Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (2024)

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Normal Fermi Surface in the Nodal Superconductor ${CeCoIn}_{5}$ Revealed via Thermal Conductivity

Sangyun Lee, Duk Y. Kim, Priscila F. S. Rosa, Eric D. Bauer, Filip Ronning, J. D. Thompson, Shi-Zeng Lin, and Roman Movshovich

Phys. Rev. Lett. 132, 236002 – Published 5 June 2024

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Abstract

The thermal conductivity of heavy-fermion superconductor ${CeCoIn}_{5}$ was measured with a magnetic field rotating in the tetragonal $a - b$ plane, with the heat current in the antinodal direction, $J | | [100]$ . We observe a sharp resonance in thermal conductivity for the magnetic field at an angle $Θ \approx 12 °$ , measured from the heat current direction [100]. This resonance corresponds to the reported resonance at an angle $Θ^{'} \approx 33 °$ from the direction of the heat current applied along the nodal direction, $J | | [110]$ . Both resonances, therefore, occur when the magnetic field is applied in the same crystallographic orientation in the two experiments, regardless of the direction of the heat current, proving conclusively that these resonances are due to the structure of the Fermi surface of ${CeCoIn}_{5}$ . We argue that the uncondensed Landau quasiparticles, emerging with field, are responsible for the observed resonance. We support our experimental results with density-functional-theory model calculations of the density of states in a rotating magnetic field. Our calculations, using a model Fermi surface of ${CeCoIn}_{5}$ , reveal several sharp peaks as a function of the field direction. Our study demonstrates that the thermal-conductivity measurement in rotating magnetic field can probe the normal parts of the Fermi surface deep inside the superconducting state.

$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (1)$
$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (2)$
$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (3)$
$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (4)$
$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (5)$

Received 28 March 2024
Accepted 6 May 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.236002

Physics Subject Headings (PhySH)

Research Areas

Density of statesElectronic structureFermi surfaceThermal conductivityd-wave

Physical Systems

Strongly correlated systemsSuperconductorsUnconventional superconductors

Authors & Affiliations

Sangyun Lee¹, Duk Y. Kim^1,*, Priscila F. S. Rosa¹, Eric D. Bauer¹, Filip Ronning¹, J. D. Thompson¹, Shi-Zeng Lin^2,3,†, and Roman Movshovich^1,‡

¹Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
²Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
³Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

^*Present address: Agency for Defense Development, Daejeon 34186, Republic of Korea.
^†Corresponding author: szl@lanl.gov
^‡Corresponding author: roman@lanl.gov

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Vol. 132, Iss. 23 — 7 June 2024

$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (6)$

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$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (7)$

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$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (10)$

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$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (11)$
Figure 1
Schematic diagram of the thermal conductivity measurement in rotating magnetic field applied within the $a - b$ plane of the tetragonal ${CeCoIn}_{5}$ . The heat current was applied along the [100] axis. $Θ$ is defined by the angle between the heat current and the direction of the magnetic field.
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$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (12)$
Figure 2
The magnetic field of 3T was rotated by 180° from the crystallographic [0–10] axis to the [010] axis. The heat current was applied along the [100] axis. The dashed line is a fit to the sum of a twofold and fourfold terms. The dotted line is fit to a twofold term only.
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$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (13)$
Figure 3
Thermal conductivity of ${CeCoIn}_{5}$ measured with rotating magnetic fields up to 7T. The heat current was applied along the [100] axis. (a)The data for the low angle range, from $- 40 °$ to 40°, highlighting the resonances at $\pm 12 °$ , with the sum of two, four, and eightfold fits to the background; (b) $κ / T$ vs. $T$ from (a)with the background fits subtracted; the resonances in field up to 5T are clearly resolved; (c) $κ / T$ vs $T$ in the regions of the high absolute value of angle, $Θ < - 50 °$ and $Θ > 50 °$ , with fits to the background obtained similarly to (a); (d) $κ / T$ vs $T$ from (c)with the background fits subtracted, showing the persistent resonances features at $Θ = \pm 78 °$ .
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$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (14)$
Figure 4
Thermal conductivity of ${CeCoIn}_{5}$ measured with an in-plane rotating magnetic field up to 7T, from Ref.[8]. The heat current was applied along the [110] axis. $Θ^{'}$ is defined by the angle between heat current and magnetic field directions. (a) $κ / T$ vs $T$ in the regions of the high absolute value of angle, $- 90 < Θ^{'} < 90 °$ , highlights the resonances at $\pm 33 °$ , as marked by the vertical red arrows.
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$Normal Fermi Surface in the Nodal Superconductor ${\mathrm{CeCoIn}}_{5}$ Revealed via Thermal Conductivity (15)$
Figure 5
Three representative Fermi surfaces of ${CeCoIn}_{5}$ and the calculated density of state as a function of the direction of the magnetic field. The field is rotated from [100] ( $Φ = 0 °$ ) to [010] ( $Φ = 0 °$ ) within the $a - b$ plane.
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