Ultrafast dynamics in the presence of antiferromagnetic correlations in electron-doped cuprate La$_{2-x}$Ce$_x$CuO$_{4\pm\delta}$

0.55 MB·

by  I. M. Vishik

Ultrafast dynamics in the presence of antiferromagnetic correlations in electron-doped
cuprate La Ce CuO
2−x x 4±δ
I. M. Vishik,∗ F. Mahmood,† Z. Alpichshev, and N. Gedik
Massachusetts Institute of Technology, Department of Physics, Cambridge, MA, 02139, USA
J. Higgins and R. L. Greene
6 Center for Nanophysics and Advanced Materials, Department of Physics,
1 University of Maryland, College Park, MD, 20472, USA
0 (Dated: August 19, 2016)
2
We used femtosecond optical pump-probespectroscopy to study the photoinduced change in re-

g flectivityofthinfilmsoftheelectron-dopedcuprateLa2−xCexCuO4(LCCO)withdopingsofx=0.08
u (underdoped) and x=0.11 (optimally doped). Above Tc, we observe fluence-dependent relaxation
A rates which onset at a similar temperature that transport measurements first see signatures of an-
tiferromagnetic correlations. Upon suppressingsuperconductivity with a magnetic field, it is found
7
that the fluence and temperature dependence of relaxation rates is consistent with bimolecular
1
recombinationofelectronsandholesacrossagap(2∆AF)originatingfromantiferromagneticcorre-

lations which comprise the pseudogap in electron-doped cuprates. This can be used to learn about
]
n coupling between electrons and high-energy (ω > 2∆AF) excitations in these compounds and set
o limits on thetimescales on which antiferromagnetic correlations are static.
c
-
r
p I. INTRODUCTION point to a phase diagram where AF coexists with super-
u conductivity at optimal doping in LCCO (x=0.11). On
s Several families of unconventional superconductors the other hand, low-energy µSR experiments indicated
.
t share a canonical phase diagram whereby a supercon- a more truncated AF phase, in which static order has a
a
m ducting dome emerges around the T=0 endpoint of an much more limited overlap with superconductivity, dis-
antiferromagnetic(AF)phase1. Thismaypointtoacom- appearing at x 0.0810. These two experiments are not
- ≈
d mon superconducting mechanism among organic, heavy necessarily in conflict, as the two are sensitive to very
n fermion, pnictide, and cuprate superconductors2, or it different timescales.
o may highlight one factor which is generally favorable for
c the formation of superconductivity. In electron-doped Ultrafast optics can access the timescales interme-
[
cuprates, the AF phase is more robust than on the hole- diate between electron relaxation times probed by

2 doped side and may coexist with superconductivity to a transport ( 10-100 fs) and the typical Larmor fre-
≈
v greater degree3. quency associated with the internal fields (0.1 µs).
4 In electron-doped cuprates which can be synthesized Optical pump-probe experiments on optimally-doped
9
6 as bulk single crystals, neutron scattering is typically Nd2−xCexCuO4±δ (NCCO) have indicated that short-
6 used to assess the onset of long-range AF order at the range AF correlations manifest in scaling behavior
0 N`eel temperature (TN) and the finite correlation length of the transient reflectivity, and that signatures of
1. at T>TN. Unlike hole-doped cuprates where the ori- these correlations persist below Tc and compete with
gin of the normal state pseudogap is still debated, the superconductivity11.
0
6 ’pseudogap’ in electron-doped cuprates, first reported as
1 a suppression of spectral weight in optics below a char- Here we show time-resolved optical signatures of AF
: acteristic temperature T∗4 (sometimes called T 5), is correlations in electron-doped cuprates, and use relax-
v W
widely thought to originate from in-plane AF correla- ation rates measured in these time-domain experiments
i
X tionswithcorrelationlengthlongerthanthe thermalde- tosetlimits ontheAFcorrelationtime andthe strength
r Brogliewavelength6,7. TheregimewhereAFcorrelations of coupling between electrons and high energy (ω
a ≥
are present is marked by a single-particle gap of magni- 2∆ ) bosons. We have measured photoinduced reflec-
AF
tude ∆ 9k T∗ appearing at energy and momenta tivity (∆R/R) in LCCO and extracted the temperature
AF B
consistent w≈ith (π,π) band folding5,8. andpump-fluencedependenceoftheinitialrateatwhich
La Ce CuO (LCCO) has the highest maximum ∆R/Rdecaysbacktoequilibrium. AboveT inbothun-
2−x x 4±δ c
T among electron-doped cuprates and exhibits super- derdoped and optimally doped samples, AF correlations
c
conductivityatlowerdoping,butitcanonlybestabilized manifest as pump-fluence-dependent decay rates which
asathin filmwhichprohibits characterizationofantifer- are characteristic of a fully-formed gap in the density
romagnetism via neutron scattering. Instead, AF which of states (DOS). When superconductivity it suppressed
is static on timescales of electron-relaxation times but withamagneticfield,itisrevealedthatthe temperature
notnecessarilylong-rangehasbeenidentifiedviaangular andfluencedependenceofinitialdecayratesisconsistent
magnetoresistance (AMR)9 with a characteristic onset with pairwise recombination of electron-hole excitations
temperature called T . These transport measurements across ∆ .
D AF
2
II. METHODS occupied states. In general, this initial excitation has
higherenergythanthelowest-lyingexcitationsinthesys-
tem. Depending on the specific system under investiga-
Ultrafastpump-probeexperimentsemployshortpulses
tion,thelowestlyingexcitationmightbethebandgapof
of light (< 1ps) to create new electronic states, destroy
a semiconductor, the single particle gap due to a charge
electronic states, or make targeted excitations in solids.
density wave (CDW) or a spin density wave (SDW), or
The latteroptionisthe focus ofthis study. Theseexper-
the superconducting gap energy (2∆). After the initial
imentsconsistoftwopulsesseparatedintime: thepump
excitation, there is typically a cascade of relaxationpro-
pulseperturbsthesampleandtheprobepulsestudiesthe
cesses driven by electron-electron or electron-phonon in-
changesinelectronicproperties. Byvaryingthetime de-
teractionswhichresultinexcitationsprimarilyatthegap
laybetweenthe pump andthe probe,onecanstudy how
edge on sub-picosecond to picosecond timescales (Fig.
the non-equilibriumelectronicstate decaysback to equi-
7(b)14,15. A second assumption in the data interpreta-
librium,whichcangiveinformationabouttherelaxation
tion is that the magnitude of the change in reflectivity
processes which are relevant to the important emergent
at800nm, ∆R/R is proportionalto the number ofgap-
phases in condensed matter systems.
| |
energy excitations, and the time evolution is hence re-
Experiments were performed with a Ti:sapphire oscil-
latorlasingat800nm(~ω=1.55eV)producingpulses60 lated to the creation and annihilation of these excita-
tionsand/ortheir diffusionoutofthe excitationvolume.
fs in duration. The repetition rate of the laser was re-
Specifically, in electron-doped cuprates the excitations
ducedto1.6MHzwithapulsepickertomitigateagainst
we will consider are photoexcited quasiparticles (broken
steady-state heating of the sample. Experiments were
Cooperpairs)andelectron-holeexcitationsacross2∆ .
performed in two different cryostatsdepending if a mag- AF
netic field was applied or not. For data in Figs. 2 and It can be counterintuitive that excitations at energies
3, the sample was excited by a pump pulse of 70 µm orders of magnitude lower than the probe frequency of
FWHM diameter,andthe fluence (Φ) ofthe pumppulse 1.55 eV can cause changes in reflectivity at the probe
was varied between 8.7 and 0.1 µJ/cm2. For data in frequency. Thiscanberesolvedbynotingthatfrequency-
Figs. 4, 5, and 6 the sample was excited by a pump dependentreflectivityisrelatedtothecomplexdielectric
pulseof150µmFWHMdiameter,andΦpump wasvaried function which in turn is related to both the real (σ1)
between 2.3 and 0.08 µJ/cm2. Results from the two ex- and imaginary (σ2) part of the optical conductivity. Be-
perimental configurations are consistent. This study ac- causeofthe Kramers-Kronigrelationbetweenσ1(ω)and
cessedpump-fluenceslowerthansomeearlierstudies12,13 σ2(ω),whichisanintegraloverallfrequencies,changesto
with the goalof making a small number of electronic ex- σ1atsmallfrequencycanultimatelymanifestaschanges,
citations and not destroying the underlying order. The albeit small ones, to the reflectivity at much higher fre-
sample response was assessed through measurement of quencies. This has been modeled using parameters ap-
the normalized change in the reflectivity, ∆R(t)/R, of propriate to hole doped cuprates16, and it was shown
a separate probe pulse which was focused on the same that converting 1% of the condensate into quasiparticles
spot on the sample as the pump. For data in Figs. at the gap edge (50 meV) can produce changes in reflec-
2 and 3, Φ =0.9µJ/cm2. For data in Figs. 4, 5, tivity at 1.55 eV of order 10−4.
probe
and 6, Φ =0.4µJ/cm2. The probe fluence was cho-
probe
sen to maximize the signal-to-noise ratio while avoiding
steady-state-heating. The c-axis-orientedLCCO was de-
positeddirectlyoninsulating(100)SrTiO substratesby B. Rothwarf-Taylor Model
3
a pulsed laser deposition technique utilizing a KrF ex-
cimer laser. Two films with Ce concentrationsof x=0.08
The relaxation dynamics in the presence of a small
(underdoped) and 0.11 (optimally doped) were studied
energy gap, such as the one due to superconductivity
with T ’s of 22K and 25K, respectively. The annealing
c (SC), can be analyzed using the Rothwarf-Taylor (RT)
process was optimized for each doping. model17. These coupled differential equations consider
the time evolution of populations of excited quasipar-
ticles (n ∆R/R) which can recombine into Cooper
III. INTERPRETING OPTICAL PUMP-PROBE pairs, em∝itti|ng a b|oson, and the population of bosons
DATA IN ELECTRON-DOPED CUPRATES
(N) which can break Cooper pairs to create quasipar-
ticles. Originally, these equations described dynamics
A. What the pump does and what the probe in Bardeen-Cooper-Schrieffer(BCS) superconductors, in
measures whichpairformation/breakingisknowntobe facilitated
by high-frequency (ω > 2∆) phonons. However, this
In the experiments shown here, both the excitation modelhasprovedtobesuccessfulinothersystemswhich
(pump) and the reflectivity measurements (probe) are havesmallenergygapsclosetotheFermilevel18,suchas
done at the same frequency, 1.55 eV (800nm). At the heavyfermions19, CDWsystems20, andSDWsystems21.
intensities and frequency used in these experiments, the Additionally, the modelpermits pair breakingby bosons
pump initially makes excitations from occupied to un- other than phonons. The Rothwarf-Taylorequations are
3
given by: (0,π) (π,π) 1 (b) 2 (c) 3 (d)
(a)
dn 2∆
=I +2γ N βn2 (1) AF
dt qp pc − 1
2 2∆
AF
dN 1 3
=Iph+ βn2 γpcN (N Neq)γesc (2) 2∆AF
dt 2 − − −
(0,0) (π,0)
where I is an external source of quasiparticles or low
qp Momentum along cut
energy excitations in non-SC systems, γ is a pair cre-
pc
ation rate of photoexcited quasiparticles or other low-
FIG. 1. Schematic of fermiology and band structure in
energyexcitations,β isabimolecularrecombinationcon- electron-doped cuprates in the presence of q = (π,π) recon-
stant, Iph is a source of non-equilibrium phonons or struction, widely attributed to AF order. The SC gap is not
other bosons, Neq is the equilibrium population of pair- shown. (a)Fermisurface. DashedlinemarksAFzonebound-
breaking phonons or other bosons, and γ is the rate ary. (b)-(d)Schematicofdispersionalong3cutsshownin(a).
esc
at which these phonons/bosons either escape from the Cut 2 is through thehot spot.
excitation volume or decay into lower frequency bosonic
excitations.
Consideringthe caseofasuperconductorwithphonon C. Bimolecular recombination and data fitting
pair breaking, we discuss various regimes of the RT
model. In the unphysical case where γ = 0 and the In the regime where relaxation is set by bimolecular
esc
rate of pair creation is comparable to the rate of recom- recombination, the excitation density as a function of
bination (γ βn), the non-equilibrium population of time is given by
pc
≈
photoexcitedquasiparticlesismaintainedindefinitelybe-
∆R n(0)
cause of detailed balance between populations of quasi- (t) n(t)= (3)
particles and phonons. This is the so-calledphononbot- R ∝ 1+βn(0)t
tleneck. It should be noted that quasiparticle diffusion
where n(0) is the excitation density at the beginning
is not included in this formulation of the RT model.
of the recombination process, usually taken at the time
In a regime where γ is finite and it still holds that
esc
when ∆R/R is maximum. Additionally, one can ac-
γpc Bn,thephonon-bottleneckwillstillexist,although | |
≈ countfor the exponentially decreasingexcitationdensity
the n will decrease over time, at a rate determined by
asafunctionofdepthintothesampletoyieldacorrected
the relative values14 of γ , γ , and βn. Finally, if
esc pc transient reflectivity23:
γ γ or bn γ , the RT equations decouple
esc pc pc
≫ ≫
and the time evolution of the quasiparticle population
is determined by bimolecular recombination–thatis, two 2∆R(0) ln(1+γ t)
0
∆R= [1 ] (4)
quasiparticles (or an electron and a hole in the case of
γ t − γ t
0 0
other small-gap excitations) recombining with one an-
other: dn = βn2. where ∆R(0) is the reflectivity change at the sample
dt −
One characteristic of bimolecular-recombination- surface, γ0 βn(0,0), and n(0,0) is the excitation den-
≡
dominated dynamics is that the decay rate, γ0, depends sityatthesamplesurface. ∆R(0)andγ0 arefreeparam-
on the number of gap-energy excitations, which is eters in the fitting.
usually proportional to pump fluence. Putting these
these attributes together yields γ n. This charac-
0
teristic linear relationship between∝excitation density D. Considerations specific to electron-doped
and recombination rate has been observed in the cuprates
SC state of hole-doped cuprates22,23 and iron-based
superconductors24. When γ is plotted as a function Dynamical mean field theory (DMFT) calculations
0
of pump fluence or a proportional quantity, the slope haveindicatedthataround10%electrondoping,thepri-
is related to the bimolecular recombination constant, maryopticalexcitations permissiblewith a1.5eV pump
β, which has physical origins. For BCS supercon- are from the quasiparticle band into the upper Hubbard
ductors in the dirty limit, β is related to the ratio band26. Additional but less probable possibilities exist
of the electron-phonon coupling function weighted by forexcitationfromthe lowenergytail ofthe Zhang-Rice
the phonon DOS at the gap energy (α2(2∆)F(2∆)) singlet band (centered at -2.1 eV in Ref. 26) into the
to the electronic density of states at the Fermi level quasiparticleband. The quasiparticleband is implicated
(N(0))25. An analogous physical origin can be derived in both superconductivity and AF, and at this doping,
in non-SC systems where non-equilibrium dynamics are itsmomentum-integratedelectronicDOSissplitintotwo
dominated by bimolecular recombination, but in either peaksseparatedby2∆ oneithersideoftheFermilevel
AF
case, another characteristic of such a system is that the (E ).
F
slope of γ vs n is independent of temperature (T) for Without momentum-integration, some momenta have
0
k T well below 2∆. metallicbandscrossingE onwhichaSCgapcanopen.
B F
4
A schematic of the Fermi surface and low-energy band doping increases.
structure is shown in Fig. 1. In the regime where there Fig. 3showstemperaturedependenceacrossT ofnor-
c
is long-range AF order, the large hole-like fermi surface malized ∆R/R taken with pump fluence < 0.3µJ/cm2.
(FS) which is found in the overdoped regime, undergoes The negative component in ∆R/R persists below T in
c
band folding at q = (π,π), yielding hole and electron bothdopingsofLCCO.Inx=0.11,anadditionalcompo-
pockets. Agap(∆AF)(sometimescalled∆PG or∆SDW) nent with positive sign in ∆R/R emerges below Tc, as
is opened everywhere that the original band crosses the was earlier observed in optimally doped NCCO11. This
folded band. This gap is centered at EF only at the so- positivecomponentcanbeattributedtoSCbecauseitis
calledhot-spotmomentum, indicatedin Fig. 1(c); closer absent above T . In underdoped x=0.08 LCCO, ∆R/R
c
tothe Brillouinzonecenter,∆AF appearsaboveEF and remains negative below Tc. Magnetic field in the next
closer to the Brillouin zone boundary, it appears below sectionclarifiesthat∆R/Rinx=0.08consistsofanega-
EF8. As the AF correlation length becomes finite, the tiveAFcomponentsuperimposedonanegativeSCcom-
DOS inside the gap begins to fill in, and the gap is com- ponent.
pletely filled by T = T∗27,28. The depression of DOS in
the hotspots and the pseudogap observed by optics are
commonlyattributedtoshort-rangeAF,whichiswhywe V. ISOLATING AF COMPONENT WITH
use this terminology, but it should be noted that other MAGNETIC FIELD
types of order, such as d-density wave can produce the
same effect29.
In this section, we separate a SC component from an
AF component in ∆R/R by applying a magnetic field
close to H 2. From the fluence dependence of both, we
c
IV. RELAXATION DYNAMICS AT B=0 can infer the primary mechanisms of relaxation for low
energy excitations related to each state.
Inthissection,wepresentfluenceandtemperaturede- PCCO films with similar Tc (23K) were used as guid-
pendentdynamicsaboveTcandtemperaturedependence ance about Hc2 of our LCCO films at the measurement
ofnormalized∆R/Rfromlowtemperaturetojustabove temperatures of 11K and 12K36. In particular, the field
Tc. where in-plane resistivity, ρxx, begins to deviate from
Earlier time-resolved reflectivity studies on electron- high-field linear magnetoresistance, marked as H100 in
doped cuprates observed a negative ∆R/R at 800 nm Ref. 36, has been shown to be the field where the con-
above Tc, and attributed this feature to the pseudo- densate is extinguished. For x=0.15 PCCO (Tc=23K),
gap and/or in-plane AF correlations11,32. We observe H100 =7.5T(7T)at 11K (12K).
a similar feature and expand on previous studies by an- Fig. 4 shows the effect of a magnetic fields up to 6.5T
alyzingitstemperature andpump-fluence dependence in appliedparalleltothec-axisoftheLCCOfilms. Asmag-
Fig. 2. For this set of data, initial relaxation rates were netic field increases, ∆R/R in x=0.11 becomes negative
derived from fitting to a single decaying exponent af- at all times (Fig. 4(b)). This confirms that the posi-
ter the time when ∆R/R is maximum. The key find- tive component is associated with superconductivity in
ing is that ∆R/R in LCCO has fluence dependence x=0.11, as suggested from temperature dependence. In
above T , which is different from hole-doped cuprates x=0.08,the magnitude of ∆R/R decreases with increas-
c
where pump-fluence-dependence is absent above T 23. ingfield(Fig. 4(a)), indicatingthatthe superconducting
c
This fluence dependence is evident both from examin- componenthasthesamesignastheAFcomponent(neg-
ing normalized data (Fig. 2 (a)-(b),(d)-(e)) and by fit- ative)atthisdopingandprobefrequency. Inbothcases,
ting the data (Fig. 2(g)-(h)). The fluence dependence excitationsacrosstheSCgapandacrosstheAFgapgive
is absent at temperatures higher than where transport distinct contributions to ∆R/R. Long-lived excitations
measurements demarcate AF correlations at T (Fig. across the AF gap may be the reason that near-infrared
D
2(c),(f)). The same behavior is observed in thin films pumping was shown to extinguish the superconducting
of Pr Ce CuO (PCCO)(Fig. 2(i)) indicating that condensate at a much higher intensity than expected37.
2−x x 4±δ
this fluence dependence in the regime where AF corre- Anominalsuperconductingcomponentisextractedby
lations are observed by transport is generic to electron- subtracting the maximum-field data from the zero-field
dopedcuprates. AboveT ,γincreaseswithtemperature data, and this is shown in Fig. 4(c)-(d) and as the pur-
D
following a power law (Tα) with an exponent α between ple dashed lines in Fig. 4(a)-(b). This subtraction pro-
1 and 2, with values which decrease with doping when cedure is most accurate if there is no microscopic coex-
severalfamiliesarecompared(Fig. 2(j)). Inmetallicsys- istence between superconductivity and the AF normal
tems,thehigh-temperaturerelaxationratehasbeencon- state, and distinct regions of the sample contribute to
nected to the strength of electron-phonon coupling33,34, AF and SC. In the case of microscopic coexistence be-
which in cuprates, has been shown to weaken with in- tween AF and SC, two complications can arise: com-
creasing doping35. A further possible relaxation mecha- petition between the two orders, which would affect the
nism in electron-doped cuprates is spin excitations, and magnitude of the gaps themselves, and populations of
the influence of magnetism progressively gets weaker as photoexcited quasiparticles and excitations across ∆
AF
5
0 (a)
8% (c)
(b)
−0.5
d)
ze 26K 45K 85K
ali
m −1
nor 0 11%
R ( (f)
R/ 85K
∆
−0.5 8.7 µJ/cm2
27K 45K 3.0
1.1
−1 (d) (e) 0.33
0 10 20 0 10 20 0 10 20
time (ps) time (ps) time (ps)

8.7µJ/cm2 8% (g) 2 (h)
2 3.0
80K
1.1
1 0.33 1 55K
γ ∼ T1.9 ± 0.1 11%
−1 (ps)γ .5 −−021x 10−4 −1 (ps)γ .5 8.7µJ/cm2
.2 R/R∆−−43 ∆R/R~e-γt 31..01
.1 −5 1µJ/cm2 .2 0.33
−6 T=45K γ ∼ T1.5 ± 0.04
−7
.05 0 10 20 30 40
time (ps) 0.1
20 50 100 200 20 50 100 200
Temperature (K) Temperature (K)
2 R
1 83..70µJ/cm2 50K (i) 114200 (j) elaxatio
n
1.1 1 ra
γ ∼ T1.4 ± 0.2 100 te e
.5 e xp
−1 (ps)γ TD,AMR Temperatur 8600 γ(t) e xLpCoCnOents (T>TD) 0 onent
PCCO
.2 40 NCCO (Hinton et al)
Onset of fluence
PCCO, x=0.14 20 dependence
TD
0.11 0 20 50 100 Tc
Temperature (K) 0
0.05 0.10 0.15 0.20
Cerium concentration, x
FIG.2. Temperatureandpump-fluencedependenceT>Tc. (a)-(c)x=0.08: normalized|∆R/R|atdifferentpumpfluencesand
three representative temperatures above Tc. Non-overlap of curves at lower temperatures indicates fluence-dependent initial
relaxation rates. (d)-(f)sameforx=0.11. (g)-(h)Relaxation rate, γ asafunction oftemperatureandfluencefor bothdopings
of LCCO above Tc. Vertical arrow marks onset of systematic fluence dependence. Dashed line shows power law fit in the
temperature regime where there is no fluence dependence of γ. Inset of (a) indicates that γ is extracted from fit to a single
exponential. (i) same for PCCO, x=0.14 (Tc≈22K). AMR value from Ref. 30. For comparison, optics yields an estimated T*
of 120K for this doping5. (j) Temperature scales in relation to transport experiments by Jin et al31. Filled circles mark the
temperatures derived in (g)-(i),and squares are relaxation rate exponentsfor LCCO, PCCO, and NCCO (Ref. 11)
being linkedto oneanother. Inthe formerscenario,sup- ferentforSCandAF,withtheformerhavingamaximum
pression of superconductivity can lead to enhancement magnitude of 3 5meV39–42 and the latter having a
of ∆ , if the two orders are antagonistic, as is seen in magnitude > 8≈0me−V3,5. Thus, the effect of suppressing
AF
iron-based superconductors38. However, for the case of SC on the magnitude of ∆ is not expected to be as
AF
electron-doped cuprates, the energy scales are quite dif- largeasitisinsystemswherethe competingordershave
6
(a) 5K relaxation times was observed in the superconducting
0 9K state23,45,46, indicating that initial quasiparticle recom-
13K
17K bination dynamics were consistent with bimolecular re-
−0.2
21K~T combinationofquasiparticles,ratherthanaphononbot-
c
d) 25K tleneck. Meanwhile, in electron-doped cuprates, the dy-
e
aliz−0.4 29K namics of the superconducting component appear to be
m 35K
or bottlenecked,withx=0.11showingalmostnofluencede-
R (n−0.6 pendence (Fig. 4(d) and x=0.08 showing little fluence
R/
∆ dependence (Fig. 4(c)) which may simply be presentbe-
−0.8
cause the condensate is not completely absent in the 6T
x=0.08 data as the normal state reference. The superfluid den-
−1 Φ=0.33µJ/cm2 sity is expected to decrease as √H in d-wave supercon-
0 10 20 30 40 ductorswithlinenodes47,48,andthissuggestsanapprox-
time (ps) imateremainingsuperfluiddensityequalto12%(3%)of
its zero field value for x=0.08 (x=0.11)LCCO measured
1 (b) at 11K (12K) and 6 T (6.5 T).
0.8 x=0.11
Φ=0.105µJ/cm2 Bimolecularrecombinationcandominatetheinitialre-
0.6
combination dynamics if either γ is small or if γ
pc esc
d) 0.4 is large. That is, if recombination is not balanced by
e
aliz 0.2 pairbreaking,either because the bosons formedfromre-
m
or 0 combinationhaveasmallprobabilityofbreakinganother
R (n −0.2 10K Cooperpair orbecause these bosonsescape fromthe ex-
R/∆ −0.4 1136 citationvolumeordecayintolowerfrequencyexcitations
before they canbreak another Cooper pair. The relative
−0.6 19
22 magnitude of the different terms in the Rothwarf-Taylor
−0.8 25K~T
c equations does not necessarily imply a certain pairing
−1 28
mechanism. For example, while underdoped hole-doped
0 10 20 30 40
time (ps) cupratesappeartohavenon-equilibriumdynamicsinthe
superconductingstatethataredominatedbybimolecular
FIG. 3. Temperature dependence across Tc. (a) x=0.08 (b) recombination of quasiparticles, overdoped hole-doped
x=0.11. Both data sets havebeen normalized by dividingby cuprates (like electron-doped cuprates) show very lit-
themaximum of |∆R/R| tle fluence dependence in the superconducting state45,
eventhoughpresumablythesamepairingmechanismex-
ists at all dopings. Similarly, among BCS superconduc-
more similar energy scales. The second scenario where tors which have a phonon-mediated mechanism, fluence-
simple subtractionmight not accurately yield the super- dependence recombination rates have been observed in
conducting component is potentially more serious, and some systems49.
is applicable to excitations made close to the node of Thefield-induced(almost)normalstate(Fig. 4(e)-(f))
the superconducting order parameter,where ∆AF opens is marked by strong pump-fluence dependence of initial
above the Fermi level (Fig. 2(b)). In this portion of the relaxation rates suggesting that the fluence dependence
Brillouin zone, electron-hole recombination across ∆AF observedinthenormalstate(Fig. 2)persiststolowtem-
may provide an additional source of photoexcited quasi- perature and needs to be accounted for when analyzing
particles, making the extended Rothwarf-Taylor model zero field data. Fig. 5 summarizes initial decay rates as
a more appropriate starting point43. For that reason, a function of pump fluence for both the SC and the AF
we will keep the discussion of the superconducting com- component at the measurement temperatures and fields
ponent derived in the manner described above qualita- in Fig. 4. Data at delay times after ∆R/R were
max
| |
tive,andleavemoresophisticatedmethodsofcomponent fit to Eqn. 4. Fig. 5 emphasizes the different fluence-
separation44 for a later study. dependentdynamicsofdecayacross∆ ascomparedto
AF
The first observation about the SC component of recombination of quasiparticles into Cooper pairs. The
∆R/R is that it changes sign between underdoped and former depends strongly on fluence, varying systemati-
optimaldoping. Itshouldbenotedthatoptimallydoped cally by more than an order of magnitude in the fluence
NCCO11 and x=0.14 PCCO also have a superconduct- regimeexamined. Thelatterhaslittlesystematicfluence
ing component with a positive sign, so this observa- dependence, with the initial decay rate varying by only
tion may be generic to all families of electron-doped a factor of 3, likely indicating a phonon bottleneck in
≈
cuprates. Previously, a sign change of ∆R/R in single- the recombination.
color pump-probe experiments was observed in hole- We explore the fluence and temperature dependence
doped cuprates across optimal doping. Additionally, in of initial decay rates in the field-induced normal state
hole-dopedcuprates,strongpump-fluence dependence of further in Fig. 6. The key observation is that the flu-
7
0T
x 10−5 2T 2.2µJ/cm2
4T 1.2
0 x=0.08 6SCT 0 2.2µJ/cm2 (c) 0 x=0.08 00..4227
T=11K 1.2 T=11K 0.13
H=6T
R/R∆−−−642 Φ=0.27µJ/cm2 R/R (normalized)∆−−−−0000....8642 x1=1K0.00008...,421 0273T−6T R/R (normalized)∆−−−−0000....8642
(e)
(a) −1 −1

−8 0 10 20 30 40 50 0 10 20 30 40 50
0 10 20 30 40 50 time (ps) time (ps)
time (ps)
0T
3T
x 10−5 5T 2.3µJ/cm2
6 .5T 1.3
6 SC 1 0 x=0.11 0.81
0.26
H=6.5T
0.8 −0.2 0.081
R/R∆ 024 xTΦ===010.21.2K16µJ/cm2 R/R (normalized)∆000...246 x=0.1 01 0021.,0.. 82..033816T1µ−J6/.c5mT2 (d) R/R (normalized)∆−−−000...864 T=12K
12K
−2 0 −1 (f)

(b) 0 10 20 30 40 50 0 10 20 30 40 50
−4 time (ps) time (ps)
0 10 20 30 40 50
time (ps)
FIG. 4. Isolating two components with magnetic field. (a) ∆R/R for x=0.08, taken at several magnetic field (B||c), 11K, and
fixed pump fluence. Dashed curve shows 6T data subtracted from 0T data in order to isolate SC component. (b) Same for
x=0.11, except SC component derived by subtracting 6.5T data from 0T data. (c)-(d) Fluence dependence of SC component
for both dopings. (e)-(f) Fluence dependence of AF component, defined as ∆R/R at the maximum field studied, for both
dopings.
encedependenceattemperaturesupto26Kisconsistent inheavy fermionmaterials19. Another possibility is that
with a bimolecular recombination process. ∆R(0)/R is the portions of the FS away from the hotspots simply
| |
proportionalto the fluence andthe totalnumberofexci- contribute less to ∆R/R.
tations, and the initial recombination rate is derived by
fitting ∆R/R(t) to Eqn. 4.
VI. DISCUSSION
At elevated temperatures, a linear relationship be-
tween γ and ∆R(0)/R is maintained, though the data
are uniformly|shifted to|higher values of γ. This is con- A. Fluence dependence above Tc
sistent with increasing thermal populations (n ) of ex-
th
citations. At elevated temperatures, thermally excited We begin by considering the appearance of fluence-
excitationscanrecombinewithphotoexcitedexcitations, dependent relaxation rates below a temperature consis-
givingapopulationevolutionofphotoexcitedexcitations tent with T from transport. It should be noted that
D
of dnph = βn2 βn n . Thisexpressionyieldsaflu- the onset of AMR does not necessarily indicate long-
dt − ph− ph th
ence dependence with the same slope, but with an offset range order or static order in LCCO, as µSR experi-
given by γ , the recombination rate due to thermal ex- ments yield a much more truncatedAF regime10. Previ-
th
citations recombining with each other. This result indi- ous theoreticalwork has been shownthat decreasing AF
catesthatthe samebimolecularrecombinationprocesses correlation length has the effect of adding DOS into the
dictate the relaxation of the photoexcited state in the gapproducedby q=(π,π) ordering27,50. TheDOSinside
absence of superconductivity both at low temperature the gap has been related to the AF correlation length
and at T . Most likely, this bimolecular recombination for the related compound Sm Ce CuO (SCCO)27,
c 2−x x 4±δ
happens across ∆ . As sketched in Fig. 1, the gap andin-gapDOSstartstogrowappreciablyforcorrelation
AF
is centered around E only at the hot spots. It should lengthssmallerthan16latticeconstants. Inthiscontext,
F
be noted that transient reflectivity can be sensitive to the fluence-dependent relaxation rates are attributed to
gaps not centered at E , such as the hybridization gap bimolecular recombination of electron-hole pairs across
F
8
0.4 (a)
0.5
0.35 x=0.08, H=6T, 11K 11K (a)
0.3 x=0.11, H=6.5T, 12K 0.4 16K x=0.08
H=6T
21K
0.25
−1) 0.3 26K
(psγ00.01.52 −1 (ps)00.2
γ
0.1
0.1
0.05
0 0
0 0.5 1 1.5 2 2.5
fluence (µJ/cm2) 0 0.5 1 1.5
0.02 ∆ R(0)/R x 10−4
(b)
x=0.08, SC component, 11K
9K (b)
x=0.11, SC component, 12K 12K x=0.11
0.015 0.5 H=6.5T
15K
18K
1) 0.4
− 21K
(psγ0 0.01 −1ps) 0.3 24K
(0
γ 0.2
0.005
0.1
0
0 0.5 1 1.5 2 2.5 0
fluence (µJ/cm2)
0 1 2 3 4 5 6 7
∆ R(0)/R x 10−5
FIG. 5. Initial decay rates as a function of pump fluence for
AF(a) and SC (b) components for both dopings.
FIG. 6. Temperature and fluence dependence of initial re-
combination rate in field-induced normal state. Bimolecular
recombination is implied by linear relationship between ini-
∆ where the AF correlationlength is sufficiently long
AF tialdecayratesandmagnitudeof∆R(0)/R,whichispropor-
to fully deplete the DOS inside the gap, as sketched tionaltofluenceandnumberofexcitations. Fittingdescribed
in Fig. 7(c). The temperature regime (T>TN,AMR) in text. (a) x=0.08, taken at H=6T. (b) x=0.11, taken at
without fluence dependence is attributed to AF with H=6.5T
shorter correlation length such that there is a contin-
uum of available states for hot electron thermalization.
Previously the onset of AF correlations in optical-pump respectively,basedontransportandopticalpump-probe
probe data was identified via a second exponential term values of T , represent lower bounds.
D
in the fitting32, and we emphasize that the presentiden- The first excitation that may potentially be impli-
tificationviafluencedependenceisapparentinrawdata. cated in bimolecular recombination is optical phonons.
However,the highestfrequencyopticalphononsin doped
electron-doped cuprates have been shown to have en-
B. Origin of bimolecular recombination ergy of 60 meV51,52, which is not sufficient to tra-
≈
verse 2∆ . It should be noted that in the regime of
AF
When a particle and a hole undergo bimolecular re- strongelectron-phononcoupling,itispossibletohavere-
combination, a boson with the energy and momentum combinationbe mediatedbymultiple phonons53,though
difference is created. We attempt to identify this boson the dimensionless electron-phonon coupling constant, λ,
based on the energy scales involved. Static optical con- in electron-doped cuprates is estimated to be 1, in
ductivity has indicated that the magnitude of the gap a moderately-coupled regime54,55. This leave≈s mag-
due to AF correlations in electron doped cuprates3,5 is netic excitations–magnons or spin waves. In undoped
2∆ 18k T∗. As shown in PCCO, T∗ as determined PrLaCuO and lightly-doped NCCO, a magnon disper-
AF b 4
≈
from optical conductivity tends to be higher than T sionhasbeenmeasuredwithamaximumenergyof 300
D
from AMR, which is within error bars of T measured meVatq=(π,π)56,57. Withelectrondoping,thed≈isper-
N
by optical pump-probe (Fig. 2). Thus, our estimates of sion shifts to higher energy at all measured momentum
2∆ of 85 meV and 124 meV for x=0.11 and x=0.08, transfer56, and near optimal doping, a dispersing collec-
AF
9
tive mode with an energy of 300meV at q= (0,0)57. t=0 t>0
≈
Bimolecular recombination of electrons and holes with ph
net momentum q = 0 may be facilitated by the latter
2∆ 2∆
excitation. Alternately,electronsandholeswithmomen- AF AF
tum difference q=(π,π), such as those at opposite hot- EF E >>2∆
spot momenta, may recombine facilitated by magnons. E- pump AF
C. Connecting to physical quantities
One point highlighted by the discrepancy between 0 DOS (AU) 1 0 DOS (AU) 1
phase diagrams suggested by µSR and AMR is that
AF correlations exist on finite timescales. Because these T<T T>T T>T
N,PP N,PP N,optics
AF correlations are responsible for the gap in the DOS
which gives rise to bimolecular recombination dynamics
observed in the normal state, we can use these time- 2∆
AF
domain experiments to set limits on these correlation
F
E
times. In particular, the gap in the DOS needs to exist -
E
long enough for bimolecular recombination to occur, so
the inverse of the recombinationrate in the limit of zero
pump-fluencesetsalowerboundonthecorrelationtime.
This procedure gives a minimum correlation time at T
c
of 6.7 0.4ps and 1.9 0.3ps for x=0.08 and x=0.11, 0 1 0 10 1
± ± DOS (AU) DOS (AU) DOS (AU)
respectively. At temperatures T/T 0.6 0.7, limits
c
≈ −
on the static timescale of AF are placed at 35ps(74ps)
FIG. 7. Summary. (a)-(b) Effect of the pump. (a) 1.5eV
from the lowest measured fluence of x=0.11(0.08). The
pump makes high energy excitations in excess of ∆AF. (b)
timescaleonwhichAFcorrelationsarearestaticisuseful
Highenergyexcitationsdecaytogapedgeviaemissionofop-
for clarifying the relationship between AF and SC. For
ticalphononsorotherhigh-energybosons. (c)-(e)Relaxation
example, if the pairing mechanism is purely electronic,
in various temperature regimes. (c) When DOS inside gap
happeningonsub-picosecondtimescales,apictureofmi- is fully depleted, relaxation proceeds via bimolecular recom-
croscopic coexistence, albeit only 2D, may still be valid bination across the gap, as evidenced by characteristic tem-
in a regime where static long-range order is absent. perature and fluence dependence of initial decay rate, shown
Theslopeofthebimolecularrecombinationrate( β) in Fig. 6. (d) When sufficient DOS are inside the gap, ad-
can be used to estimate the coupling between cha∝rged ditional decay channels appear, and relaxation rates are no
particles and magnetic excitations, analogous to how β longer fluence dependent. (e) At sufficiently high tempera-
ture, corresponding to the pseudogap temperature in optics,
is relatedto the ratio of electron-phononcoupling to the
the∆AF fills in completely.
DOSatE inBCSsuperconductors. Inordertoestimate
F
acouplingparameter,weneedanestimateofthenumber
of excitations that are created for a given pump fluence.
As an upper bound, we assume that 100% of the pump recombination dynamics. This observation indicates ei-
fluence goestowardscreatingelectron-holeexcitationsof
ther a high efficiency of pair-breaking by gap-frequency
energy2∆AF. Analysisoftherateoffluencedependence bosonsand/oraslowdiffusionand/oranharmonicdecay
inthefield-inducednormalstateatlowtemperature(Fig.
rate of gap frequncy bosons. The field-induced normal
5)andaboveT inamagneticfield(Fig. 6)indicatethat
c state, which consists of either long-range AF order or
electron-magnon coupling in x=0.08 is between 2 and 4
long-length in-plane correlations is marked by a strong
times stronger than in x=0.11, a much larger difference
fluence dependence of ∆R/R. The specific functional
than the relative T ’s of the two dopings..
c form of this fluence dependence suggests that the relax-
ation mechanism of the photoexcited state is dominated
by bimolecular particle-hole recombination across a gap,
VII. CONCLUSIONS likely mediated by magnetic excitations, as sketched in
Fig. 7. Fluence dependence persists to a temperature
We have performed optical pump-probe experiments similar to T observed by AMR, suggesting that this
D
onunderdopedandoptimallydopedLCCOinthesuper- transport signature of AF correlations also corresponds
conducting state, in the normal state, and in the field- to a fully depleted gap in the DOS (Fig. 7(c)). At-
induced normal state. In the superconducting state, we tributing the fluence-dependence of the normal state to
observe distinct components in ∆R/R attributed to AF bimolecularrecombinationallowsustoputlimitsonboth
and SC. The latter shows a sign change going from un- thetimescaleonwhichAFcorrelationsarestaticandthe
derdopedtooptimaldoping,andalsoshowsbottlenecked strength of electron-magnoncoupling.
10
ACKNOWLEDGMENTS pump-probe work was supported by the Gordon and
Betty Moore Foundation’s EPiQS initiative through
grant GBMF4540. Materials growth and characteriza-
We acknowledge helpful discussions with S. Lederer, tionwassupportedbyAFOSRFA95501410332andNSF
T. Senthil, D. Torchinsky, and P. Werner. Optical DMR1410665.
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