Table Of ContentIn-Chain Tunneling Through Charge-Density Wave Nanoconstrictions and
Break-Junctions
K. O’Neill, E. Slot, and H. S. J. van der Zant
Kavli Institute of Nanoscience Delft, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands
R. E. Thorne
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853
6
(Dated: 19 December, 2005)
0
0 We have fabricated longitudinal nanoconstrictions in the charge-density wave conductor (CDW)
2 NbSe3 using a focused ion beam and using a mechanically controlled break-junction technique.
n Conductance peaks are observed below the TP1= 145K and TP2= 59K CDW transitions, which
a correspond closely with previous values of the full CDW gaps 2∆1 and 2∆2 obtained from photo-
J emission. These results can be explained by assuming CDW-CDW tunneling in the presence of an
9 energy gap corrugation ǫ2 comparable to ∆2, which eliminates expected peak at ∆1 +∆2. The
nanometer length-scales our experiments imply indicate that an alternative explanation based on
] tunnelingthrough back-to-backCDW-normal junctions is unlikely.
l
e
-
r Charge-density wave (CDW) conduction remains of
t
s major interest despite its experimental discovery nearly
.
t 30 years ago. Much of the existing work has focused
a
on transport properties of as-grown single crystals [1].
m
More recently, micro/nanofabricationmethods for CDW
- materials has allowed the study of mesoscopic CDW
d
n physics [2, 3, 4]. Structures for tunneling spectroscopy
o are of particular interest because of the unusual gap
c structure with large one-dimensional fluctuation effects
[ expected in these highly anisotropic materials, and be-
3 cause of predictions of unusual mid-gap excitations of
v thecollectivemode[5]. Tunnelingstudiesinfullygapped
1 CDW conductors like the ”blue bronze” K MoO suf-
0.3 3
7 fer from band-bending effects at the interface akin to
1
semiconductor-insulator-metal junctions. These effects
9
are absent in the partially gapped CDW conductor
0
NbSe , which remains metallic down to 4.2K.
5 3 FIG. 1: (a) Differential conductance dI vs applied voltage
0 dV
Tunneling perpendicular to the direction b of quasi- at T=4.2Kof aFIB-fabricated NbSe3 nanoconstriction. (b)
/
t one-dimensional chains, along which the CDW wavevec- and (c) show images taken in theFIB duringfabrication.
a
torlies,hasbeenstudiedinribbon-likewhiskersofNbSe
m 3
by Scanning Tunneling Microscopy (STM) [6], by lead
d- contacts evaporated over the native oxide on the b−c NbSe3 single crystal, produced by dry etching with a
n plane [7, 8], and by tunneling through a gold wire or a Ga Focused Ion Beam (FIB), shows conductance peaks
o NbSe crystal that is laid across another NbSe crystal, at 106mV and 190mV corresponding to 2∆ and 2∆ ,
3 3 1 2
c forming junctions in the a − b or b − c planes [9, 10]. as illustrated in Figure 1. We reproduce the data at
:
v Peaks in the T=4.2K differential conductance at 35 and 4.2K using a Mechanically Controlled Break-Junction
i 101mV [6], 35mV [7], 36mV and 90mV [9], and 37mV (MCBJ) technique, demonstrating that the FIB results
X
and 100mV[10] frommetal-NbSe junctions correspond are not dominated by Ga ion damage. Our results can
3
r well with the CDW gaps ∆ =110mV and ∆ =45mV be explained by CDW-CDW tunneling in the presence
a 1 2
for NbSe ’s T = 145K and T = 59K CDWs as ofalargetransversegapcorrugation,althoughtunneling
3 P1 P2
determined by angle-resolved photo-emission (ARPES) through back-to-back CDW-normal junctions cannot be
[11]. CrossedNbSe -NbSe crystals[9]yieldedpeakvolt- conclusively ruled out.
3 3
ages of 60mV and 142mV, and interlayer tunneling in CDWs form in metals with quasi-one-dimensional
micro-fabricated NbSe mesas yielded peaks at 50mV Fermi surfaces. Electron-hole pairs near the Fermi level
3
and120mV[3]. Asingle in-chaintunneling study [2]us- k form a macroscopic condensate and associated peri-
F
ing a gold ribbon mechanically positioned near the end odic modulations of the electron density and atomic po-
of a NbSe crystal gave a peak at 100mV for the T sitions. The condensate arises from the electron-phonon
3 P1
CDW. interaction, as described by the mean-field Hamiltonian
Here we demonstrate that a small constriction in a HP = Pkσǫka†kσakσ − Pkσ(cid:16)a†kσak+kFσ∆eiφ+h.c.(cid:17)
2
[12], where a a† is the electron creation (annihila- (a)
kσ (cid:16) kσ(cid:17)
tion) operator for the states with wavevector k and spin 1.5 lk
σsa.teLipkreocdouncveesnpteioankaslinsutpheerdcoennsdiutyc-toofr-ss,ttahteesC(DDOWSc)oantd±en∆- (kΩ) 1.0 ρ bu
rtoelramtivoedetlofothreelFeecrtmroinetnuenrngye.linAgpipnlysuinpgertchoensdeumctiocornjudnucc-- V/dI 0.5 V=0 0 T (K) 250
d
tions [13] to CDW systems, tunneling between occupied
V=200mV
and unoccupied states in a CDW-insulating-CDW junc- 0.0
tionshouldproducepeaksintheconductanceatvoltages
0 100 200 300
equalto ±2∆. In a CDW-normaljunction, peaks should
e
be observed at voltages equal to ±∆. temperature (K)
e
(b)
TofabricatenanoconstrictionsusingtheFIB,asingle- 4
crystal whisker of NbSe with a typical width of 20µm
3
was placed on a silicon dioxide/silicon substrate having ) 3
2µmwideAuelectricalcontactsthatwerepre-patterned S
m
byphoto-lithographictechniques. TheNbSe3crystalwas V( 2
then carved using an FEI/Philips FIB-200 focused ion d
/
beam. Atlowmagnification(10,000×),twolargetrans- dI 1 FIB
verse cuts were made from either side to create a con- dI/dV-0.5 mS
striction in the b/b⋆ direction. At high magnification (c)
(50,000×), further line cuts were made at low currents
)
of 350pA until the constriction had a width of around S 14
m
100nm and its resistance (which dominated the overall ( 12
V
sample resistance) exceeded 150Ω at room temperature. d
/ 10 MCBJ
Images ofboth cuts, takenin the FIB, are shownin Fig- I
d
ure 1(b). To find the cross-sectional dimension of the
junction we can make a simple estimate using the clas- -200 0 200
sical (diffusive) resistance formula, the contact’s room
voltage (mV)
temperature resistance of 165Ω,NbSe3’s bulk resistivity (d)
(1.86Ωµm),andacontactlengthofaround100nm(esti- 200
upper transition
matedfromthedeviceimageinFigure1(b)),whichgives
T =145K
a conducting area of roughly 20 nm2. P
150
Differential conductance versus voltagedata was mea- V)
m
sured between T = 145K and 4.2K using a conven- (
P1
tional four-probe technique [14]. Figure 2(a) shows that e 100
g
a
theconstriction’szero-biasresistanceincreasesmonoton- t
l
ically with decreasing temperature, and at 4.2K has a o
v
50
value close to 2kΩ. This contrasts with the bulk be-
lower transition
havior of NbSe3, which shows large resistance increases T =59K
P
just below the two Peierls transitions and then a strong
0
metallic (roughly linear) decrease down to 4.2K (inset).
0 40 80 120 160
To fabricate constrictions by the mechanically-
controlled break-junction technique, a single crystal temperature (K)
whisker of NbSe was placed on a Kapton-tape capped
3
piece of flexible phosphor-bronze. The crystal was held
totheKapton,whichhadpre-patternedgoldgoldelectri- FIG. 2: (a) ddVI of the FIB nanoconstriction at V = 0mV
and V = 200mV as a function of temperature. Anomalies
calcontacts,usingcellulose. Thecrystalwascontrollably
due to the two Peierls transitions at 145K and 59K seen
brokenat4.2Kina custom-builtcryostat[15], whichal-
in the bulk resistivity (inset) are absent. (b) dI vs volt-
lowed the sample to be broken and re-contacted several dV
age of the FIB constriction at temperatures (top to bottom)
times in the course of an experiment. Transport mea-
of 4.2K, 20K, 30K, 40K, 50K, 80K, 100K, 120K, 130K,
surements at T = 4.2K were performed in two-probe 135K, 140K and 145K. The 4.2K data is repeated, offset
configuration, with a contact resistance of ∼ 10Ω es- downward by −0.5mS, for clarity. (c) dI vs voltage of the
dV
timated from the total sample plus contact resistance break-junctionsampletakenatdifferentstresses/separations.
before breaking. Because of the quasi-one-dimensional (d)Temperaturedependenceofpeakpositionsobtainedfrom
bonding and very strong bonds along the chains, the theFIBconstrictiondataof(b)(filledcircles)comparedwith
NbSe crystal’s response to stress likely involved succes- X-ray diffraction experiments of the CDW order parameter
3
sive breaking of fibers within its cross-section, as in the [16] (open squares).
3
breaking of a rope. (a)
Figure 2(b) shows the differential conductance of the
FIB sample as a function of voltage for several temper-
atures, with the lowest temperature differential conduc-
tance offset downwards for clarity. At T = 4.2K, peaks 2∆
occur at ±105meV and ±190meV, symmetric around 2
zero bias, with a width ∼ 30meV and an estimated er- EF 2∆1
ror∼6meV.Thepeakpositionsmovetosmallervoltage 2ε2
with increasing temperature. Above its corresponding
∼ 2T /3, each peak becomes an inflection, and above
P
E
T each inflection disappears, indicating a strict associ-
P
ation of each peak with each Peierls instability. Figure
2(c)showsthecorrespondingdataatT =4.2Kfromthe 0 π/b
MCBJ sample. Peaks are clearly visible at ±81mV and kperp DOS N(E)
±196mV.
(b)
The agreement between the MCBJ and FIB samples
indicatethatthetransportpropertiesoftheFIBsamples V
e
are not qualitatively changedby any damage or disorder m
causedbyGalliumatoms. ThemeasuredT =4.2Kpeak ) ε1=0 50
pemosiistsiioonnscsporercetsrpooscnodpwyemlletaosruerceemnetnatnsgloef-rtehseolvfuedllpChDotWo- a.u. ε=2
(
gaps 2∆ and 2∆ of 90 and 220meV, respectively, [11]. V
1 2 d 0
Figure 2(d) shows the position of the conduction peaks I/ =
d 2
(orinflections)withtemperature. Theirtemperaturede- ε
pendencecloselymatchesthatoftheCDWorderparame-
terdeterminedfromX-raydiffractionmeasurements[16].
Smallsub-gapfeaturesarealsoobservedinboththeFIB
and more clearlyin the MCBJ samples (indicated by ar- 0 50 100 150 200 250
rows), possibly due to soliton effects [5]. Careful anal-
voltage (mV)
ysis of Fig. 2(b) shows the absence of any feature at
∆1+∆2 ≃145meV, which might be expected for tunnel-
e
ingbetweentheTP1 CDWononesideoftheconstriction FIG. 3: Semiconductor model for transitions between quasi-
and the TP2 CDW on the other. particle excited states of the CDW, with corrugation ǫ2
Theconductancepeakwidthsdonotsignificantlyvary present in the transverse momentum direction of the TP2 =
below TP for either transition, implying a temperature- 59KbutnottheTP1=145KCDWstates. (a)Left: Density
indepen2dent intrinsic broadening of the CDW DOS. of states N(E,k⊥) as a function of perpendicular wavevec-
Down to the lowest temperatures, the conductance also tor and energy, showing how corrugation of the TP2 CDW
changes the relative positions of the DOS maxima. Brighter
shows a substantial tail as the voltage decreases below
regionsdenotehigherDOS.Right: Projection ofN(E,k⊥)at
tahtetghaepn,oinmdiincaaltignagptheantertghye.DTOhSisdoisesconnostisctuetnotffwsihtharopply- a fixed wavevector k⊥ = πb. (b) Simulated ddVI vs. V using a
BCSdensityofstatesbroadenedby24meV,andcorrugations
tical absorption measurements [17], and calculations of ǫ2 = 0 and 50meV. All calculations assume ∆1 = 100meV
the zero-temperature CDW DOS with one-dimensional and ∆2 =41meV.
fluctuations [18]. Suppression of conductance peaks at
> 2T /3 for each CDW is likely due to the strong ef-
P
fect of thermal fluctuations on the DOS in a quasi-one-
NbSe tunneljunctions atlowbiases[8]andofbulk low-
dimensional system [19]. 3
temperature thermal and electrical conduction [22] have
Our results may be explained in terms of CDW-CDW
both suggested a transverse bandwidth comparable to
tunneling in the presence of a transverse corrugation of
the T gap itself.
P2
the T CDW’s energygap, asshownin Figure 3. Inter-
P2
We consider a semiconductor tunneling model [13] in-
chaincouplingresultsinbandstructuredispersioninmo-
menta perpendicular to the chains (b−direction), which cluding finite transverse dispersion in the c−direction.
This dispersion is characterized by a single parameter
should produce transversecorrugationsin the CDW gap
andimperfect nesting[20]. InNbSe3,the measuredelec- ǫ0 = 2tt2⊥bcsoins((bbkkFF)), t⊥ and tb being the bandwidths of the
trical anisotropy implies a bandwidth in the c−direction dispersion perpendicular and parallel to the chains, and
a factor of 10 larger than in the a−direction, qualita- b the inter-chain separation. Figure 3(a) illustrates this
tively consistent with band structure calculations [21], dispersion, showing by brightness the density of states
so that the former should dominate in tunneling involv- N(E,k )asafunctionofenergyandperpendicularwave
⊥
ing the T gap. Analysis of measurements on metal- vector within one half Brillouin zone (left), and the den-
P2
4
sityofstatesataN(E)atafixedwavevector(right). The spite the strong zero-bias low-temperature resistance in-
conductanceisthencalculatedbyintegratingtheproduct crease, the FIB constriction shows no hints of anomalies
N(E,k )N(E−eV,k )overallenergiesE andwavevec- atthetwoPeierlstransitions. Theseareclearlyseeneven
⊥ ⊥
tors k , assuming a BCS T = 0 DOS broadened by a inthesmallestcross-sectionnanowires(500nm2)studied
⊥
Gaussiandistribution ofwidth σ =24meVto mimic the to date.
experimental peak broadening. The computed dI(V) The back-to-back junction interpretation might be vi-
dV
curves for ǫ2 = 0 (no corrugation) and ǫ2 = 50meV are able if the FIB somehow disorders the constricted re-
shown in Figure 3(b). As expected, with no corruga- gion in a way that eliminates the Peierls transitions and
tion ddVI(V) exhibits a strong peak at (∆1 +∆2)/e. As causes the resistance to increase strongly with temper-
ǫ2 is increased, this peak splits in energy and shrinks in ature, while producing a resistivity whose magnitude is
height. While all conductance peaks remain visible with smallerthaninnanowireshavingsimilartemperaturede-
a divergent DOS, with a broadened DOS the peaks at pendence. But even in this case the observed zero-bias
∆1 + ∆2 − ǫ2 and 2∆2 merge at around 100meV, re- junction resistance cannot easily be accounted for [24].
sultinginaconductancecurvethatcloselyresemblesthe In addition, the relevance of the back-to-back junction
presentdata. The transversegapcorrugationwe assume explanation to MCBJ samples, where the sample has
to obtain the best fit to our data is in agreement with simply been broken and brought back close together is
the conclusion of Sorbier et al. [8] that the corrugation unclear due to the absence of an intermediate conduct-
forthe TP2 CDWǫ2 is slightlylargerthantheCDWgap ing structure. We therefore attribute the conductance
∆2. peaks in our devices to CDW-CDW tunneling.
An alternative explanation is that the peak structure In conclusion, we have fabricated in-chain nanocon-
results from back-to-back N-CDW junctions. Provided strictionsinaCDWmaterial. Theseconstrictionsbehave
that the relaxation length of the non-equilibrium distri- like a tunnel junctions, and conductance peaks are ob-
butions is long compared with the characteristic length servedat biases that correspondwell with the full CDW
of the transition from CDW to normalstates, one would gaps 2∆ and 2∆ determined from independent mea-
1 2
expect ddVI peaks corresponding to 2∆1 and 2∆2, and no surements. The peaks disappear at around two-thirds
intermediate peak. We can estimate the dimensions of the respective Peierls transition temperature, in agree-
the constricted region assuming that the narrow region ment with calculations of the effects of fluctuations on
consists of NbSe3 chains. The length of the constriction the DOS for one-dimensional compounds.
can be determined by comparing the low-field residual WethankS.Za˘itzev-ZotovandS.Artemenkoforfruit-
resistanceratio RR((TT==249.23KK)) with NbSe3 nanowiresofdif- ful discussions. This work was supported by the Inter-
ferent cross-sectional dimensions [23]. We find that our national Association for the Promotion of Co-operation
FIB junction most closely resembles a wire with resis- with Scientists from the New Independent States of the
tance per unit length R/L∼ 106 Ω/µm at 4.2 K, corre- Former Soviet Union (INTAS-NIS), the Foundation for
sponding to a cross-section of 600nm2. From the mea- Fundamental Research on Matter (FOM), and the Na-
sured junction resistance R(T = 4.2 K) = 1798 Ω we tional Science Foundation (NSF) (Grants No. DMR
obtain a junction length ∼ 1.8nm. This is compara- 0101574 and No. INT 9812326). K.O’N. was supported
ble to the known CDW amplitude coherence length in by the Marie Curie Fellowship organization. We thank
NbSe , and is too short to allow the full loss of CDW J.vanRuitenbeek forthe useofequipmentinthe MCBJ
3
orderrequiredto achievethe tunneling characteristicsof work, and S. Otte and R. Thijssen for technical assis-
back-to-back CDW-normal junctions. Furthermore, de- tance.
[1] G. Gru¨ner, Rev.Mod. Phys. 60, 1129 (1988). Rev. Lett.76, 676 (1996).
[2] A. A. Sinchenko, Y. I. Latyshev, S. G. Zybtsev, I. G. [9] T. Ekino and J. Akimitsu, Japanese Journal of Applied
Gorlova,andP.Monceau,Phys.Rev.B60,4624(1999). Physics 26, 625 (1987).
[3] Y. I. Latyshev et al., J. Phys. A: Math. Gen. 36, 9323 [10] T.EkinoandJ.Akimitsu,PhysicaB194-196,1221-1222
(2003). (1994).
[4] S.V.Za˘itsev-Zotov,Physics-Uspekhi6,533(2004);S.V. [11] J. Sch¨afer et al.,Phys. Rev.Lett. 91, 066401 (2003).
Za˘itsev-Zotov, V. Y. Pokrovski, and P. Monceau, JETP [12] H.Fr¨ohlich,Proc.R.Soc.LondonSer.A223(1954); R.
letters 73, 25, (2001). E.Peierls,QuantumTheoryofSolids (OxfordUniversity
[5] S. Brazovskii, I. E. Dzyaloshinskii, and I. M. Krichever, Press, 1955).
Physics Letters A 91, 40 (1982). [13] G. E. Blonder, M. Tinkham and T. M. Klapwijk, Phys.
[6] Z. Dai, C. G. Slough, and R. V. Coleman, Phys. Rev. B Rev. B 25, 4515 (1982).
45, R9469 (1992). [14] TwootherFIBsampleswithinsulatingpropertiesshowed
[7] A.Fournel,J.P.Sorbier,M.Konczykowski,andP.Mon- features near 2∆1 and 2∆2. One of these had inflection
ceau, Phys.Rev. Lett.57, 2199 (1986). points near 200 mV and 106 mV, the other had a peak
[8] J.P. Sorbier,H.Tortel, P.Monceau, and F.Levy,Phys. at 170 mV and an inflection at ∼100 mV.
5
[15] J. M. van Ruitenbeek et al., Rev. Sci. Instrum. 67, 108 [22] G. Mih´aly, A. Virosztek, and G. Gru¨ner, Phys. Rev. B
(1996). 55, R13456 (1997).
[16] R. M. Fleming, D. E. Moncton, and D. B. McWhan, [23] E. Slot, M. A. Holst, H. S. J. van der Zant, and S. V.
Phys.Rev.B 18, 5560 (1978). Za˘itsev-Zotov, Phys. Rev.Lett. 93, 176602 (2004).
[17] A. Perucchi, L. Degiorgi, and R. E. Thorne, Phys. Rev. [24] The boundary between metallic and non-metallic be-
B 69, 195114 (2004). haviour lies at the resistivity of roughly 150mΩcm (J.
[18] K.Kim,R.H.McKenzie,andJ.W.Wilkins,Phys.Rev. H.Mooij,Phys.Stat.Sol.(a),17,521(1973)).Conserva-
Lett.71,4015(1993);R.H.McKenzieandJ.W.Wilkins, tivelytakingthejunctioncross-sectiontobe100×100nm
Phys.Rev.Lett. 69, 1085 (1992). and themeasured room temperatureresistance of about
[19] P. A. Lee, T. M. Rice, and P. W. Anderson, Phys. Rev. 150Ω,theconstrictionlengthwouldbe1nm,whichagain
Lett.31, 462 (1973). istoosmalltobeconsistentwithback-to-backtunneling.
[20] X. Huang and K. Maki, Phys. Rev. B 42, 6498 (1990);
X.Z.HuangandK.Maki,Phys.Rev.B40,2575(1989).
[21] J. Sch¨afer, private communication.
