Bennemann K.H., Ketterson J.B. Superconductivity: Volume 1: Conventional and Unconventional Superconductors; Volume 2: Novel Superconductors

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13 Unconventional Superconductivity in Novel Materials

M. Brian Maple Department of Physics and Institute for Pure and Applied Physical Sciences.

University of California, San Diego La Jolla, California, USA

Eric D. Bauer Department of Physics and Institute for Pure and Applied Physical Sciences.

University of California, San Diego La Jolla, California, USA

Vivien S. Zapf Department of Physics and Institute for Pure and Applied Physical Sciences.

University of California, San Diego La Jolla, California, USA

Jochen Wosnitza Hochfeld-Magnetlabor Dresden (HLD), Forschungszentrum Dresden-Rossendorf,

Dresden, Germany

13.1 Introduction .............................................................................640

13.2 Conventional Superconductors Containing Localized Magnetic Moments .......................641

13.2.1Introduction........................................................................641

13.2.2Superconducting-MagneticInteractions...............................................641

13.2.3ParamagneticImpuritiesinSuperconductors..........................................642

13.2.4MagneticFieldInducedSuperconductivity.............................................657

13.3 f-Electron Heavy Fermion Superconductors .................................................659

13.3.1Introduction........................................................................659

13.3.2Normal-StateProperties.............................................................661

13.3.3Superconducting-StateProperties.....................................................665

13.3.4 UPd

............................................................................667

13.3.5QuantumCriticalPoints.............................................................672

13.3.6Non-FermiLiquidBehavior..........................................................680

13.3.7MagneticallyOrderedHeavy-FermionSuperconductors.................................685

13.3.8MultipleSuperconductingPhases.....................................................688

13.3.9ConcludingRemarks................................................................695

13.4 Organic Superconductors ..................................................................696

13.4.1Introduction........................................................................696

13.4.2Normal-StateProperties.............................................................697

13.4.3SuperconductingStateProperties.....................................................705

13.4.4ConcludingRemarks................................................................717

13.5 Layered Cuprate and Ruthenate Superconductors ............................................717

13.5.1Introduction........................................................................717

13.5.2TheMaterials.......................................................................718

13.5.3StructureandChargeCarrierDoping.................................................722

13.5.4SuperconductingProperties..........................................................724

13.5.5Normal-StateProperties.............................................................732

13.5.6ConcludingRemarks................................................................740

13.6 Comparison of the Properties of Different Classes of Novel Superconductors ...................741

References...............................................................................744

640 M.B. Maple et al.

13.1 Introduction

The past three decades have witnessed a series of

spectacular developments in the field of supercon-

ductivity, driven by advances in the synthesis of new

and complex materials. This has spawned several

classes of novel superconducting materials, includ-

ing magnetically ordered superconductors, heavy

fermion superconductors, organic superconductors,

high T

cuprate superconductors, ruthenate super-

conductors, as well as several other interesting su-

perconducting materials such as Ba

1−x

BiO

,the

fcc “buckeyball” compound Rb

,andMgB

.The

extraordinary physical properties of these materials

are reviewed in this chapter.

The focus of this chapter is on the unconven-

tional superconductivity displayed by heavy fermion

f -electron materials, organic compounds, and cop-

per and ruthenium oxides (Sects.13.3–13.6).In these

novel materials, the superconductingphase often oc-

curs in the vicinity of a magnetic phase in the hyper-

space of temperature, chemical composition, pres-

sure and magnetic field. This has been widely re-

garded as evidence that spin ﬂuctuations play an im-

portant role in the pairing of superconducting elec-

trons in these materials. In a few cases, this scenario

has received additional support from experiments

such as electron tunneling, although it has not been

definitively established. The unconventional super-

conductivity observed in many of these materials is

characterized by an anisotropic energy gap that ap-

pears to vanish at points or along lines on the Fermi

surface. This suggests that the superconducting elec-

trons are paired in states with angular momentum

greater than zero (p or d-wave superconductivity).

Multiple superconducting phases have been discov-

ered in the heavy fermion compounds UPt

and

1−x

and attributedto a multicomponent su-

perconducting order parameter coupled to a second

order parameter.In the case of UPt

,the secondorder

parameter appears to be antiferromagnetic in nature.

Recently, superconductivity has been observed un-

der pressure in several antiferromagnetic Ce-based

compounds (e.g.,CeIn

[1],CePd

[2]) at low tem-

peratures near the critical pressure where the N´eel

temperature extrapolates to 0 K (quantum critical

point). An even more surprising development is the

discovery of superconductivity under pressure in a

ferromagnetic U-based compound (UGe

[3]) within

the ferromagnetic phase in the vicinity of the critical

pressure where the Curie temperature drops abruptly

to 0 K. These striking results all point toward an in-

timate relationship between superconductivity and

magnetism in these novel materials.

In order to provide a perspective for the role

played by magnetism in the unconventional super-

conductivity of the heavy fermion f -electron, or-

ganic, and cuprate and ruthenate compounds de-

scribed in Sects. 13.3–13.6, the extraordinary phe-

nomena produced by the interplay between super-

conductivity and magnetism in conventional super-

conducting systemsare brieﬂy described in Sect.13.2.

In conventional superconductors, the pairing of su-

perconducting electrons is mediated by phonons,the

superconducting electronsarepairedin singlet states

with zero angular momentum (s-wave superconduc-

tivity), and the superconducting energy gap is con-

stant, or nearly so, over the Fermi surface. Conven-

tional s-wave spin-singlet superconductivity is ad-

versely affected by the presence of localized mag-

netic moments in both paramagnetic and magneti-

cally ordered states. Nevertheless, the interaction be-

tween superconductivity and magnetism generates

new and unusual physical phenomena that include:

(i) the destruction of superconductivity at a second

criticaltemperatureT

< T

,whereT

isthesuper-

conducting criticaltemperature,(referred to as reen-

trant superconductivity)in a superconductingmate-

rial containing paramagnetic impurities thatexhibits

the Kondo effect; (ii) the coexistence of supercon-

ductivity and antiferromagnetic order; (iii) the de-

struction of superconductivity by the onset of ferro-

magnetic order at a second critical temperature T

 

< T

,where

is the Curie temperature and

is the superconducting critical temperature; (iv)

the development of a new sinusoidally modulated

magnetic state with a wavelength  ∼ 10

Åthat

coexists with superconductivity in a narrow tem-

perature range above T

due to superconducting-

ferromagnetic interactions; and (v) magnetic field

induced superconductivity(known as the Jaccarino–

Peter effect [4]).