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Quantum Phase Transitions in a Cuprate Superconductor Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta}

Quantum Phase Transitions in a Cuprate Superconductor Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta}
Quantum Phase Transitions in a Cuprate Superconductor Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta}

a r X i v :c o n d -m a t /0402025v 2 [c o n d -m a t .s u p r -c o n ] 23 A p r 2004

Quantum Phase Transitions in a Cuprate Superconductor Bi 2Sr 2?x La x CuO 6+δ

Yoichi Ando,?S.Ono,X.F.Sun,and J.Takeya

Central Research Institute of Electric Power Industry,Komae,Tokyo 201-8511,Japan

F.F.Balakirev,J.B.Betts,and

G.S.Boebinger ?

NHMFL,Los Alamos National Laboratory,Los Alamos,New Mexico 87545

(Dated:February 2,2008)

To elucidate a quantum phase transition (QPT)in Bi 2Sr 2?x La x CuO 6+δ,we measure charge and heat transport properties at very low temperatures and examine the following characteristics for a wide range of doping:normal-state resistivity anisotropy under 58T,temperature dependence of the in-plane thermal conductivity κab ,and the magnetic-?eld dependence of κab .It turns out that all of them show signatures of a QPT at the 1/8hole doping.Together with the recent normal-state Hall measurements under 58T that signi?ed the existence of a QPT at optimum doping,the present results indicate that there are two QPTs in the superconducting doping regime of this material.

PACS numbers:74.25.Fy,74.25.Dw,74.72.Hs

One of the emerging paradigms in the condensed mat-ter physics is the ubiquitous competitions in strongly-correlated systems.For example,strong correlations in transition-metal oxides such as manganites and nickelates often result in nanoscale structures consisting of compet-ing phases [1,2].The competitions between di?erent ground states sometimes give rise to a quantum phase transition (QPT)[3],which takes place at zero tempera-ture when quantum ?uctuations cause a cooperative or-dering of the system to disappear or change;in fact,the strong correlations in heavy-fermion systems [4]and in ruthenates [5]are known to be responsible for a QPT between competing ground states.In high-T c cuprates,competitions between the kinetic energy,the local ex-change interaction,and the long-range Coulomb inter-action produce nanoscale self-organized structure called stripes [6,7,8],and it is of signi?cant current interest that various competing ground states may alternate at QPTs depending on material parameters and/or exter-nal parameters,causing the electronic properties to be largely governed by the competitions [9].

An important issue associated with the competing ground states is the quantum criticality,which helps one to sort out the physics in terms of universal scaling [10].However,the quantum criticality becomes impor-tant only when the competition results in a second-order QPT,while some microscopic phase separations and as-sociated colossal e?ects can happen [11]when the QPT is ?rst order.Therefore,?nding a QPT in a strongly-correlated system is one thing,and determining whether there is an associated quantum criticality is quite an-other.In the case of cuprates,our understanding of the QPTs and the underlying orders is still far from satis-factory;in particular,most of the previous experimental works of cuprates regarding the QPT [10,12,13]just fo-cused on the universal scaling behavior,but identifying the exact position and the nature of the putative QPT is probably even more important.To accomplish the latter,

one needs to ?nd a qualitative change in the electronic properties at very low temperatures as a function of a control parameter (such as doping),which is normally a formidable task and experiments along this line are just emerging [14,15,16].

Very recently,a pulsed magnetic ?eld experiment [16]found strong evidence at low temperatures that there is indeed a QPT at optimum doping in a cuprate super-conductor Bi 2Sr 2?x La x CuO 6+δ(BSLCO).In that work,the doping dependence of the normal-state Hall coe?-cient measured under 58-T magnetic ?eld was found to show a sharp break at optimum doping,indicative of a phase transition resulting in a dramatic change in the Fermi-surface states.Notably,the break in the doping dependence became sharper and sharper with lowering temperature,suggesting that the observed feature is truly a result of a zero-temperature transition;incidentally,it was argued that a QPT associated with the d -density-wave order [17]can produce such a sharp signature in the Hall coe?cient [18].

However,there remains a puzzle in the BSLCO case:In the in-plane resistivity measurements of BSLCO un-der 60T [19]that preceded the Hall measurements,it was found that the insulator-to-metal crossover,which may also signify a QPT,occurs near the 1/8(=0.125)doping,and this does not ?t well with the QPT at op-timum doping (0.16holes per Cu).Therefore,the evi-dence for the QPT in BSLCO is rather controversial and a comprehensive picture for the zero-temperature phase transition(s)in BSLCO needs to be established as a step towards drawing a general phase diagram of the cuprates.In this work,to elucidate the zero-temperature phase dia-gram of BSLCO,we measure various transport properties at low temperature and carefully search for experimental signatures of a sharp change in the electronic properties as a function of doping.It is worthwhile to note that the transport properties are inherently suited to study the zero-temperature properties of a system,because they

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and the correspondence between x and p has been sorted out [21].In this work,we essentially employ two exper-imental techniques we have been specialized in:resistiv-ity measurements under pulsed magnetic ?elds up to 58T [19]and thermal conductivity measurements at very low temperatures [22,23].Details of each technique are described in the cited papers.For this work,di?erent sets of samples [24]are prepared for the measurements of the in-plane resistivity ρab [Fig.1(b)],out-of-plane resistivity ρc [Fig.1(c)],in-plane thermal conductivity κab below 300mK (Fig.2),and the magnetic-?eld de-pendence of κab (Fig.3);here,the data for a total of 21samples are presented,all of which are similar in size (~1–2×1×0.05mm 3).We concentrate on identifying the QPT(s)in the superconducting doping regime by look-ing at a qualitative change in the electronic properties at very low temperatures,and it is not the interest of the present study to determine whether the QPT we ?nd is accompanied by the quantum criticality.

The ?rst property we look at is the charge con?ne-ment characteristics [25]in the zero-temperature limit:We measure ρab and ρc in the normal state by suppress-

κ0

/ T ( m W / c m K 2

)

p

0T measured in the mK the residual quasipar-of the linear ?t (thin data.(b)Doping de-dashed curve is a guide to 0/T (marked by a shaded in the superconducting pulsed magnetic ?elds,anisotropy ratio ρc /ρab .dependences of ρc /ρab and 1(c)show the raw One can easily see in change in the temper-namely,for p ≥0.14zero-temperature limit,with lowering tem-that the characteristics is one of the most pe-culiar electronic properties of the cuprates [25],changes across p ?1/8(=0.125).It appears that for p <1/8the charge con?nement becomes increasingly more e?ective with decreasing temperature,suggesting that the ground state is strictly two dimensional;on the other hand,since ρc /ρab stays ?nite for p >1/8,the ground state can be viewed as an anisotropic three-dimensional state on this side,though the anisotropy is extremely large.Such a change in the e?ective dimensionality naturally points to a transformation in the fundamental nature of the ground state in the zero-temperature limit,and thus is indica-tive of a QPT at p ?1/8in the normal state under high magnetic ?elds.

The second property we look at is the in-plane thermal conductivity κab in the mK region,where we can sepa-rate the contributions of phonons and quasiparticles to the heat transport [22,26]and therefore the quasiparti-cle behavior at zero ?eld (in the superconducting state)can be traced with this tool.Figure 2(a)shows the plots of κab /T vs.T 2for 77–170mK;in these plots,the zero-temperature intercept of the linear ?t to the lowest-temperature data gives the residual quasiparticle term

3

FIG.3:in κab with quasiparticles K signi?es the for a QPT at p ?κ0/T ,which at zero spectrum pend on the Fermi the nodes in ?ts are have (the phonon slopes are a factor of the data limited,we for example,are As shown in a jump our error p =0.14tially the at optimum state of be κ0/T for p within the [27].reported for the exact it is probably related to the “insulating”nature of the normal state under high magnetic ?eld [19]and is pos-sibly a result of some novel localization e?ects [30,31].In any case,the jump of κ0/T across p ?1/8signi?es a change in the nature of the superconducting state at zero temperature,and thus gives evidence for a QPT in the superconducting state.

We further look at the magnetic-?eld dependence (H ),prob-the spin LSCO [23],tem-H It is oc-at levels.this H in-to is wave ab (H )QPT The above results show that the low-temperature transport properties give evidence for a QPT taking place at p ?1/8in all three possible states of a type-II super-conductor:superconducting Meissner state,mixed state under intermediate magnetic ?elds,and the normal state under high magnetic ?elds.Therefore,the present set of data adds another QPT to the phase diagram suggested by the normal-state Hall measurements [16],which gave

4

evidence for a QPT at optimum doping.Furthermore, the present results con?rm that the insulator-to-metal crossover observed in the previousρab measurements[19] was indeed due to a QPT.Based on these results,the phase diagram concluded for BSLCO can be summa-rized as follows:The QPT at p?1/8(QPT1)sepa-rates two regimes,Regime1(p<1/8)and Regime2 (1/80.16)from Regime2;throughout Regimes1and2the e?ective carrier density in the zero-temperature limit measured by the Hall coe?cient shows a linear increase with T c[16],which is reminiscent of the Uemura relation for the super?uid density[37],and there appears to be an abrupt change in the Fermi-surface states at QPT2[16].Intriguingly,the heat transport properties in the superconducting state do not give any hint of QPT2.

The existence of two QPTs in BSLCO probably tells us that the physics of the cuprates in the superconducting doping regime is governed by competitions between at least three di?erent ground states.Whatever the nature of the ground states,it is clear that a number of phases are competing in the cuprates and therefore a promising model of high-T c superconductivity must have multiple competing phases as possible ground states.It is yet to be seen how or whether the competition is related to the occurrence of superconductivity,but it is intriguing to see that the cuprates are no exception of the strongly-correlated systems where ubiquitous competitions govern the essential physics.

We thank S.Chakravarty,S. A.Kivelson, A.N. Lavrov,and S.Sachdev for helpful discussions and sug-gestions.The work at the NHMFL was supported by NSF and DOE.

?Electronic address:ando@criepi.denken.or.jp

?Present address:National High Magnetic Field Labora-tory,Tallahassee,Florida32310.

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