ElusiveQuantum electronic materials: phases insights in correlated from near oxides field nano-optics and graphen insightD.N. Basov,from infraredColumbia nano-Universityscopy D.N. Basov Columbia University

Support: Quantum materials: insights from near field nano-optics D.N. Basov, Columbia University Domain walls/ Weyl states CDW droplets / cuprates Phase separation / stripes Nd IrO HgBa CuO metal 2 7 2 4 V2O3 insulator

1 µm 2 µm 1 µm Ma et al. Campi et al. McLeod et al. Science 350, 538 (2015) Nature 525, 359 (2015) Nature Physics (2017) Edge currents & states 2DEG-QHE

1 µm Lai et al. PRL 107, 176809 (2011)

λIR Quantum materials: insights from near field nano-optics D.N. Basov, Columbia University

Outline: Why nano-light? “Complete” response function Phase transitions at the nanoscale σ(ω,t,x,q ) McLeod et al. Nature Physics (2017) Jang et al. Nature Materials (2016) delay Light-matter polaritons & search for Berry plasmons Ni et al. Nature Phot 10 244 (16) Basov et al. Science (2016) probe

Guangxin Ni et al. Nature Photonics 10, 244 (2016) Quantum materials: insights from near field nano-optics D.N. Basov, Columbia University

Outline: Why nano-light?

K K’ t=0 Phase transitions at the nanoscale McLeod et al. Nature Physics (2017) Jang et al. Nature Materials (2016)

Light-matter polaritons & search for Berry plasmons nm Ni et al. Nature Phot 10 244 (16) delay Basov et al. Science (2016)

probe with C. Dean, J. Hone, M. Fogler & T. Low Quantum materials: insights from near field nano-optics D.N. Basov, Columbia University

Outline: Why nano-light?

Phase transitions at the nanoscale McLeod et al. Nature Physics (2017) Jang et al. Nature Materials (2016)

Light-matter polaritons & search for Berry plasmons Ni et al. Nature Phot 10 244 (16) Basov et al. Science (2016) Quantum materials and infrared nano-optics V2O3

100 GHz 1000 100 meV 1000

Density Phonons Plasmons m Spins Superfluids Excitons

µ waves – + – – + – – – – – – – – – 10 – + – Cyclotron modes and Landau Level transions Correlated Drude response metal Metals insulator Magnec resonances phonons Inter-band transions Superconducng gap polarons McLeod et al Nature Physics (2016) Fe- & Cu-based superconductors (pseudo)gap in cuprates Charge transfer gap Magnec resonances Hund’s coupling Van der Waals Josephson plasmons (anisotropic) plasmons Excitons & gap: MX ……. semiconductors Hyperbolic phonon polaritons 2 cyclotron resonance & LLs Excitons & gap: bP Topological insulators Surface & bulk plasmons & Weyl metals bulk 1ML helicons phonons Inter-band transions

Tunable Fermi Energy EF Graphene Tunable band gap in bilayer & band parameters

Dirac plasmons

1 10 100 1000 10000 cm-1

-1

IR wavelength: Wavenumbers, cm 1000 µm 100 µm 10 µm

D.N. Basov, M.Fogler, A.Lanzara, F. Wang and Y. Zhang, RMP 86, 959 (2014) D.N. Basov, R.A. Averitt, D. van der Marel, M. Dressel, K. Haule RMP 83, 471 (2011) D.N. Basov and A,V. Chubukov Nature-Physics 7, 272 (2011)

Quantum materials and infrared nano-optics V2O3

100 GHz 1000 100 meV 1000

Density Phonons Plasmons m Spins Superfluids Excitons

µ waves – + – – + – – – – – – – – – 10 – + – Cyclotron modes and Landau Level transions Correlated Drude response metal Metals insulator Magnec resonances phonons Inter-band transions Superconducng gap polarons McLeod et al Nature Physics (2016) Fe- & Cu-based superconductors (pseudo)gap in cuprates Charge transfer gap Magnec resonances Hund’s coupling Van der Waals Josephson plasmons (anisotropic) plasmons Excitons & gap: MX ……. semiconductors Hyperbolic phonon polaritons 2 cyclotron resonance & LLs Excitons & gap: bP Topological insulators Surface & bulk plasmons & Weyl metals bulk 1ML helicons phonons Inter-band transions

Tunable Fermi Energy EF Graphene IR Tunable band gap in bilayer & band parameters

Dirac plasmons

1 10 100 1000 10000 cm-1

-1

IR wavelength: Wavenumbers, cm Δx 1000 µm 100 µm 10 µm

x < 8-10 nm << D.N. Basov, M.Fogler, A.Lanzara, F. Wang and Y. Zhang, RMP 86, 959 (2014) Δ λ D.N. Basov, R.A. Averitt, D. van der Marel, M. Dressel, K. Haule RMP 83, 471 (2011) D.N. Basov and A,V. Chubukov Nature-Physics 7, 272 (2011) σ(ω,t,x,q) Quantum materials: insights from infrared nano-optics D.N. Basov, Columbia University

Outline: Why nano-light?

Phase transitions at the nanoscale McLeod et al. Nature Physics (2017) Jang et al. Nature Materials (2016)

Light-matter polaritons & search for Berry plasmons V2O3 Ni et al. Nature Phot 10 244 (16) Basov et al. Science (2016)

10 µm metal insulator McLeod et al Nature Physics (2016) V2O3: a prototypical Mott insulator

Low-T High-T J. Phys.: Condens. Matter 21 (2009) 355401 CMeneghiniet al J. Phys.: Condens. Matter 21 (2009) 355401Monoclinic CMeneghiniet al Corundum

AFI ordering

Figure 2. Schematic view of the experimental set-up. Data were Figure 2. Schematic view of the experimental set-up. Data were collected with x-ray polarization (ϵ)inthehexagonalplane(ϵ c ), ⊥ H collected with x-ray polarization (ϵ)inthehexagonalplane(ϵ cH), i.e. along x and y (top) and parallel to the hexagonal C axis cH ⊥ Figure 1. Schematic view of V2O3 structures: only V ions are shown i.e. along x and y (top) and parallel to the hexagonal C axis cH (bottom). The fluorescence emission was collected using two Figure 1. Schematic view of V2O3 structures: only V ions are shown for the sake of clarity. Left: the hexagonal cell with the trigonal for the sake of clarity. Left: the hexagonal cell with the trigonal (bottom). The fluorescence emission was collected using two photodiodes (P). photodiodes (P). (primitive) cell inside; right: relationship between corundum (room (primitive) cell inside; right: relationship between corundum (room temperature PM phase) and monoclinic (low temperature AFI phase) temperature PM phase) and monoclinic (low temperature AFI phase) unit cells. X-ray absorption measurements were performed aligning collected at the ID26 beamline of the European Synchrotron unit cells. X-ray absorption measurements were performed aligning collected at the ID26 beamline of the European Synchrotron the x-ray beam polarization along the three orthogonal directions of Radiation Facility (ESRF) in the fluorescence mode. The x-ray the x-ray beam polarization along the three orthogonal directions of Radiation Facility (ESRF) in the fluorescence mode. The x-ray the hexagonal lattice: the c axis and, perpendicular to it, the x and y the hexagonal lattice: the c axis and, perpendicular to it, the x and y beam energies were selected using a double-crystal Si(220), beam energies were selected using a double-crystal Si(220), (corresponding to the monoclinic bm axis, see the text) directions (corresponding to the monoclinic bm axis, see the text) directions highlighted on the left. fixed-exit monochromator, providing an energy resolution of highlighted on the left. fixed-exit monochromator, providing an energy resolution of 0.3eVattheVK-edge. Energyscansweredonein 0.3eVattheVK-edge. Energyscansweredonein ∼ ∼ the so-called gap-scan mode, that is, tuning the maximum the so-called gap-scan mode, that is, tuning the maximum though the AFI and PI phases were reported, respectively, as of the undulator emission to the actual monochromator though the AFI and PI phases were reported, respectively, as of the undulator emission to the actual monochromator monoclinic and trigonal by x-ray diffraction studies [7], in [23] rocking curve. Two mirrors provided an harmonic-free, monoclinic and trigonal by x-ray diffraction studies [7], in [23] rocking curve. Two mirrors provided an harmonic-free, no evident differences were found for the local structure in small (diameter 300 µm), intense x-ray spot size on the no evident differences were found for the local structure in small (diameter 300 µm), intense x-ray spot size on the ∼ ∼ the two phases and both were fitted better by the monoclinic sample, linearly polarized in the horizontal plane. The the two phases and both were fitted better by the monoclinic sample, linearly polarized in the horizontal plane. The structure than by the trigonal one. Even though we basically fluorescence intensity emitted from the sample was collected in structure than by the trigonal one. Even though we basically fluorescence intensity emitted from the sample was collected in agree with the analysis of [23], two key ingredients were still the total-fluorescence mode by measuring the current from two agree with the analysis of [23], two key ingredients were still the total-fluorescence mode by measuring the current from two missing in their treatment for a full characterization of the PI photodiodes (figure 2), mounted parallel to the polarization of missing in their treatment for a full characterization of the PI photodiodes (figure 2), mounted parallel to the polarization of phase, i.e. a full temperature dependence study of the signal, the incoming beam in order to minimize the elastic contribution phase, i.e. a full temperature dependence study of the signal, the incoming beam in order to minimize the elastic contribution and a comparative study of the behavior of first-and further- to the spectrum and the self-absorption effect [28]. and a comparative study of the behavior of first-and further- to the spectrum and the self-absorption effect [28]. nearest neighbors. In particular, since the measurements The 2.8% chromium-doped V2O3 single crystal was nearest neighbors. In particular, since the measurements The 2.8% chromium-doped V2O3 single crystal was of [23]inthePIphasewerecollectedatatemperature mounted in a closed-cycle He refrigerator for temperature of [23]inthePIphasewerecollectedatatemperature mounted in a closed-cycle He refrigerator for temperature (180 K) only 15 K above the transition temperature of their scans between 100 K and room temperature. The (180 K) only 15 K above the transition temperature of their scans between 100 K and room temperature. The Al-doped compound (whereas those of [7]wereperformedat sample temperature was continuously monitored using a K Al-doped compound (whereas those of [7]wereperformedat sample temperature was continuously monitored using a K room temperature), the authors may have missed the point, thermocouple mounted near to the sample ( 5mm).Inorder room temperature), the authors may have missed the point, thermocouple mounted near to the sample ( 5mm).Inorder ∼ ∼ suggested by RXS from [24], that the paramagnetic insulating to exploit the directional sensitivity of polarized EXAFS, the suggested by RXS from [24], that the paramagnetic insulating to exploit the directional sensitivity of polarized EXAFS, the crystal structure changes with temperature even within the absorption spectra were collected by correctly orienting the crystal structure changes with temperature even within the absorption spectra were collected by correctly orienting the PI phase. Other EXAFS measurements have been reported single crystal with respect to the linear polarization of the x- PI phase. Other EXAFS measurements have been reported single crystal with respect to the linear polarization of the x- in the literature for the stoichiometric compound [19]: we ray beam (figure 1). in the literature for the stoichiometric compound [19]: we ray beam (figure 1). shall comment on them in section 7,whenwecomparetheir Absorption spectra were collected in quick-EXAFS modes shall comment on them in section 7,whenwecomparetheir Absorption spectra were collected in quick-EXAFS modes conclusions to ours in order to characterize the differences (20 s per scan) in the energy range 5300–6300 eV (about 4000 conclusions to ours in order to characterize the differences (20 s per scan) in the energy range 5300–6300 eV (about 4000 between PI and PM phases. points per scan). The geometric set-up and the high energy between PI and PM phases. points per scan). The geometric set-up and the high energy resolution of the ID26 optic yielded very narrow Bragg peaks resolution of the ID26 optic yielded very narrow Bragg peaks 3. Experimental set-up (few energy points) in the spectra. In order to remove them, 3. Experimental set-up (few energy points) in the spectra. In order to remove them, for each temperature several (60–90) spectra were collected for each temperature several (60–90) spectra were collected In our experiment a 2.8% chromium-doped V2O3 single- at different angles by rocking the sample ( 2◦)aroundthe In our experiment a 2.8% chromium-doped V2O3 single- at different angles by rocking the sample ( 2◦)aroundthe crystal (about 5 5 2mm3)samplewasused. Itis vertical axis. With this procedure Bragg peaks± were shifted crystal (about 5 5 2mm3)samplewasused. Itis vertical axis. With this procedure Bragg peaks± were shifted × × × × the same sample already used for the experiments performed in energy along the spectra so that they could be easily singled the same sample already used for the experiments performed in energy along the spectra so that they could be easily singled in [9, 24, 26, 27]. The material was grown in a skull out and removed. We could in this way register many scans, in [9, 24, 26, 27]. The material was grown in a skull out and removed. We could in this way register many scans, melter under a controlled atmosphere and slowly cooled. Bragg peak free, for each temperature point. The average of melter under a controlled atmosphere and slowly cooled. Bragg peak free, for each temperature point. The average of The single crystals were then harvested and annealed. X- all the scans provided exceptional quality, low noise, XAS The single crystals were then harvested and annealed. X- all the scans provided exceptional quality, low noise, XAS ray absorption spectra at V K-edge (E0 5465 eV) were spectra suitable for accurate quantitative structural studies. ray absorption spectra at V K-edge (E0 5465 eV) were spectra suitable for accurate quantitative structural studies. = = 3 3 Phase separation in V2O3: insights from IR nano-imaging With Ivan Schuller (UCSD)

Near-field! probe! E Einc scat

300 nm V2O3 film!

λIR 5 microns

Insulang Metallic A. McLeod et al. Nature Physics 13, 80 (2017) Phase separation in V2O3: insights from IR nano-imaging With Ivan Schuller (UCSD)

In situ resistance!

λIR 5 microns

Insulang Metallic A. McLeod et al. Nature Physics 13, 80 (2017) Phase separation in V2O3: insights from IR nano-imaging With Ivan Schuller (UCSD)

In situ resistance!

λIR 5 microns

Insulang Metallic A. McLeod et al. Nature Physics 13, 80 (2017) V2O3 : hidden phases in the insulator to metal transion region Population % Population

T=184 K 177 K 174 K 171 K 169 K T=164 K

Near field amplitude

B. Spivak & S. A. Kivelson. Ann Phys 321 2071, 255–256 (2005).

A. McLeod et al. Nature Physics 13, 80 (2017) Quantum materials: insights from infrared nano-optics D.N. Basov, Columbia University

Outline: Why nano-light?

K K’ t=0 Phase transitions at the nanoscale McLeod et al. Nature Physics (2016) Jang et al. Nature Materials (2017)

Light-matter polaritons & search for Berry plasmons nm Ni et al. Nature Phot 10 244 (16) delay Basov et al. Science (2016)

probe with C. Dean, J. Hone, M. Fogler & T. Low On surface plasmon polaritons

λ0 λP incident wavelength Volume polariton wavelength plasmon

εΑ > 0 λ0/λP=80-200 – – – Plasmon-polaritons εΒ < 0 (graphene, black P )

Phonon-polaritons, (hBN, topological insulators) On many kinds of polaritons in van der Waals materials

λ0 incident wavelength λP polariton wavelength

ε > 0 / =80-200 Α λ0 λP – – + + – – + Magnon-polaritons, – Plasmon- polaritons ε < 0 – – – (Cr Ge Te ) Β – + + + + – – 2 2 6 (graphene, black P ) IR

Exciton-polaritons Phonon-polaritons Cooper-pair polaritons (Cuprates, FeSe)

Boron nitride, Bi2Se3 MoS2, WSe2

D. N. Basov, M. M. Fogler, and F. J. García de Abajo Science 354, 195 (2016) Visualizing many kinds of polaritons…

λ0 incident wavelength λP polariton wavelength Volume plasmon ε > 0 / =80-200 Α ω λ0 λP – – + + – – + Magnon-polaritonsIR , – Plasmon- polaritons ε < 0 – – – (Cr Ge Te ) Β – + + + + – – 2 2 6 (graphene, black P )

Phonon-polaritons, (hBN, topological Exciton-polaritons 1/λp IR insulators) (MoS2, WSe2) Polaritonic images: a tool to study New Physics of quantum materials Plasmon polaritons in graphene

λp/2 Fei et al Nature 487, 82 (2012) 200 nm Chen et al. Nature 487, 77 (2012) Plasmons in gapped Dirac materials: Berry plasmons

K -K Frequency

ω-

ω+

IqI

L. Levitov, G.Refael, J.Song, Bi-layer graphene, MoS2, many other… N.Fang, S. Das Sarma, T.Low, … Plasmons in gapped Dirac materials: Berry plasmons

K -K

Δ Frequency λp ω- λp

ω+

ωIR

1/λp 1/λp IqI

L. Levitov, G.Refael, J.Song, N.Fang, S. Das Sarma, T.Low, … Plasmons on demand in hBN-G-hBN structures delay ω, cm-1 1000

950 probe

900 s 850 L. Wang, et al. Science 342, 614 (2013) Wang, et al. Science 342, 614 (2013) nm Sample edge t=0 IR

Plasmon polaritons in graphene

200 nm

nm

Guangxin Ni et al. (Nature Photonics 10, 244 2016) Hyper-spectral images of non-equilibrium plasmons delay ω, cm-1 1000

950 probe

900

s 850 Wang, et al. Science 342, 614 (2013) nm -1 (cm ) Sample edge 1000

950

900

850 400 400 400 400 200 200 200 200 0 0 0 0 L (nm) Guangxin Ni et al. (Nature Photonics 10, 244 2016) 1. Nano-light σ(ω,t,xq) 2. New electronic phases in oxides

1µm A. McLeod et al. Nature Physics 13, 80 (2017) J. Zhang et al. Nature Materials 15, 956 (2016)

4. Search for Berry plasmons 3. Spectroscopy & imaging with polaritons t=0

nm Guangxin Ni et al. Nature Photonics 10, 244 (2016) D.N. Basov et al. Science (2016)