7/28/2019 Superconductivity Death of a Fermi Surface

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SUPERCONDUCTIVITY

Death of a Fermi surface

Every metal, semimetal and doped semiconductor has a Fermi surface that

determines its physical properties. A new state of matter within the pseudogap

state of a high-temperature superconductor destroys the Fermi surface, the

process of which provides information about the new state.

KYLE MCELROYis in the Materials Sciences Division, Berkeley National

Laboratory, Berkeley, California 94720, USA.

e-mail: kpmcelroy@lbl.gov

Materials with strong electronic correlationsare breeding grounds or new states omatter the copper oxide superconductors1

being a perect example. Although the parent (non-superconducting) oxide compound is expected tobe a metal, Coulomb repulsion between electronsleads to localization and insulating behaviour. Suchinsulators, in which correlation eects dominate, areknown as Mott insulators. Upon chemical doping,which adds charge carriers, many strange statesemerge rom this Mott insulator. Among these arenot only superconductivity with incredibly highcritical temperatures o up to 150 K, but, or low

doping concentration, a most mysterious state omatter known as the (much-debated) pseudogapphase. On page 447 o this issue2, Kanigel et al. bolsterone view o the pseudogap state, as a precursor tosuperconductivity, by careully showing that it hasa simple phenomenology that, when taken in thelow-temperature limit, looks very similar to thesuperconducting state.

By varying the hole concentration andtemperature, researchers have ound a wide varietyo unexpected phenomena in the copper oxidesuperconductors (Fig. 1). Te states close to the Mottinsulator region that is, or low hole density areparticularly intriguing. In this regime, called the

pseudogap state, indications o a most unusual stateo matter have been ound. Tis regime diers romthose in conventional conductors in the behaviouro electronic states right near the Fermi surace. Inmost materials, like in the non-interacting electrongas, electrons simply fll up the lowest availableelectronic states in momentum space. Te top o thisflled volume creates a surace o states called theFermi surace that governs the low-energy (roomtemperature) physics. Te situation is dierent inthe pseudogap state: below the temperature T* anenergy gap opens up on part o the Fermi surace3,removing states rom this low-energy region.Although the development o such a gap oenindicates a breaking o some symmetry by a new

electronic phase, in this case the gap consumes only

part o the Fermi surace (hence the pseudo in itsname) and leaves behind small, disconnected Fermiarcs4 (as shown in Fig. 2) where low-energy, metallicexcitations seem to survive.

Despite previous work, the identity o this phaseremains unclear. On the one hand, a completely newelectronic state may exist inside the pseudogap phase,eating up many o the states and thereore leavingew available to pair up and superconduct. On theother hand, the similarity between this partial gapand that in the superconducting state has led manyto the conclusion that the partial gap results rompreormed Cooper pairs (above Tc). According tothis theory, at low enough temperatures these pairs

will condense into a collective superconducting state,but above this temperature in the pseudogap stateuctuations in the phase o the waveunctions preventthe condensation5. Hence, the electronic states shouldlook similar to the superconducting ones except thatthey lack the hallmark o zero resistance. Recently,transport studies6 o the very-low-energy states nearthe lowest hole-doping levels in YBa2Cu3O6.33 that stillsuperconduct have supported this conclusion. Acrossthe critical doping range bridging the pseudogapand the superconductivity (marked by the redellipse in Fig. 1), the thermal conductivity behavesin a continuous manner, suggesting little dierencebetween the states in the pseudogap and those inthe superconductor.

1/2 filling Hole doping (p)

Superconductor

Metal

Pseudogap

Mottinsulator

T*

T

Figure 1 Phase diagram of

a typical hole-doped copper

oxide superconductor. As

the number of holes is

increased from the half-filled

Mott insulator (one electron

per state) an assortment of

electronic states appear. At

high doping these include

both superconducting and

metallic phases. At low doping

other strange states of matter

can be found, including the

pseudogap state that persists

up to T*. The red ellipse

indicates previous work

connecting the pseudogap to

the superconducting state.

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442 nature physics| VOL 2 | JULY 2006 | www.nature.com/naturephysics

In their latest work, Kanigel et al. study the

electronic states throughout the pseudogap phaseto characterize the shape o the gap. o do this,the authors use angle-resolved photoemissionspectroscopy to careully map out the electronicstates o the pseudogap throughout the Brillouin zoneo Bi2Sr2CaCu2O8+x. By ollowing where these statesmake their closest approach to the Fermi surace,they are able to trace how the gap in this state ormsbelowT* and quickly consumes the states startingnear the at aces o the zone (Fig. 2), leaving onlythe Fermi arcs that become shorter and shorteras the temperature is lowered. An extrapolationto zero temperature shows that eventually thepseudogap enguls the whole Fermi surace, and

the disconnected Fermi arcs shrink down to justour points along the zone diagonals. Interestingly,

the shape o this gap is the same as that o thesuperconducting state ound at higher dopings andlower temperatures. So throughout the pseudogapphase, the electronic states on the Fermi arcs lookvery much like they are preparing, and indeed pre-pairing, themselves or the superconducting state.

Along the curved parts o the Fermi surace,the pseudogap structure seems to be a precursor to

superconductivity. But near the zone ace (Fig. 2) thestraight parts o the Fermi surace reveal somethingdierent. Along these sections the arcs do notcontinue to grow as the temperature increases.Instead, the missing electronic states begin tofll in along these sections until the pseudogaptransition is reached, where the gap abruptly closes.Tis qualitatively dierent behaviour seems toindicate that as the Fermi arcs are getting readyor superconductivity, these straight segments aredoing something entirely dierent. Signifcantly, itis exactly these straight segments that interact moststrongly with other degrees o reedom, and maylead to other states o matter. Additionally, their

parallel nature allows them to interact more stronglywith a particular wave vector that connects them, q*(orange arrows in Fig. 2), thereby opening a gap bybreaking another symmetry, such as translation. Soperhaps, while the electrons along the Fermi arcsare preparing or superconductivity, yet anotherstate o matter or instance, one with chargeordering7 lives along these straight segmentsinside the pseudogap.

REFERENCES1. Bednorz, J. G. & Mller, K. A. Z. Phys. B64, 189193 (1986).

2. Kanigel, A. et al.Nature Phys.2, 447451 (2006).

3. imusk, . & Statt, B. Rep. Prog. Phys. 62, 61122 (1999).

4. Norman, M. R. et al. Nature 392, 157160 (1998).

5. Nagaosa, N. & Lee, P. A. Phys. Rev. B45, 966970 (1992).

6. Sutherland, M. et al. Phys. Rev. Lett. 94, 147004 (2005).7. Hanaguri, . et al. Nature430, 10011005 (2004).

Zone

face

q*

Fermiarc

Figure 2 The square Brillouin

zone of a copper oxide

superconductor. The normal

state Fermi surface above T*,

is characterized by straight

(dashed) and curved sections

(green), making pockets

centred on the corners of the

zone. In the pseudogap phase,the low-energy states occupy

ungapped regions that exist

over four small, disconnected

metallic arcs (green) known

as Fermi arcs. Within this

state the gap slowly engulfs

the states (black arrows) as

the temperature is lowered,

leaving only the four blue

points ungapped. The straight

sections of the Fermi surface

(shaded ellipses), which share

a connecting wave vector

q* (orange arrows), behavedifferently their gap

abruptly opens all at once, as

if another electronic state is

gapping them.

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