Probing the superfluid velocity with a superconducting tip: the Doppler shift effect.

Abstract

We address the question of probing the supercurrents in superconducting (SC) samples on a local scale by performing scanning tunneling spectroscopy (STS) experiments with a SC tip. In this configuration, we show that the tunneling conductance is highly sensitive to the Doppler shift term in the SC quasiparticle (QP) spectrum of the sample, thus allowing the local study of the superfluid velocity. Intrinsic screening currents, such as those surrounding the vortex cores in a type II SC in a magnetic field, are directly probed. With Nb tips, the STS mapping of the vortices, in single crystal 2H-NbSe(2), reveals both the vortex cores, on the scale of the SC coherence length xi, and the supercurrents, on the scale of the London penetration length lambda. A subtle interplay between the SC pair potential and the supercurrents at the vortex edge is observed. Our results open interesting prospects for the study of screening currents in any superconductor.

Full text

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arXiv:cond-mat/0511699v2 [cond-mat.supr-con] 30 Nov 2005
Probing the superfluid velocity with a superconducting tip:
the Doppler shift effect
A. Kohen1, Th. Proslier1, T. Cren1, Y. Noat1, W. Sacks1, H. Berger2and D. Roditchev1
1Institut des Nanosciences de Paris, I.N.S.P., Universit´ es Paris 6 et 7,
C.N.R.S. (UMR 75 88), 75015 Paris, France and
2Institute of Physics of Complex Matter, E.P.F.L., 1015 Lausanne, Switzerland
(Dated: February 2, 2008)
We address the question of probing the supercurrents in superconducting (SC) samples on a local
scale by performing Scanning Tunneling Spectroscopy (STS) experiments with a SC tip. In this
configuration, we show that the tunneling conductance is highly sensitive to the Doppler shift term
in the SC quasiparticle spectrum of the sample, thus allowing the local study of the superfluid
velocity. Intrinsic screening currents, such as those surrounding the vortex cores in a type II SC
in a magnetic field, are directly probed. With Nb tips, the STS mapping of the vortices, in single
crystal 2H-NbSe2, reveals both the vortex cores, on the scale of the SC coherence length ξ, and the
supercurrents, on the scale of the London penetration length λ. A subtle interplay between the SC
pair potential and the supercurrents at the vortex edge is observed. Our results open interesting
prospects for the study of screening currents in any superconductor.
A fundamental property of the superconducting
(SC) state is its response to an applied magnetic field.
In particular, the field penetrates type II superconduc-
tors in the form of quantized flux, or vortices, each
one carrying a flux quantum of φ0=h/2e, which are
arranged in a lattice [1]. Each vortex is surrounded
by screening currents which decay over λ, the mag-
netic penetration length, and has a core extending
over the coherence length ξ. The SC pair potential,
∆(r), decays from its maximal value outside the core,
down to zero in its center. As shown by Bardeen,
Cooper & Schrieffer (BCS), in the spatially homoge-
nous case the SC state has an excitation spectrum
given by Ek= (ε2
quasiparticle density of states (DOS) in which a gap
of width ∆, with a peak at its edge, opens at the
Fermi level. In the vortex state, the DOS in the SC
becomes spatially inhomogeneous due to both the cur-
rents flowing around the vortices and the variations in
∆(r). The two different effects are expected to occur
on the length scales λ and ξ respectively. As can be
seen from the BCS spectrum, a consequence of chang-
ing ∆(r) is a modification of the DOS gap width. In
addition, as shown by Caroli et al.[2], bound states
are formed in the vortex core since ∆(r) acts as a po-
tential well. The bound states affect the low energy
DOS and are significant close to the vortex center.
The Scanning Tunneling Microscope (STM) is an
instrument of choice to map the DOS variations on a
nanometer scale. The technique is based on the tun-
neling current (I), flowing between a normal metal
tip and a sample, measured as a function of the tip
position and the bias voltage (V ). Combined with
spectro-scopy (STS), the conductance dI/dV (r,V )
reflects the sample local DOS, which has been ex-
ploited to study the vortex lattice in several materials
[3, 4, 5, 6, 7, 8, 9]. The main focus of these experi-
ments was a detailed study of the vortex core bound
states and/or the measurement of ξ, as inferred from
the spectra due to the spatial variation of ∆(r). Study
of the screening currents, and thus measuring λ, had
proven to be more delicate.
k+∆2)1/2. This results in a unique
In general when an uniform current flows in a SC
sample, the excitation spectrum can be rewritten as:
Ek = (ε2
k+ ∆2)1/2+ mvF· vs
, (1)
where vFis the Fermi velocity and vsis the superfluid
one [10]. As long as the Doppler energy, mvF· vs, is
small with respect to ∆, the main effect on the DOS
is a reduction in the peak height. However this ef-
fect is relatively small, only a few percent in magni-
tude, and is therefore not effective, with STM, as a
means to study the supercurrents. While other meth-
ods are sensitive to magnetic field variations, such as
Hall probe or SQUID microscopies [11], and are able
to measure λ, they lack the high spatial resolution
of STM. Moreover these techniques are insensitive to
∆(r) and thus cannot be used to determine ξ.
In pioneering STS experiments, Hess et al.[4] found
that even far from the core the spectra differed from
the zero field one, the main difference being a small in-
gap shoulder. The position of this shoulder is shifted
to lower energies as one approaches the core and fi-
nally merges with the peaks of the core bound states.
They interpreted this effect in terms of the Doppler
shift caused by the screening currents. However, as
was theoretically shown by [12], this model is not jus-
tified when the core states extend to large distances
and especially for low energies, when they dominate
the spectrum. Thus the the simple model based on
the Doppler shift, while giving the correct qualitative
result, fails to be quantative and should be replaced
by a full solution of the Eilenberger equations [12].
Here we take a different approach and use a super-
conducting tip, in STM/STS, to directly detect the
pair supercurrents, due to their Doppler shift effect
on the quasiparticle spectrum. The use of SC tips
in low temperature STM was suggested [13] and later
realized by several groups [14, 15, 16, 17, 18]. The
potential advantages of the SIS (SC-vacuum-SC) con-
figuration are an enhanced spectroscopic energy res-
olution and the possibility to measure the Josephson
pair tunneling [15]. SC tips have so far been applied
only at a single point; no scanning spectroscopy has

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yet been reported. A priori, their use to image the
vortex lattice could result in complications. First, the
local magnetic field might affect the SC properties of
the tip and second, there is a force between the dia-
magnetic SC tip and the vortices. A displacement of
the vortices, leading to a distortion of the STS images,
is possible. In this letter we report the successful use
of superconducting Nb tips for STS mapping of the
vortex lattice in a NbSe2 sample. Owing to the en-
hanced spectroscopic resolution of the SC tip, we are
able to detect both the existence of the in-core bound
states, and the supercurrents flowing around the vor-
tex. The latter is achieved by the strong effect of the
Doppler shift on the gap-edge peak amplitude.
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FIG. 1:
ductance for a normal metal tip and a SC sample, with ∆
= 1 meV, T = 2.3 K, Doppler energy: 0, 0.3, 0.5 meV. (b)
conductance with a superconducting tip ∆tip = 1.5 meV,
and identical parameters as in (a). (c) SIS conductance
with large Doppler shift = 0.65 meV and varying surface
gap ∆sample = 0, 0.3, 0.6 meV. (d) Experimental tunnel
conductance for a NbSe2 sample with a SC Nb tip (SIS)
and with a normal Pt/Ir tip (NIS), T=2.3 K.
Calculations of: (a) normalized tunneling con-
The effect of the supercurrents on a NIS spectrum,
as calculated using BCS, is shown in Fig.1a. One can
see that if mvF·vs< ∆, where Eq.(1) for the Doppler
shift holds, the corresponding change in the tunneling
conductance spectrum is very small and thus is diffi-
cult to observe experimentally. However, in the SIS
geometry (i.e. with a SC tip) the same change in the
sample DOS due to the Doppler shift leads to a signif-
icant drop in the tunneling conductance peak ampli-
tude, as shown in Fig.1b. The enhancement of the ef-
fect is clearly due to the overlap of the tip and sample
DOS gap edges. Closer to the vortex core, the princi-
pal change of the quasiparticle DOS should be the de-
crease in the magnitude of ∆, manifested by the grad-
ual shift of the tunneling conductance peaks towards
lower energies, see Fig.1c. Thus, in the SIS configura-
tion, one would expect two different behaviors in the
SIS tunneling conductance spectra while approaching
the vortex core: the decrease in the peak amplitude
at large distances and the peak shift to lower ener-
gies close to the vortex core. As we will demonstrate,
the corresponding length scales may be identified, in
a first approximation, as the penetration length λ and
the coherence length ξ, respectively. The peak ampli-
tude variation, together with the Doppler shift energy,
give the profile of the supercurrent intensity as a func-
tion of distance from the vortex center. By solving the
London equation, a quantitative fit yields the values
of both ξ and λ.
NbSe2 crystals, grown using the standard Iodine
Vapor Transport technique [19], were studied using
our home-made UHV STM setup allowing a minimum
temperature of 2 K and an applied magnetic field up to
6T. Our low temperature STM unit, described in [20],
is digitally controlled and the high-speed data acquisi-
tion allows a full spectroscopic mapping of the sample.
The preparation and characterization of our Nb tips is
reported in [18]. As a simple check, we first measured
the spectra of the NbSe2sample in zero field, and at T
= 2 K (see Fig.1d). These exhibit the typical features
of a SIS junction: sharp peaks appear at the volt-
ages ±(∆tip+ ∆sample)/e. For comparison, we show
the spectrum using a normal Pt/Ir tip (NIS junction).
We thus obtain ∆Nb=1.5 meV and ∆NbSe2=1.0 meV,
in agreement with their bulk values.
FIG. 2:
tex lattice, applied field .06 T, 330 nm × 330 nm area,
T=4.5K. The maps (1-8) correspond to the bias voltages
as indicated in the figure. The strongest contrast is ob-
tained at V = ±(∆Nb+∆NbSe2)/e, maps 2 & 7, and at
V = ±∆Nb/e, maps 4 & 5. (b) Normalized conductance
spectra measured in the vortex core (NIS) and in between
the vortices (SIS). Arrows mark the selected voltages for
the conductance maps in (a).
(a) Fixed scale conductance maps of the vor-
In Fig.2 we show a typical STS result of a 330×330
nm2scan of the sample surface at T=4.5 K and in a
magnetic field of 0.06 T. At each point, of a 256×256
point topographic image, a complete I(V ) tunnel-

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ing spectrum was acquired in the sample bias range
from -10 mV to +10 mV. The conductance spectra,
dI/dV (V ), were directly derived from raw I(V ) data.
In Fig.2a we present 8 most significant conductance
maps selected from 256 measured. The maps are dis-
played in a fixed gray scale without any additional
contrast treatment. It is clear from the maps nos2,
4, 5 and 7 that the familiar triangular vortex lattice
is successfully revealed by STS with a SC tip. Here,
the inter-vortex distance of 190 nm matches the the-
oretical value d = (2φ0/√3B)1/2≃ 200 nm, for B
= 0.06 T. First, contrary to the case of STS with a
non-superconducting tip, the vortices do not appear
in the conductance maps near zero bias but rather at
higher bias values. The maximum contrast is achieved
at eV≃∆tipand eV≃∆tip+∆sample. Second, one ob-
serves an almost perfect symmetry of the contrast
with respect to the Fermi level. Indeed, the map no2
taken at -2.4 mV is almost identical to no7 obtained
at +2.4 mV. In these two maps the vortices appear
black due to the lower tunneling conductance in the
vortex cores. The maps nos4 and 5, taken at -1.4 mV
and +1.4 mV respectively, are also quasi-identical, but
the vortices appear in white as the regions of higher
conductance.
The origin of the map contrast is better understood
from the two spectra plotted in Fig.2b. The first, ob-
tained in the center of the vortex, σNIS(V ), shows the
characteristic NIS shape, while the second, σSIS(V ),
taken at a point in between the vortices, shows the
SIS one. At voltages above (∆tip+∆sample)/e, such as
V8, both spectra have a common conductance value
and no contrast is observed.
peak (at V7) develops in the SIS spectrum at eV
≃ ∆tip+ ∆samplewhere it exhibits a higher conduc-
tance than the NIS one. The two spectra then cross at
V6. For V<V6, σSIS<σNIS and a second high con-
trast can be found for eV≃∆tip, at V5. Finally at
V=0, σSIS ≃ σNIS: the contrast is negligible. We
see why the contrast is inverted between maps 7 and
5 (respectively 2 and 4), and is small in map 6 (or
3). Qualitatively, features in the sample DOS, besides
being enhanced, are shifted in energy by an amount
∆tip. By selecting the sharpest positive and nega-
tive maps, we find the values ±1.4 mV and ±2.4 mV,
respectively, and thus determine in a different way:
∆Nb=1.4 meV and ∆NbSe2=1.0 meV.
For lower V , a high
To study the vortex bound states and the superfluid
velocity profile, we focused on a single vortex lattice
unit cell and reduced the temperature to T=2.3K,
thus improving both spatial and energy resolutions.
The conductance maps at three selected bias voltages
(among 256) are shown in Fig.3. The apparent size
and shape of the vortices depend sensitively on the
particular bias: Map (a), obtained at the SIS spectral
peak, eV≃∆tip+∆sample, shows a much larger diame-
ter than map (c), obtained at eV≃∆tip, which reveals
essentially the vortex core. Such an enlargement is
precisely due to the Doppler effect of the screening
currents. Map (b), obtained at the SIS/SIN crossing-
point voltage (V6in Fig. 2b) where little contrast was
expected, reveals a particular star shaped halo.
FIG. 3: Conductance maps of a 210×210 nm2area, T=2.3
K, applied field .05 T. Maps selected at voltages: V =2.6
mV, 2.2 mV and 1.6 mV corresponding to (a) the SIS peak,
(b) the SIS/SIN intersection point and (c) the NIS peak.
These emphasize respectively: (a) the long range varia-
tions in the SIS peak height, (b) the vortex star shaped
halo and (c) the vortex core. The scale of each map is
readjusted to obtain the best contrast, hence the apparent
lower resolution in (b).
The dynamics of the spectral shape, for different
distances from the vortex center, is displayed in Fig.4.
To reduce noise, each spectrum is the average over a
circle of radius r, concentric with the vortex. One
clearly sees the evolution from a SIS spectrum (A)
obtained far from the vortex, with a wide apparent
gap and pronounced peaks, to NIS spectra with low
peaks and a narrower gap, obtained in the vicinity of
the core. At even smaller distances (r<
observe a subtle dip - hump feature (D, H) developing
just above the gap edge, becoming more pronounced
as we approach the vortex center (B). There, a slight
increase of the amplitude of the peak is observed. The
effect is the signature of the vortex core states which
exist near the Fermi energy, but which are shifted to
a voltage above ∆tip/e in our case.
∼10 nm) we
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FIG. 4: Evolution of the conductance spectra as a func-
tion of distance from the vortex center. Far from the vor-
tex (A) the spectra show SIS features with high peaks at
(∆tip+∆sample)/e. The peak height is first lowered and
then followed by a shift to a lower voltages, near ≃ ∆tip/e.
Close to the vortex center (B) a dip hump feature appears
(D, H), associated with a slight increase in the peak.

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The spatial changes in the spectra, as a function of
distance r from the core, are summarized in Fig. 5 by
the plots of the peak position and amplitude. Start-
ing from a large distance, the peak height, initially at
2.4, is continuously diminished, finally leveling off at
a value ∼1.5 at r = rc≃ 110˚ A (dashed line). This
lowering of the peak amplitude (predicted in Fig.1b
and clearly visible in Fig. 4) is due to the increase in
the superfluid velocity as one approaches the vortex
core, which saturates at the critical velocity, v ≃ vc
at r ≃ rc. On the contrary, the peak energy is roughly
constant (at ∼2.6 meV) for all r>
creases rapidly (r ∼ rc) down to its minimum value
∼1.8 meV at the vortex center. Thus, the peak posi-
tion as a function of r, shifted downwards by ∼ ∆tip,
matches the pair potential profile. As the mid-point
of this profile is commonly used to estimate
find directly ξ ≃ 80˚ A and from the peak amplitude
profile, λ ≃ 750˚ A. In short, Fig.5 gives a picture of the
pair potential and supercurrent profiles of a vortex, of
core radius rc.
∼2rcbut then de-
√2ξ, we
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FIG. 5:
(squares) as a function of distance from the vortex center.
Inset shows the Doppler shift energy, in units of ∆NbSe2,
as a function of distance from the vortex core (circles).
The solid line is a theoretical fit,
best fit obtained using λ=68 nm and ξ=6.6 nm.
Gap-edge peak energy (circles) and amplitude
π
2
ξ
λK1(r/λ) with the
The values of λ and ξ may be extracted in a differ-
ent way, through the Doppler shift energy (from Eq.
1) as a function of r (see inset of Fig.5). We have
fitted the data with the function:
rived from the London equation for an isolated vortex,
where K1(x) is the modified Bessel function of order1.
(This approximation neglects Fermi surface and gap
anisotropies.) The best fit is found using ξ=66˚ A and
λ=680˚ A and is shown as the line in the inset. Finally,
the Doppler shift at r = ξ, together with the Fermi
momentum mvF = ¯ hkF ≃ ¯ hπ/2a, where a ≃ 3.5˚ A is
the lattice constant, leads to vc≈ 180 m s−1for the
magnitude of the critical velocity.
Our results, i.e. the vortex mapping using a SC
tip, the detailed evolution of the SIS to SIN spectra,
and the Doppler shift energy variation with distance
from the core, all indicate that no perturbation was
observed, arising from an interaction between the SC
π
2
ξ
λK1(r/λ), de-
diamagnetic tip and the vortices. Furthermore, the
Nb tips remain superconducting even under a field up
to ∼ 0.3 T (the field in the vortex core for an applied
field of 0.05 T) a higher value than the bulk critical
field, 0.2 T. Our previous studies on the effect of mag-
netic fields on our Nb tips, with a normal metal Au
sample, have shown that the tip critical field is en-
hanced up to 1 T (at T=4.2K). This result is due to
the tip’s apex size being smaller than both ξ and λ
with the critical field depending on the exact tip ge-
ometry [18]. In a small number of experiments, cur-
rently under study, we did observe a distorted vortex
shape.
In conclusion, we have presented detailed STS map-
ping of the vortex lattice using a superconducting tip,
which opens new possibilities for studying the velocity
profile of the pair currents, in any SC sample (type I
included). We have demonstrated that the features in
the sample DOS are shifted in energy by an amount
∆tip, as expected, but the principle result is the direct
effect of the Doppler shift on the SIS peak amplitude,
allowing a detailed mapping, on the nanometer scale,
of the currents in the superconductor. It could then
be applied to cases where there is an external cur-
rent source, an oblique magnetic field, or to confined
superconductors, where giant vortices are predicted.
The presence of spontaneous local currents in high-
Tc superconductors, near the low-temperature pseu-
dogap transition, could be checked. Finally, we have
demonstrated the stability of our Nb tips for use in
STS, paving the way for the future measurement of
the Josephson current.
The authors thank F. Debontridder and F. Breton for
their technical assistance. Sample preparation was sup-
ported by the NCCR research pool MaNEP of the Swiss
NSF.
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