Nodal Structure of Unconventional Superconductors Probed by the Angle Resolved Thermal Transport Measurements

Abstract

Over the past two decades, unconventional superconductivity with gap symmetry other than s-wave has been found in several classes of materials, including heavy fermion (HF), high-T_c, and organic superconductors. Unconventional superconductivity is characterized by anisotropic superconducting gap functions, which may have zeros (nodes) along certain directions in the Brillouin zone. The nodal structure is closely related to the pairing interaction, and it is widely believed that the presence of nodes is a signature of magnetic or some other exotic, rather than conventional phonon-mediated, pairing mechanism. Therefore experimental determination of the gap function is of fundamental importance. However, the detailed gap structure, especially the direction of the nodes, is an unresolved issue in most unconventional superconductors. Recently it has been demonstrated that the thermal conductivity and specific heat measurements under magnetic field rotated relative to the crystal axes are a powerful method for determining the shape of the gap and the nodal directions in the bulk. Here we review the theoretical underpinnings of the method and the results for the nodal structure of several unconventional superconductors, including borocarbide YNi${}_2$B${}_2$C, heavy fermions UPd${}_2$Al${}_3$, CeCoIn${}_5$, and PrOs${}_4$Sb${}_{12}$, organic superconductor, $\kappa$-(BEDT-TTF)${}_2$Cu(NCS)${}_2$, and ruthenate Sr${}_2$RuO${}_4$, determined by angular variation of the thermal conductivity and heat capacity.

arXiv commenttopical review, 55 pages, 35 figures. Figure quality has been reduced for submission to cond-mat, higher quality figures available from the authors or from the publisher

References in corpus (105)

• Heavy fermion superconductivity and magnetic order in non-centrosymmetric $CeP{t}_{3}Si$
• Time-Reversal Symmetry Breaking Superconductivity in Sr2RuO4
• Fulde-Ferrell-Larkin-Ovchinnikov Superconducting State in CeCoIn5
• Angular Position of Nodes in the Superconducting Gap of Quasi-2D Heavy-Fermion Superconductor CeCoIn_5
• A New Heavy-Fermion Superconductor CeIrIn5: Relative of the Cuprates?
• Unconventional superconductivity in CeIrIn${}_5$ and CeCoIn${}_5$: Specific heat and thermal conductivity studies
• S-wave/spin-triplet order in superconductors without inversion symmetry: Li${}_2$Pd${}_3$B and Li${}_2$Pt${}_3$B
• Similarities between organic and cuprate superconductors
• Superconductivity and Quantum Criticality in CeCoIn_5
• Time-Reversal Symmetry-Breaking Superconductivity in Heavy Fermion PrOs4Sb12 detected by Muon Spin Relaxation
• Avoided Antiferromagnetic Order and Quantum Critical Point in CeCoIn${}_5$
• Orbital dependent superconductivity in Sr_2RuO_4
• Multiple Superconducting Phases in New Heavy Fermion Superconductor PrOs4Sb12
• First order superconducting phase transition in CeCoIn${}_5$
• Evidence for incommensurate spin fluctuations in Sr_2RuO_4
• Pairing due to Spin Fluctuations in Layered Organic Superconductors
• Superconducting Gap Structure of Spin-Triplet Superconductor Sr_2RuO_4 Studied by Thermal Conductivity
• Superconducting Gap Structure of kappa-(BEDT-TTF)2Cu(NCS)2 Probed by Thermal Conductivity Tensor
• A relation between the resonance neutron peak and ARPES data in cuprates
• Distinguishing d-wave from highly anisotropic s-wave superconductors
• Thermodynamical Study on the Heavy-Fermion Superconductor PrOs4Sb12: Evidence for Field-Induced Phase Transition
• Evidence for Unconventional Strong-coupling Superconductivity in PrOs_4Sb_12 : An Sb Nuclear Quadrupole Resonance (NQR) Study
• Gap Structure of the Spin-Triplet Superconductor Sr2RuO4 Determined from the Field-Orientation Dependence of Specific Heat
• Texture in the Superconducting Order Parameter of CeCoIn_5 Revealed by Nuclear Magnetic Resonance
• Gap Function with Point Nodes in Borocarbide Superconductor YNi_2B_2C
• Line nodes in the superconducting gap function of noncentrosymmetric CePt_3Si
• Unconventional Superconductivity and Electron Correlations in Cobalt Oxyhydrate Na${}_{0.35}$CoO${}_2$$\cdot y$H${}_2$O
• Quasiparticles in the vortex lattice of unconventional superconductors: Bloch waves or Landau levels?
• Anisotropic thermodynamics of d-wave superconductors in the vortex state
• Transport Properties of d-Wave Superconductors in the Vortex State
• kappa-(BEDT-TTF)_2Cu[N(CN)_2]Br: a Fully Gapped Strong-Coupling Superconductor
• Low Temperature Penetration depth of κ-(ET)_2Cu[N(CN)_2]Br and κ-(ET)_2Cu(NCS)_2
• Spin triplet superconductivity with line nodes in Sr2RuO4
• Anomalous NMR Magnetic Shifts in CeCoIn_5
• Vortex Contribution to Specific Heat of Dirty $d$-Wave Superconductors: Breakdown of Scaling
• Multiband superconductivity in the heavy fermion compound PrOs4Sb12
• Thermal Conductivity of superconducting (TMTSF)_2ClO_4: evidence for a nodeless gap
• Angular position of nodes in the superconducting gap of YBCO
• New High Field State of Flux Line Lattice in Unconventional Superconductor CeCoIn_5
• Field-angle Dependence of the Zero-Energy Density of States in the Unconventional Heavy-Fermion Superconductor CeCoIn5
• Probing the superconducting gap symmetry of PrOs${}_4$Sb${}_{12}$: A penetration depth study
• Determination of the Superconducting Gap Structure in All Bands of the Spin-Triplet Superconductor Sr2RuO4
• Spin-triplet superconductivity due to antiferromagnetic spin-fluctuation in Sr_2RuO_4
• Quasiparticle Density of States of Clean and Dirty s-Wave Superconductors in the Vortex State
• Anisotropy of magnetothermal conductivity in Sr2RuO4
• Unpaired Electrons in the Heavy-Fermion Superconductor CeCoIn_{5}
• Heat Conduction in $\kappa$-(BEDT-TTF)${}_2$Cu(NCS)${}_2$
• Highly Anisotropic Gap Function in Borocarbide Superconductor LuNi_2B_2C
• Ansiotropic s- wave superconductivity in borocarbides LuNi2B2C and YNi2B2C
• Identifying the pairing symmetry in the Sr2RuO4 superconductor
• Universal Heat Transport in Sr2RuO4
• Direct Observation of Nodal Quasiparticles in an Unconventional Superconductor: Field-angle Dependent Heat Capacity of YNi2B2C
• Nodal structure of quasi-2D superconductors probed by magnetic field
• Quasiparticle thermal conductivity in the vortex state of high-T${}_c$ cuprates
• Spectroscopic Evidence for Multiple Order Parameter Components in the Heavy Fermion Superconductor CeCoIn_5
• d_{x^2-y^2}- vs. d_{xy}- like pairings in organic superconductors κ-(BEDT-TTF)_2 X
• Low Energy Quasiparticle Excitation in the Vortex State of Borocarbide Superconductor YNi_2B_2C
• Field dependence of the zero energy density of states around vortices in an anisotropic gap superconductor
• Anisotropic superconducting gap in transuranium superconductor PuRhGa${}_5$: Ga NQR study on a single crystal
• Normal-state Hall Angle and Magnetoresistance in quasi-2D Heavy Fermion CeCoIn_5 near a Quantum Critical Point
• Anomalous quasiparticle transport in the superconducting state of CeCoIn5
• Phase-sensitive tests of the pairing state symmetry in Sr2RuO4
• A critical assessment of the pairing symmetry in NaxCoO2.yH2O
• Fermi surface and heavy masses for UPd${}_2$Al${}_3$
• Reentrant vortex lattice transformation in four-fold symmetric superconductors
• Point-Contact Spectroscopy of the Heavy-Fermion Superconductor CeCoIn${}_5$
• Orientational field-dependence of low-lying excitations in mixed state of unconventional superconductors
• Spin singlet pairing in the superconducting state of NaxCoO2\cdot1.3H2O: evidence from a ^{59}Co Knight shift in a single crystal
• Pairing Symmetry Competition in Organic Superconductors
• Mixed-state quasiparticle transport in high-T_c cuprates: localization by magnetic field
• Superconductivity of the $S{r}_{2}C{a}_{12}C{u}_{24}{O}_{41}$ spin ladder system: Are the superconducting pairing and the spin-gap formation of the same origin?
• Evidence for Uniform Coexistence of Ferromagnetism and Unconventional Superconductivity in UGe_2: A ^73Ge-NQR Study under Pressure
• Temperature Dependence of the Flux Line Lattice Transition into Square Symmetry in Superconducting LuNi${}_2$B${}_2$C
• Pronounced enhancement of the lower critical field and critical current deep in the superconducting state of PrOs${}_4$Sb${}_{12}$
• Superconducting Gap Function in Antiferromagnetic Heavy-Fermion UPd_2Al_3 Probed by Angle Resolved Magnetothermal Transport Measurements
• Hexagonal and Square Flux Line Lattices in CeCoIn5
• Non-Locality and Strong Coupling in the Heavy Fermion Superconductor CeCoIn${}_5$: A Penetration Depth Study
• Thermodynamics of d-wave superconductors in a magnetic field
• Thermal Conductivity of the Pyrochlore Superconductor KOs2O6: Strong Electron Correlations and Fully Gapped Superconductivity
• 59Co-NMR Knight Shift of Aligned Crystals and Polycrystalline Samples of Superconducting Na0.3CoO2.1.3H2O
• A study of the superconducting gap in RNi${}_2$B${}_2$C (R = Y, Lu) single crystals by inelastic light scattering
• CeCoIn5 - a quantum critical superfluid
• Possible Spin-triplet Superconductivity in NaxCoO2yH2O - 59Co NMR Study
• Quasiclassical theory of superconducting states under magnetic fields: Thermodynamic properties
• Unconventional Superconductivity in Heavy Fermion Systems
• Evidence for the Coexistence of Anisotropic Superconducting Gap and Nonlocal Effects in the Non-magnetic Superconductor LuNi2B2C
• Nonmonotonous Magnetic Field Dependence and Scaling of the Thermal Conductivity for Superconductors with Nodes of the Order Parameter
• ^{115}In-NQR evidence for unconventional superconductivity in CeIn_3 under pressure
• Quasiclassical Approach to Transport in the Vortex State and the Hall Effect
• Thermal Conductivity Tensor in YBa${}_2$Cu${}_3$O${}_{7-x}$: Effects of a Planar Magnetic Field
• Theory of anisotropic s-wave superconductivity with point-node like gap minima: analysis of (Y,Lu)Ni_2B_2C
• Effects of Fermi surface and superconducting gap structure in the field-rotational experiments: A possible explanation of the cusp-like singularity in YNi${}_2$B${}_2$C
• Superconductivity in Organic Compounds with Pseudo-Triangular Lattice
• Dirac quasiparticles in the mixed state
• Weak-Field Thermal Hall Conductivity in the Mixed State of d-Wave Superconductors
• Influence of gap structures to specific heat in oriented magnetic fields: Application to the orbital dependent superconductor, Sr${}_2$RuO${}_4$
• Anisotropic Diamagnetic Response in Type-II Superconductors with Gap and Fermi-Surface Anisotropies
• Comment on "Spectroscopic Evidence for Multiple Order Parameter Components in the Heavy Fermion Superconductor CeCoIn${}_5$"
• Comment on "Spectroscopic Evidence for Multiple Order Parameters in the Heavy Fermion Superconductor CeCoIn5"
• Angle-dependent magnetothermal conductivity in d-wave superconductors
• Field-angle resolved specific heat and thermal conductivity in the vortex phase of UPd_2Al_3
• Thermal conductivity in the vortex state of the superconductor UPd_2Al_3
• Heat Conduction in the Heavy Fermion Superconductor $UP{d}_{2}A{l}_3$
• Anisotropy of in-plane magnetization due to nodal gap structure in the vortex state
• Thermal conductivity in the vortex state of d-wave superconductors

Cited by in corpus (102)

• Gap symmetry and structure of Fe-based superconductors
• Odd-frequency superconductivity
• Line nodes in the energy gap of high-temperature superconducting BaFe_2(As_{1-x}P_x)_2 from penetration depth and thermal conductivity measurements
• Exotic Superconducting Properties in the Electron-Hole Compensated Heavy Fermion `Semimetal' URu2Si2
• Protected boundary states in gapless topological phases
• Anomalous Transport Phenomena in Fermi Liquids with Strong Magnetic Fluctuations
• Exotic Superconducting States in FeSe-based Materials
• Non-Fermi liquid behavior in the magnetotransport of CeMIn5 (M: Co and Rh): Striking similarity between quasi 2D heavy fermion and high-Tc cuprates
• Nodal gap structure of BaFe_2(As_{1-x}P_x)_2 from angle-resolved thermal conductivity in a magnetic field
• Anisotropic Structure of the Order Parameter in FeSe0.45Te0.55 Revealed by Angle Resolved Specific Heat
• Pairing states of spin-3/2 fermions: Symmetry-enforced topological gap functions
• Evidence for even parity unconventional superconductivity in Sr${}_2$RuO${}_4$
• Fully gapped superconductivity with no sign change in the prototypical heavy-fermion CeCu2Si2
• Twofold spontaneous symmetry breaking in a heavy fermion superconductor UPt${}_3$
• Direct visualization of the nematic superconductivity in Cu${}_x$Bi${}_2$Se${}_3$
• Field-angle-dependent specific heat measurements and gap determination of a heavy fermion superconductor URu2Si2
• Searching for gap zeros in Sr2RuO4 via field-angle-dependent specific-heat measurement
• Unconventional superconductors under rotating magnetic field I: density of states and specific heat
• Superconducting Gap Structure of LaFePO Studied by Thermal Conductivity
• Unconventional superconducting gap structure protected by space group symmetry
• Classification of multipole superconductivity in multi-orbital systems and its implications
• Three-Dimensional Majorana Fermions in Chiral Superconductors
• Determining gap nodal structures in Fe-based superconductors: angle-dependence of the low temperature specific heat in an applied magnetic field
• Intertwined Orders in Heavy-Fermion Superconductor CeCoIn${}_5$
• Unconventional thermal metallic state of charge-neutral fermions in an insulator
• Unconventional superconductors under rotating magnetic field II: thermal transport
• Fully gapped pairing state in spin-triplet superconductor UTe${}_2$
• Thermal conductivity evidence for d_{x^2-y^2} pairing symmetry in the heavy-fermion CeIrIn5 superconductor
• Superconducting gap with sign reversal between hole pockets in heavily hole-doped Ba1-xKxFe2As2
• Quasiparticle interference in heavy Fermion superconductor CeCoIn_5
• Theory of thermal conductivity in extended-$s$ state superconductors: application to ferropnictides
• Rotational Isotropy Breaking as Proof for Spin-polarized Cooper Pairs in the Topological Superconductor CuxBi2Se3
• Anomalous Energy Transport across Topological Insulator Superconductor Junctions
• Double helix nodal line superconductor
• Hall effect in heavy-fermion metals
• Paramagnetically induced gapful topological superconductors
• Andreev reflection and order parameter symmetry in heavy-fermion superconductors: the case of CeCoIn${}_5$
• Conventional s-wave superconductivity in BiS2-based NdO0.71F0.29BiS2 revealed by thermal transport measurements
• Spin-sensitive Long-ranged Proximity Effect for Triplet Superconductors
• Theory of quasiparticle vortex bound states in Fe-based superconductors: application to LiFeAs
• Thermal Transport for Probing Quantum Materials
• Magneto-transport properties governed by the antiferromagnetic fluctuations in heavy fermion superconductor CeIrIn${}_5$
• Evidence for two energy gaps and Fermi liquid behavior in SrPt${}_2$As${}_2$ superconductor
• Flux Line Lattice Melting and the Formation of a Coherent Quasiparticle Bloch State in the Ultraclean URu${}_2$Si${}_2$ Superconductor
• Fate of Majorana modes in ${\mathrm{CeCoIn}}_5$/${\mathrm{YbCoIn}}_5$ superlattices -a test bed for reduction of topological classification-
• Quasiparticle Excitations in the Superconducting State of FeSe Probed by Thermal Hall Conductivity in the Vicinity of the BCS-BEC Crossover
• Nodes vs. minima in the energy gap of iron-pnictides from field-induced anisotropy
• Tilted vortex cores and superconducting gap anisotropy in 2H-NbSe2
• Negative thermal magnetoresistivity as a signature of chiral anomaly in Weyl superconductors
• A precursor state to unconventional superconductivity in CeIrIn${}_5$
• Mechanism of superconductivity and electron-hole doping asymmetry in $\kappa$-type molecular conductors
• Superconducting gap function in the organic superconductor (TMTSF)2ClO4 with anion ordering; First-principles calculations and quasiclassical analysis for angle-resolved heat capacity
• Supercurrent-induced topological phase transitions
• Angular resolved specific heat in iron-based superconductors: the case for nodeless extended $s$-wave gap
• GPU-based acceleration of free energy calculations in solid state physics
• Kramer-Pesch approximation for analyzing field-angle-resolved measurements made in unconventional superconductors: A calculation of the zero-energy density of states
• Superconducting order parameter in nonmagnetic borocarbides RNi${}_2$B${}_2$C (R=Y, Lu) probed by point-contact Andreev reflection spectroscopy
• Transport properties of 3D extended s-wave states in Fe-based superconductors
• Rashba spin-orbit coupling effects in quasiparticle interference of non-centrosymmetric superconductors
• Geometric pi Josephson junction in d-wave superconducting thin films
• Field-angle-resolved anisotropy in superconducting CeCoIn5 using realistic Fermi surfaces
• Enhanced quasiparticle heat conduction of the multigap superconductor Lu2Fe3Si5
• Inversion of specific heat oscillations with in-plane magnetic field angle in 2D d-wave superconductors
• Influence of disorder on the signature of pseudogap and multigap superconducting behavior in FeSe
• Vortex state in d-wave superconductors with strong paramagnetism: transport and specific heat anisotropy
• Topological Phase Transitions in Line-nodal Superconductors
• Specific Heat To Hc2: Evidence for Nodes or Deep Minima in the Superconducting Gap of Under- and Overdoped Ba(Fe1-xCox)2As2
• Heat-Capacity Measurements of Energy-Gap Nodes of the Heavy-Fermion Superconductor CeIrIn5 Deep inside the Pressure-Dependent Dome Structure of its Superconducting Phase Diagram
• Full t-matrix approach to quasiparticle interference in non-centrosymmetric superconductors
• Searching for zeroes: unconventional superconductors in a magnetic field
• Spin-Orbital Hallmarks of Unconventional Superconductors Without Inversion Symmetry
• Magneto-thermal-switching properties of superconducting Nb
• Field-rotational magnetocaloric effect: A new experimental technique for accurate measurement of the anisotropic magnetic entropy
• Field-angle-dependent low-energy excitations around a vortex in the superconducting topological insulator CuxBi2Se3
• Doping evolution of the superconducting gap structure in heavily hole-doped Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$: heat transport study
• Unconventional Superconductivity arising from Multipolar Kondo Interactions
• Rashba versus Kohn-Luttinger: Evolution of p-wave superconductivity in magnetized two-dimensional Fermi gas subject to spin-orbit interaction
• Dielectric Resonator Method For Determining Gap Symmetry Of Superconductors Through Anisotropic Nonlinear Meissner Effect
• Cooper Pair Shape in Normal-metal/Superconductor Junctions
• Nodal gap detection through polar angle-resolved density of states measurements in uniaxial superconductors
• Fate of the Hebel-Slichter peak in superconductors with strong antiferromagnetic fluctuations
• Role of Fermi surface anisotropy in the study of gap anisotropy using magnetic-field-angle dependence of thermal oscillations in AyFe2-xSe2 superconductors
• Supercurrent-Induced Weyl Superconductivity
• Multigap Superconductivity in the Ferromagnetic Superconductor UCoGe Revealed by Thermal Conductivity Measurements
• Heat transport in nonuniform superconductors
• Time-reversal symmetry violation and the structure of Superconducting Order Parameter of PrOs${}_4$Sb${}_{12}$
• Effect of uniaxially anisotropic Fermi surface on the quasiparticle scattering inside a vortex core in unconventional superconductors
• Field-angle Resolved Flux-flow Resistivity as a Phase-sensitive Probe of Unconventional Cooper Pairing
• Theory of tunneling spectroscopy in UPd2Al3
• Heat transport study of field-tuned quantum criticality in CeIrIn5
• Coupling between heavy fermion superconductor CeCoIn${}_5$ and antiferromagnetic metal CeIn${}_3$ through the atomic interface
• Connection between in-plane upper critical field $H_{c2}$ and gap symmetry in layered $d$-wave superconductors revisited
• Momentum space imaging of locally noncentrosymmetric superconductors
• Thermal Transport in Superconductors with coexisting Spin Density Wave Order
• Vortex Core Structure in Multilayered Rashba Superconductors
• Normal Fermi Surface in the Nodal Superconductor CeCoIn${}_5$ Revealed via Thermal Conductivity
• Possible two-component pairings in electron-doped Bi${}_2$Se${}_3$ based on a tight-binding model
• Field angle-dependent thermal conductivity in nodal superconuctors
• Phase-Sensitive Flux-Flow resistivity in Unconventional Superconductors
• Unconventional superconductivity in YNi2B2C
• Intrinsic Mechanism for Magneto-Thermal Conductivity Oscillations in Spin-Orbit-Coupled Nodal Superconductors
• Geometric pi Josephson junction: Current-phase relations and critical current