Soft Phonon Modes at Charge-Density-Wave Transitions

Soft phonon modes at charge-density-wave transitions

Frank Weber

Institute for Solid State Physics, Neutron Scattering Group

E(q)

qCDW = 2kF temperature wave vector q

KIT – The Research University in the Helmholtz Association www.kit.edu Motivation

Competing phases in superconducting materials

Spin-density-wave Fe-based superconductors Pseudo-gap phase Cuprate superconductors Charge-density-wave Transition-metal dichalcogenides Tunable interactions of different degrees of freedom via Super- CuxTiSe2 conductivity Intercalation

Morosan et al. Nat. phys. 2, 544 (2006).

2 Institute for Solid State Physics Motivation

Competing phases in superconducting materials

Sipos et al. Nat. mat. 7, 960 (2008).

3 Institute for Solid State Physics Motivation

Competing phases in superconducting materials

Dimensionality

Xi et al., Nat Nano 10, 765 (2015).

4 Institute for Solid State Physics Motivation

Electron-phonon-coupling important for CDW order & superconductivity

CDW: 1-dimensional metals are unstable towards a structural phase transition in presence of electron-phonon coupling (Peierls, 1955) E(q) CDW

qCDW = 2kF

Super- temperature wave vector q conductivity

Superconductivity: The Eliashberg function ( ) can be derived from phonon2 𝛼𝛼 𝐹𝐹 𝜔𝜔 spectroscopy.

: effective electron-electron ∗ interaction potential 𝜇𝜇

5 Institute for Solid State Physics Outline

Soft phonon mode in the Peierls scenario of charge-density-wave transitions

ZrTe3

2H-NbSe2

6 Institute for Solid State Physics Peierls scenario for CDW formation R. E. Peierls, Quantum Theory of Solids (Oxford University Press, New York / London, 1955).

Assumptions: 1D metal half filled band: 2 = / non-zero electron-phonon coupling 𝑘𝑘𝐹𝐹 𝜋𝜋 𝑎𝑎

Peierls: system unstable towards doubling of the unit cell gap opening in one-electron band energy

7 Institute for Solid State Physics Peierls scenario for CDW formation R. E. Peierls, Quantum Theory of Solids (Oxford University Press, New York / London, 1955).

= + Ground state for > 0 ∆𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 ∆𝐸𝐸𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒log ∆𝐸𝐸𝑙𝑙𝑙𝑙0𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 2 0 𝑢𝑢0 ∆𝐸𝐸𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒∝ 𝑢𝑢 𝑢𝑢 ≤ (small 2) ∆𝐸𝐸𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙∝ 𝑢𝑢 ≥ 𝑢𝑢

8 Institute for Solid State Physics Peierls scenario for CDW formation R. E. Peierls, Quantum Theory of Solids (Oxford University Press, New York / London, 1955).

1D metal: perfect Fermi surface nesting for = 2

→ Peak 𝐹𝐹in imaginary part of electronic𝑞𝑞⃗ 𝑘𝑘 susceptibility → Peak in real part of electronic′′ 𝜒𝜒 susceptibility ′ 𝜒𝜒

9 Institute for Solid State Physics Soft phonon mode in CDW materials

Soft phonon mode: E(q) Sharp Kohn anomaly defined by : 𝑇𝑇 ≫ 𝑇𝑇𝐶𝐶𝐶𝐶𝐶𝐶 = ′ 2 𝜒𝜒 𝐶𝐶𝐶𝐶𝐶𝐶 = q = 2k 𝑇𝑇 𝑇𝑇 1 + 23 2 ′ CDW F 2 2 𝑁𝑁 ℊ𝑞𝑞 ⋅ 𝜒𝜒 𝑞𝑞 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 ′ 𝜔𝜔S. K. Chan 𝜔𝜔and V. Heine− 𝑞𝑞 𝑞𝑞 Journal of Physics F: Metal Physics𝑀𝑀 3, 795 (1973).𝑈𝑈� − 𝑉𝑉� ⋅ 𝜒𝜒 wave vector q

10 Institute for Solid State Physics Soft phonon mode in CDW materials

Soft phonon mode: Sharp Kohn anomaly defined by ′ 𝜒𝜒

Quasi 1D conductor:

K2Pt(CN)4Br0.3 D2O (KCP)

⋅ 𝑥𝑥 R. Comes et al., Phys Status Solidi B 71, 171 (1975).

E(q)

qCDW = 2kF

wave vector q

11 Institute for Solid State Physics Soft phonon mode in CDW materials

Soft phonon mode: Sharp Kohn anomaly Temperature dependence

E(q)

qCDW = 2kF

wave vector q

12 Institute for Solid State Physics Soft phonon mode in CDW materials

Soft phonon mode: Sharp Kohn anomaly Temperature dependence

TbTe3: = 330 K M. Maschek et al., Phys. Rev. B 91, 235146 (2015). 𝑇𝑇𝐶𝐶𝐶𝐶𝐶𝐶

E(q)

qCDW = 2kF

wave vector q

13 Institute for Solid State Physics Soft phonon mode in CDW materials

Soft phonon mode: Sharp Kohn anomaly Temperature dependence

TbTe3: = 330 K M. Maschek et al., Phys. Rev. B 91, 235146 (2015). Mean field𝑇𝑇𝐶𝐶𝐶𝐶𝐶𝐶behavior J. Pouget et al., Phys. Rev. B 43, 8421 (1991).

E(q)

qCDW = 2kF

wave vector q

14 Institute for Solid State Physics Soft phonon mode in CDW materials

Soft phonon mode: Sharp Kohn anomaly Temperature dependence

TbTe3: = 330 K M. Maschek et al., Phys. Rev. B 91, 235146 (2015). Mean field𝑇𝑇𝐶𝐶𝐶𝐶𝐶𝐶behavior J. Pouget et al., Phys. Rev. B 43, 8421 (1991).

E(q)

qCDW = 2kF

wave vector q

15 Institute for Solid State Physics Experiment – phonons with neutrons & x-rays

Phonons on a triple axis spectrometer (TAS) TASs can reach all points in reciprocal space Q and energy E (as long as the scattering triangle can be closed)

Typically uses thermal neutrons Inelastic x-ray scattering at sector 30 Layout of the 1T Advanced Photon Source, ANL Triple-Axis-Spectrometer run by our group:

16 Institute for Solid State Physics Experiment – phonons with neutrons

Phonons on a triple axis spectrometer (TAS) TASs can reach all points in reciprocal space Q and energy E (as long as the scattering triangle can be closed)

Phonon dispersion in the superconductor YNi2B2C (Weber et al., PRB 2014) Density-functional-perturbation- theory (DFPT) Phonon dispersion based on electronic & atomic structure phonon structure factors (for all Brillouin zones) Electron-phonon-coupling ( and dependent)

Rolf Heid,𝑸𝑸 Roland𝐸𝐸 Hott, Klaus-Peter Bohnen Institute for Solid State Physics (KIT)

17 Institute for Solid State Physics ZrTe3 – Peierls works M. Hoesch, A. Bosak, D. Chernyshov, H. Berger, and M. Krisch, Physical Review Letters 102, 086402 (2009). M. Hoesch, X. Cui, K. Shimada, C. Battaglia, S.-i. Fujimori, and H. Berger, Physical Review B 80, 075423 (2009).

Fermi surface nesting Sharp Kohn anomaly

Superstructure peak sharply rising for

𝑇𝑇 ≤ 𝑇𝑇𝐶𝐶𝐶𝐶𝐶𝐶

18 Institute for Solid State Physics ZrTe3 – Peierls works - almost M. Hoesch, A. Bosak, D. Chernyshov, H. Berger, and M. Krisch, Physical Review Letters 102, 086402 (2009). M. Hoesch, X. Cui, K. Shimada, C. Battaglia, S.-i. Fujimori, and H. Berger, Physical Review B 80, 075423 (2009).

Fermi surface nesting Sharp Kohn anomaly

Superstructure peak sharply rising for

Elastic𝐶𝐶𝐶𝐶𝐶𝐶peak at (short𝑇𝑇 ≤ 𝑇𝑇 range order) 𝑇𝑇 ≫ 𝑇𝑇𝐶𝐶𝐶𝐶𝐶𝐶 19 Institute for Solid State Physics 2H-NbSe2 – phonon softening F. Weber et al., Physical Review Letters 107, 107403 (2011). F. Weber et al., Physical Review B 87, 245111 (2013). Superlattice peak rises only at = = 33 K

𝑇𝑇Phonon𝑇𝑇𝐶𝐶𝐶𝐶𝐶𝐶 softening E T , = 0.5 ± 0.03 𝛿𝛿 phon ∝ 𝑇𝑇 − 𝑇𝑇𝐶𝐶𝐶𝐶𝐶𝐶 𝛿𝛿

20 Institute for Solid State Physics 2H-NbSe2 – phonon softening withouth nesting F. Weber et al., Physical Review Letters 107, 107403 (2011). F. Weber et al., Physical Review B 87, 245111 (2013). Superlattice peak rises only at = = 33 K

𝑇𝑇Phonon𝑇𝑇𝐶𝐶𝐶𝐶𝐶𝐶 softening E T , = 0.5 ± 0.03 𝛿𝛿 phon ∝ 𝑇𝑇 − 𝑇𝑇𝐶𝐶𝐶𝐶𝐶𝐶 𝛿𝛿 BUT: No Fermi-surface nesting

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