

shows up as a dark void in ﬁlled-state STM images and

as a depressed adatom in the empty state images (see Ex-

tended Data Fig. 6). This observation indicates that the

spz-like dangling bond orbital of the Si atom is empty,

and because the adatom forms three covalent backbonds

with the Si substrate, the Si adatom is expected to be

non-magnetic. This is conﬁrmed via ﬁrst-principles Den-

sity Functional Theory (DFT) total-energy calculations

(which show that the Si adatoms are placed 0.6 Å be-

low the Sn adatoms) and by STM image simulations (see

Methods and Extended Data Fig. 6). In addition, spin-

polarized DFT calculations (see Methods) conﬁrm the

nonmagnetic nature of this defect.

It is not possible to ascertain the nature of all native

defects on the surface (see Extended Data Fig. 7a) and

thus rule out any magnetic scattering contribution to the

QPI pattern. We therefore created a new type of defect

by depositing a tiny excess amount of (nonmagnetic) Sn

atoms at 120 K. STM images indicate that additional

Sn adatoms are located at three-fold symmetric inter-

stitial adatom sites, surrounded by three Sn adatoms of

the 2D host lattice (see Extended Data Fig. 6). The

excess Sn atoms easily move under the STM tip at tun-

neling biases in excess of ±0.8V, indicating that they

are weakly bound to the surface. The interstitial adatom

FIG. 4. Defect states and edge states on the (√3×√3)-Sn surface (p=0.08).a, STS point spectra (0.5 K) for each

Sn atom along the blue-dotted line in the topographic image (Vs= 0.5 V, It= 1 nA) at the top with a substitutional Si

defect in the middle. The bottom spectrum corresponds to the left end of the line. The spectrum recorded right on top of the

defect is indicated by a triangle. Spectra near the defect site exhibit two gap states at EB=±0.6meV. b, A (√3×√3)-Sn

superconducting domain (Vs= 0.8V, It= 0.1nA) next to a semiconducting Si(111)(2√3×2√3)R30◦-Sn domain on the far

left side of the image (bright strip) . c-e, Registry-aligned real-space conductance maps g(r, V = 0 mV) of the (√3×√3)-Sn

domain measured at diﬀerent temperatures. In panels b-e, the vertical dashed lines label the domain boundary; the dashed

circles label the locations of the same defect. f, Averaged zero-bias conductance as a function of distance from the domain

boundary. Each line is obtained from a conductance map g(r, V = 0 mV), recorded at the indicated temperature. The ﬁrst six

curves are ﬁtted with an exponential decay. g, Fitted decay lengths as a function of temperature. The dashed line is a guide

to the eye. h, STS spectra taken at 0.5 K along the dotted line in panel b, starting at the domain boundary on the left. i,

The 15 bottommost spectra from panel hafter subtracting the dI/dV spectrum recorded deep inside the (√3×√3) domain.

These spectra highlight the edge state contribution (indicated by shading) to the measured dI/dV spectra. j, Simulated DOS

of a chiral d+ idsuperconductor, approaching the open edge of a cylinder (see Methods). As with panel i, a spectrum from the

center of the cylinder is subtracted to highlight the contribution from the edge state to the total DOS inside the superconducting

gap. Spectra in panel h,iand jare shifted vertically for clarity.

location is validated by DFT total energy minimization

and STM image simulations. In particular, notice the

excellent agreement between the experimental and theo-

retical STM images, as shown in Extended Data Fig. 6.

This level of agreement gives us conﬁdence that the cal-

culations capture the local electronic structure correctly.

Importantly, spin-polarized DFT indicates that these de-

fect centers are also nonmagnetic. The latter can be un-

derstood from the fact that the interstitial Sn atom and

its three nearest neighbors have negligible contribution

to the DOS at the Fermi level (Extended Data Fig. 6),

thus pre-empting a potential magnetic instability.

Figure 4aplots the STS spectra across a substitutional

Si defect, which reveals the existence of two in-gap states

(p= 0.08). These states appear in pairs located symmet-

rically about the Fermi level reminiscent of YSR bound

states though the substitutional defect is nonmagnetic.

All defects on the surface we have checked produce these

YSR-like in gap states albeit at diﬀerent energies, in-

cluding the native vacancy defects, interstitial Si, excess

Sn adatoms, as well as various other defects (see Ex-

tended Data Fig. 7). This is to be expected in a chiral

d-wave scenario because potential and magnetic defects

are both pair breaking [32,33]. In the s-wave scenario,

on the other hand, one would have to assume that these

defects are all magnetic [34], which seems unlikely (see

Extended Data Fig. 5). Interestingly, the nonmagnetic

interstitial Sn adatoms produce the strongest star-like

scattering features in real-space QPI maps and the most

intense ﬂower features in the corresponding power spec-

trum (see Extended Data Fig. 7e-g). These enhanced

scattering features near the excess Sn adatoms suggest

that the s-wave scenario can be dismissed because time-

reversal symmetry should not be broken in such a case.

Alternatively, one might suggest that nonmagnetic impu-

rities are present in a magnetically ordered background,

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

EvidenceforchiralsuperconductivityonasiliconsurfaceF.Ming,1X.Wu,2,3C.Chen,2K.D.Wang,2P.Mai,4T.A.Maier,4J.Strockoz,5,6J.W.F.Venderbos,5,6C.Gonzalez,7,8J.Ortega,9S.Johnston,10,11andH.H.Weitering10,111StateKeyLaboratoryofOptoelectronicMaterialsandTechnologies,SchoolofElectronicsandInformationTechnology...

展开>> 收起<<

Evidence for chiral superconductivity on a silicon surface F. Ming1X. Wu2 3C. Chen2K. D. Wang2P. Mai4T. A. Maier4J. Strockoz5 6 J. W. F. Venderbos5 6C. Gonzalez7 8J. Ortega9S. Johnston10 11and H. H. Weitering10 11.pdf

共25页,预览5页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Evidence for chiral superconductivity on a silicon surface F. Ming1X. Wu2 3C. Chen2K. D. Wang2P. Mai4T. A. Maier4J. Strockoz5 6 J. W. F. Venderbos5 6C. Gonzalez7 8J. Ortega9S. Johnston10 11and H. H. Weitering10 11

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: