Advanced Spectroscopies of Modern Quantum Materials

Transcription

1 Advanced Spectroscopies of Modern Quantum Materials The part about Advanced spectroscopies Some course goals: Better understand the link between experiment and the microscopic world of quantum materials. The goal of this course is to expose students to key questions in this field, and have them become comfortable with critically evaluating experimental research papers on the topics covered.

2 By D-Kuru - Own work, CC BY-SA 3.0 at, Origins

3 Origins Hydrogen Iron By D-Kuru - Own work, CC BY-SA 3.0 at,

4 A bit more sophisticated... X-ray Absorption Spectroscopy (XAS) Fermi energy Ce metal Core state i.e. 1s electron Yb 2 O 3 Incoming Photon Energy (ev) Incoming photon energy (ev) B. T. Thole, et al. PRB 1985

5 Experimental Method Interesting system detection Interaction Response Measurement

6 Example: Neutron Scattering

7 Example: Neutron Scattering Probe: neutrons with S = ½. Wavelength: ~ 1 A. Interactions: Strong force and dipole-dipole. Measured response: Scattering cross section. System info (susceptibility): e.g. magnetic - S m (q,w). Magnetic scattering cross section d # σ dωde = k ) k * r, S. (q, ω) Interaction Elastic Inelastic Strong Force nuclear scattering Magnetic (dipole-dipole). Location of nuclei in the solid. Bragg peaks. Position and orientation of magnetic moments in solid. (e.g. Antiferromagnetism). Lattice vibrations, phonons. Spin excitations / magnons in the solid.

8 Many options of probes... Massive Particles: Electrons (S = ½, -e) Positrons (S = ½, +e) Neutrons (S = ½, 0) Muons (S = ½, -e) Example: Neutrons Probe (perturbation): S = ½. Wavelength: ~ 1 A. Measured response: Scattering cross section. Susceptibility: e.g. Magnetic - c m (q,w).

9 Many options of probes... Electro-magnetic fields (aka photons, radiation, X-rays): Propagation in free space (Maxwellian Physics): E = e E, e *(6.8 :;<) B = 1 ω k E Energy quantization E = ħω = hf = DE F hc = 12.4 kev A Quantum Description A r, t = I QR,M ħ 2ε, Vω M ε a QR,M e * M.8 :;< + ε a U QR,M :* M.8 :;< e p p qa Massive Particles: Electrons (S = ½, -e) Positrons (S = ½, +e) Neutrons (S = ½, 0) Muons (S = ½, -e) Example: Neutrons Probe (perturbation): S = ½. Wavelength: ~ 1 A. Measured response: Scattering cross section. Susceptibility: e.g. Magnetic - c m (q,w).

10 Linear Response Theory Interesting system detection Interaction Response Measurement Note: Often this scheme can be described in the Linear Response formalism. Measured Response = Susceptibility X Probe Tells us something about the system!

11 From Introduction to Many-Body Physics by Piers Coleman

12 Linear Response Theory Interesting system detection Interaction Response Measurement Warning: Requires the probe-system interaction to be gentle. In some spectroscopic methods, under certain conditions, this is NOT the case. Measured Response = Susceptibility X Probe Tells us something about the system!

13 The path to enlightenment is as sharp and narrow as a razor's edge. or How to be creative to extract maximal information from the measurement... without being TOO creative!

14 In this class: 4 methods in more detail. Angle-resolved PhotoEmission Spectroscopy - ARPES photon in electron out Inna Vishik*, Chuck Fadley, Eduardo H. da Silva Neto* (Scanning) Tunneling Microscopy/Spectroscopy STM/S electron in (or) electron out Eduardo H. da Silva Neto*, Mohammad Hamidian*, Shirley Chiang Resonant (Inelastic) X-ray Scattering R(I)XS photon in photon out Eduardo H. da Silva Neto*, Chuck Fadley Time-domain Spectroscopies photon in photon out Inna Vishik* * Denominates new faculty members of the UC Davis Physics Department.

15 Photoemission (ARPES) Incident Photon Quantum Material Hemispherical Analyzer Example: Copper 111 surface Photon energy: 5 to 100 ev (typically) Measure: the direction and energy of the photo-electron. Physics Result: Map the electronic states of the system in energy and momentum (i.e. the band structure, Fermi surfaces). A. TAMAI et al. PRB 87, (2013)

16 Photoemission (ARPES) Incident Photon Quantum Material Hemispherical Analyzer Example: Bi 2 Se 3 Topological Insulator Photon energy: 5 to 100 ev (typically) Measure: the direction and energy of the photo-electron. Physics Result: Map the electronic states of the system in energy and momentum (i.e. the band structure, Fermi surfaces). More examples in quantum materials: Lu, Vishik, Yi, Chen, Moore, Shen Ann. Rev. Cond Mat. Phys. (2014) Chen YL, Chu JH, Analytis JG, Liu ZK, Igarashi K, et al Science 329:659 62

17 Tunneling (STM/S) ~ 1 Angstrom Quantum Material Tip (a sharp piece of metal). Measure: tunneling current through the vacuum barrier. Result: Electronic states as a function of energy and space (atomic resolution). E.g. Charge Density Waves. What is the probe? The tip. What is the detector? The tip. ~ 50 Angstroms e.g. Cd-dopants CeCoIn 5 Yazdani, da Silva Neto & Aynajian, Ann. Rev. Cond Mat. Phys. (2016)

18 Tunneling (STM/S) ~ 1 Angstrom Quantum Material Measure: tunneling current through the vacuum barrier. Result: Electronic states as a function of energy and space (sub-atomic resolution). E.g. Charge Density Waves. What is the probe? The tip. What is the detector? The tip. ~ 200 Angstroms Tip (a sharp piece of metal). Example: Copper 111 surface a Yazdani, da Silva Neto & Aynajian, Ann. Rev. Cond Mat. Phys. (2016)

19 Resonant Inelastic X-ray Scattering Incident Photon Quantum Material Point detector (e.g. photodiode), spectrometer (inelastic). Photon energy: 500 ev to 1keV (soft), or 2.5 to 5 kev (hard). Measure: the direction and energy of the scattered photon. Result: Periodic spatial distribution of electronic states. Result (details under debate): Phonon and magnon dispersions. Several excitations with momentum resolution. Spin-orbital separation in Sr 2 CuO 3 Nature 485,

20 Time Domain Spectroscopy (TDS) Probe Pulse Quantum Material Use short pulses of light (~ femtoseconds) to study scattering processes and collective modes in materials in time domain Two pulses: Pump pulse: prepare electronic system in nonequilibrium state (e.g. direct excitations, hot electrons, large electric field) Probe pulse: interrogate how electrons have responded to perturbation and how they return back to equilibrium as a function of time delay from pump Many experiments based on light matter interaction can be implemented in a time-domain version Detector... Transient reflectivity of K 0.3 MoO 3 (blue bronze) Demsar et al. PRL (1999)

21 What are quantum materials? General remarks about spectroscopy. Interaction-Response-Measurement. Creative Interpretation Summary of RIXS, TDS, ARPES, STM/S. On Monday: STM/S (Eduardo) How sharp does a tip need to be to see atoms? On Wednesday: ARPES (Inna) Take the survey...