Soft phonon modes at charge-density-wave transitions Frank Weber, Neutron Scattering Group E(q) temperature q CDW = 2k F wave vector q KIT The Research University in the Helmholtz Association www.kit.edu
Motivation Competing phases in superconducting materials Spin-density-wave Pseudo-gap phase Charge-density-wave Superconductivity Fe-based superconductors Cuprate superconductors Transition-metal dichalcogenides Tunable interactions of different degrees of freedom via Intercalation Cu x TiSe 2 Morosan et al. Nat. phys. 2, 544 (2006). 2
Motivation Competing phases in superconducting materials Spin-density-wave Pseudo-gap phase Charge-density-wave Superconductivity Fe-based superconductors Cuprate superconductors Transition-metal dichalcogenides Tunable interactions of different degrees of freedom via Intercalation Pressure 1T-TaS 2 Sipos et al. Nat. mat. 7, 960 (2008). 3
Motivation Competing phases in superconducting materials Spin-density-wave Pseudo-gap phase Charge-density-wave Superconductivity Fe-based superconductors Cuprate superconductors Transition-metal dichalcogenides Tunable interactions of different degrees of freedom via Intercalation Pressure Enhanced T CDW in single layer of NbSe 2 Dimensionality Xi et al., Nat Nano 10, 765 (2015). 4
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 Superconductivity temperature q CDW = 2k F wave vector q Superconductivity: The Eliashberg function αα 2 FF(ωω) can be derived from phonon spectroscopy. μμ : effective electron-electron interaction potential 5
Outline Soft phonon mode in the Peierls scenario of charge-density-wave transitions ZrTe 3 2H-NbSe 2 6
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: 2kk FF = ππ/aa non-zero electron-phonon coupling Peierls: system unstable towards doubling of the unit cell gap opening in one-electron band energy 7
Peierls scenario for CDW formation R. E. Peierls, Quantum Theory of Solids (Oxford University Press, New York / London, 1955). EE tttttttttt = EE eeeeeeeeeeeeeeeeeeee + EE llllllllllllll EE eeeeeeeeeeeeeeeeeeee uu 2 Ground state for uu log uu 0 0 > 0 EE llllllllllllll uu 2 0 (small uu) 8
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 qq = 2kk FF Peak in imaginary part of electronic susceptibility χχ Peak in real part of electronic susceptibility χχ 9
Soft phonon mode in CDW materials Soft phonon mode: Sharp Kohn anomaly defined by χχ : ωω 2 2 qq = ωω bbbbbbbb 2NN 3 g qq 2 χχ MM 1 + 2 UU qq VV qq χχ E(q) TT TT CCCCCC q CDW = 2k F TT = TT CCCCCC S. K. Chan and V. Heine Journal of Physics F: Metal Physics 3, 795 (1973). wave vector q 10
Soft phonon mode in CDW materials Soft phonon mode: Sharp Kohn anomaly defined by χχ Quasi 1D conductor: K 2 Pt(CN) 4 Br 0.3 xx D 2 O (KCP) R. Comes et al., Phys Status Solidi B 71, 171 (1975). E(q) q CDW = 2k F wave vector q 11
Soft phonon mode in CDW materials Soft phonon mode: Sharp Kohn anomaly Temperature dependence E(q) q CDW = 2k F wave vector q 12
Soft phonon mode in CDW materials Soft phonon mode: Sharp Kohn anomaly Temperature dependence TbTe 3 : TT CCCCCC = 330 K M. Maschek et al., Phys. Rev. B 91, 235146 (2015). E(q) q CDW = 2k F wave vector q 13
Soft phonon mode in CDW materials Soft phonon mode: Sharp Kohn anomaly Temperature dependence TbTe 3 : TT CCCCCC = 330 K M. Maschek et al., Phys. Rev. B 91, 235146 (2015). Mean field behavior J. Pouget et al., Phys. Rev. B 43, 8421 (1991). E(q) q CDW = 2k F wave vector q 14
Soft phonon mode in CDW materials Soft phonon mode: Sharp Kohn anomaly Temperature dependence TbTe 3 : TT CCCCCC = 330 K M. Maschek et al., Phys. Rev. B 91, 235146 (2015). Mean field behavior J. Pouget et al., Phys. Rev. B 43, 8421 (1991). E(q) q CDW = 2k F wave vector q 15
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
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 YNi 2 B 2 C (Weber et al., PRB 2014) Density-functional-perturbationtheory (DFPT) Phonon dispersion based on electronic & atomic structure phonon structure factors (for all Brillouin zones) Electron-phonon-coupling (QQ and EE dependent) Rolf Heid, Roland Hott, Klaus-Peter Bohnen (KIT) 17
ZrTe 3 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 TT CCCCCC 18
ZrTe 3 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 TT TT CCCCCC Elastic peak at TT TT CCCCCC (short range order) 19
2H-NbSe 2 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 TT = TT CCCCCC = 33 K Phonon softening E phon T TT TT CCCCCC δδ, δδ = 0.5 ± 0.03 20
2H-NbSe 2 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 TT = TT CCCCCC = 33 K Phonon softening E phon T TT TT CCCCCC δδ, δδ = 0.5 ± 0.03 BUT: No Fermi-surface nesting 21