Ultrafast angle-resolved photoemission spectroscopy of quantummaterials

Christopher L. Smallwood1, Robert A. Kaindl2 and Alessandra Lanzara2,3 (a)

1 JILA, University of Colorado and National Institute of Standards and Technology, Boulder, CO 80309, USA2 Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA3 Department of Physics, University of California, Berkeley, CA 94720, USA

PACS 78.47.J- – Ultrafast spectroscopyPACS 74.25.Jb – Electronic structure (photoemission, etc.)PACS 74.40.Gh – Nonequilibrium superconductivity

Abstract – Techniques in time- and angle-resolved photoemission spectroscopy have facilitateda number of recent advances in the study of quantum materials. We review developments inthis field related to the study of incoherent nonequilibrium electron dynamics, the analysis ofinteractions between electrons and collective excitations, the exploration of dressed-state physics,and the illumination of unoccupied band structure. Future prospects are also discussed.

Introduction. – Spectroscopy, the study of interac-tions between light and matter, has long been a drivingforce in physics. Enormous progress has been achieved inthis field since the invention of the laser as a source ofcoherent light [1,2], which quickly led to the developmentof pulsed lasers and nonlinear optics [3, 4]. Today, lasersand nonlinear conversion schemes are capable of produc-ing ultrashort pulses of durations ranging from picosec-onds down to a few femtoseconds, and spanning a rangeof wavelengths from the terahertz to the ultraviolet [5]. In-tense table-top lasers have been more recently employedto generate extreme-ultraviolet and X-ray pulses, enablingthe creation of the shortest pulses to date, with a durationof only 67 attoseconds [6].

This impressive progress has, in turn, enabled spec-troscopy of matter at the highest possible temporal resolu-tion. In tandem with this, it is becoming recognized thatsome of the most interesting properties of solid-state quan-tum materials involve microscopic dynamics at such timescales. In the past years, numerous groups have turned thepowerful eye of ultrafast spectroscopy toward the study ofcorrelated and nanoscale quantum materials, such as su-perconductors, topological insulators, and charge densitywave materials. Fascinating effects, which do not exist atequilibrium, are beginning to be unearthed.

Among the most exciting developments within thisfield are those combining time-resolved techniques with

(a)E-mail: alanzara@lbl.gov

the power of angle-resolved photoemission spectroscopy(ARPES). In equilibrium, ARPES is capable of resolv-ing the occupied electronic structure in momentum space,uniquely revealing the dispersion of quasiparticles andmany-body correlations in materials ranging from bulkand low-dimensional semiconductors, to metals, to super-conductors and strongly correlated solids. By perturbinga material with an ultrashort laser pulse and following theresulting transient ARPES spectra in the time-domain,one can obtain insight into the dynamics both of quasi-particle occupations and of the electronic structure itself.In this way, important hidden physics of quantum mate-rials can be brought to light. To this end, this perspec-tive reviews the impact of recent advances in time-resolvedARPES on the study of quantum materials.

The perspective is organized into six sections. We beginwith a summary of the time-resolved ARPES technique.Following this, advances in the study of ultrafast dynam-ics in quantum materials are reviewed, divided into fourcategories: (a) developments where the pump pulse is usedto create incoherent nonequilibrium dynamics; (b) devel-opments where the pump pulse results in coherently oscil-lating collective excitations, such as phonons and chargedensity waves; (c) developments in the creation and mon-itoring of dressed-state phenomena; and (d) developmentsin 2-photon-photoemission (2PPE), in which pump andprobe pulses are used to illuminate and explore unoccu-pied portions of band structure. Finally, ongoing develop-

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(Bi2212). The vertical axis is energy. The horizontal axis is crystal momentum, corresponding to a slice through a gappedportion of the band structure (see Fermi surface inset). Evolution of nonequilibrium band structure can be observed byvarying the time delay between pump and probe pulses, depicted here at -1 ps, 0.7 ps, and 4.0 ps. (b) Schematic of a typicalexperiment. A crystalline sample is irradiated in vacuum by infrared and ultraviolet pulses, separated by a variable time delay(top). The infrared pulse drives the material’s electrons into a nonequilibrium state (center). Following this, the ultravioletpulse photoexcites electrons into the vacuum, where their energies and momenta are measured to obtain a snapshot of bandstructure at time t = delay (bottom).

ment and future prospects in the field are discussed.

The nuts and bolts of ultrafast ARPES. – Atits core, time-resolved or ultrafast ARPES consists oftwo wedded experimental principles: photoemission, andpump-probe spectroscopy. In a photoemission experi-ment, ultraviolet (UV) photons are incident on a crys-talline material in vacuum. If the photon energy ex-ceeds the the material’s work function (typically about4.5 eV), electrons are ejected into free space where theirenergies and exit angles can be measured. The powerof the technique, particularly in its momentum-resolvedform, lies in the fact that relatively simple conservationlaws exist to ensure that the energy and momentum ofthe photoelectrons in vacuum are directly related to theenergy and crystal momentum of these same electronswhen they were still inside the material. As a result,the technique reveals quite direct experimental maps ofelectronic band structure, and has been successfully usedto characterize a wide variety of materials [7–11]. Asan example, in the left frame of Fig. 1(a), an ARPESspectrum of the cuprate high-temperature superconductorBi2Sr2CaCu2O8+δ (Bi2212) yields a momentum-resolvedmeasurement of the superconducting order parameterthrough a directly measurable electronic excitation gap(dashed lines and white double arrow). It also displaysevidence for electron-boson coupling in the form of re-duced band velocity at low binding energies relative tohigh binding energies, and in the form of an accompany-ing dispersion kink at −70 meV (horizontal black arrow).

In spite of its advantages, equilibrium ARPES still suf-fers from a few drawbacks: (1) measurable electronicstates must initially be occupied; (2) although importantinformation on interactions can be gleaned from the self-

energy of the dispersion, much of the microscopic dynam-ics cannot be deconvolved from the lineshape analysis; and(3) unique physical phases may become accessible onlyafter driving the system far from equilibrium. These is-sues are circumvented by incorporating pump-probe tech-niques, where instead of shining only ultraviolet light ona sample, the material is irradiated in short succession bytwo femtosecond-duration light pulses. One of these, typi-cally tuned to an infrared frequency and designated as the“pump,” drives the material system into a nonequilibriumstate, but does not yet result in photoemitted electrons.The other pulse, typically designated as the “probe,” pro-vides a photon energy within the vacuum ultraviolet (≈ 6eV) or extreme-ultraviolet (≈ 10–60 eV) frequency range,resulting in photoemission of electrons that are ultimatelydetected. Nonequilibrium dynamics are studied by mon-itoring changes in the electron emission spectrum as thetime delay between pump and probe pulses is varied.

Figure 1 shows an example of the experimental datathat can be acquired using the technique to measureBi2212 [Fig. 1(a)], as well as a schematic example of a typ-ical ultrafast ARPES experiment [Fig. 1(b)]. In Fig. 1(a),the left panel is acquired at negative delay time, whichcorresponds to an equilibrium ARPES spectrum. At apositive delay of 0.7 ps (center panel), significant changesoccur in the ARPES plot, revealing both a modificationof the underlying electronic dispersion as well as an over-all reduction of the intensity. These changes measuredin Bi2212 signify a reduction of superconductivity and amodification of the electron-boson interaction within thematerial, to be discussed in more detail in the sections tofollow. At a delay of 4 ps, the changes are less pronounced(right panel), marking a tendency of the band structureto relax back toward equilibrium on longer timescales.

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Time-resolved experimental apparatuses have been un-der development since the 1980s [12–14], although thetechnology continues to mature with improved momen-tum, energy, and time resolutions, as well as increased sen-sitivity and tuning ranges. Notable developments includethe replacement of 1D time-of-flight electron spectrome-ters with 2D hemispherical analyzers [15, 16], or even 3Dtime-of-flight spectrometers [17, 18], the incorporation ofhigh-harmonic sources to generate probe photons that canaccess large values of electronic crystal momentum [19–22],and the incorporation of tunable pump frequencies to aidin selective nonequilibrium photoexcitation [23,24].

Nonequilibrium dynamics in the incoherentregime. – One of the first and still most important waysin which time-resolved spectroscopy has had an impact oncorrelated quantum materials research has been its abilityto use near-infrared pump pulses in the incoherent regimeto generate and monitor metastable nonequilibrium states.

A scheme where the observation of these dynamics hasproven particularly useful is that in which a sample is illu-minated with a near-infrared pump pulse, and then mea-sured using a probe pulse obtained using fourth-harmonicgeneration with β-barium borate (BBO) nonlinear crys-tals. In 2007, this scheme was used—with a 1.5 eV pumppulse and 6 eV probe pulse—to acquire the first trulymomentum- and time-dependent ARPES data on any ma-terial, measuring quasiparticle dynamics in Bi2212 [25].With an energy resolution of 50 meV, a momentum reso-lution of 0.045 A−1, and a substantial pump fluence of 100µJ/cm2, the authors of this initial work found relativelylittle temperature dependence to their results. The find-ings were associated with a quasi-thermal model of metal-lic quasiparticle relaxation [26] that was in turn used toestimate the normal-state electron-phonon coupling con-stant. Quasi-thermal models have also been used to deriveestimates of electron-boson coupling in a number of mate-rials beyond cuprates, including gadolinium [27] and theparent compounds of iron-based superconductors [28].

More recently, we and others have improved signifi-cantly on the energy and momentum resolution of theseinitial works. By pumping at lower fluence values thanthose previously explored, a number of studies using 1.5eV pump/6 eV probe time-resolved ARPES have shownthat it is possible to explore a wide variety of phe-nomena associated not just with metallic-state dynam-ics, but also with dynamics associated with the super-conducting ground state of cuprates [29–42]. Evidencefor the electron-boson coupling interaction within thislow-fluence, low-temperature regime can be observed intime-resolved ARPES spectra of cuprate superconductorsthrough a variety of features. Among the most strikingis the dramatic effect that a 1.5 eV pump pulse has on awell-known 70-meV kink that appears in the dispersion ofcuprate superconductors along the nodal direction [43], re-sulting from electron-boson coupling. As shown by Fig. 2,photoexcitation at 1.5 eV in Bi2212 results in a suppres-

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[panel (c)]. Adapted from Zhang et al. [35]. Reprinted withpermission from the Nature Publishing Group.

sion in quasiparticle spectral weight in the nodal ARPESspectra [Fig. 2(a), middle panel] [29], as well as an in-crease in ARPES linewidth [Fig. 2(b)] [35, 40], which isconfined to binding energies less than 70 meV. In addi-tion, the pump induces a marked change in band veloc-ity [35,40]. This is particularly visible in Fig. 2(c), where alinear bare band approximation has been subtracted fromfitted dispersions in Fig. 2(a) to generate an effective realpart of the electronic self-energy. Theoretical work [44,45]has demonstrated that a weakened dispersion kink doesnot necessarily imply a fundamental reduction in electron-boson coupling. However, it is striking to note that kinkeffects become sharply reduced when the equilibrium tem-perature is increased above Tc (though some effects arestill evident at the highest pump fluences [33]), which mayindicate a connection to the mechanism of superconduc-tivity.

Beyond its ability to resolve changing band velocitiesand bosonic renormalization effects, time-resolved ARPEShas opened windows into the interactions between quasi-particles and the superconducting condensate that haveno analogue in equilibrium ARPES. Recently, for exam-ple, studies have measured the dynamics of the excita-

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Fig. 3: Fluence- and momentum-dependent quasiparticle relax-ation in the superconducting state of Bi2212. (a)-(b) Quasi-particle relaxation rates, integrated within a range of energyand momenta along nodal (a) and off-nodal (b) slices throughthe Brillouin zone, are fluence-dependent, with faster recoveryoccurring at higher fluences. (c) At fixed fluence, quasiparti-cle relaxation rates are faster away from the node than at thenode. Adapted from Smallwood et al. [31]. Reprinted withpermission from AAAS.

tion gap in Bi2212 at both low and intermediate flu-ence [31,34,35], establishing a measurement of the criticalfluence necessary to destroy superconductivity, and char-acterizing the timescales on which these processes occur.Perhaps more interestingly, in the presence of a gap, quasi-particle relaxation rates in the cuprates become markedlyboth fluence-dependent [31,37,39,46–48] and momentum-dependent [31]. As shown by Fig. 3, fluence-dependentquasiparticle dynamics have been observed along a vari-ety of momentum directions in Bi2212, both along a cutintersecting the superconducting gap node [Fig. 3(a)] andin regions of k-space where the superconducting gap is fi-nite [Fig. 3(b)]. Moreover, at constant pump fluence, thequasiparticle relaxation rate increases markedly with in-creasing gap size [Fig. 3(c)]. The results open possibilitiesfor using the momentum-dependent structure of relaxationrates to access momentum-dependent coupling effects be-tween superconductivity and charge density waves, anti-ferromagnetic order, and phonons.

Though time-resolved ARPES studies making use offourth-harmonic generation are unparalleled in their mo-mentum and energy resolution, they suffer from an inabil-ity to access the full Brillouin zone of many materials. Re-cent years have seen increasing efforts to combine ultrafastARPES with table-top laser sources of extreme-UV lightaround 10–50 eV, which can be obtained by high-harmonicgeneration (HHG) in gases driven by intense laser pulses.

The energy resolution of such HHG-based techniques isoften limited by the harmonic width or monochromatorsettings to 150–500 meV (compared to 20 meV or lessfor nonlinear crystal experiments) [20–22]. Recent effortsin UV-driven XUV sources are enabling much narrowerbandwidths of 70 meV directly from the source, obtainedat high repetition rates of 50-kHz and with significantflux [49]. Ultrafast ARPES experiments making use ofsuch techniques have begun to explore nonequilibrium dy-namics in a variety of materials [50–55], with among themost prominent developments being an elucidation of thephysics of charge-density-wave (CDW) materials including1T -TaS2, 1T -TiSe2, and La1.75Sr0.25NiO4 [56–58].

For example, developments in time-resolved ARPEShave given researchers direct access to timescales forcharge-order collapse, manifest experimentally throughthe changing magnitude of the CDW gap. Remark-ably, early measurements on 1T -TiSe2 revealed that thisquenching can occur as rapidly as within 20 fs [56]. Thisis in sharp contrast to the timescale for the collapse ofthe superconducting gap in Bi2212, which is delayed by asmuch as 600 fs [34]. As high-harmonic techniques have im-proved, researchers have been able to compare time scalesbetween various charge-density-wave materials, and to usethis information to differentiate among excitonic, Peierls,and Mott effects driving CDW formation [58].

Collective mode oscillations. – With impulsive ex-citation, ultrafast ARPES has also been shown capable ofinducing oscillating spectral signatures reflecting the cou-pling of electrons to collective modes. One of the more in-triguing phenomena is the observation of a pump-inducedoscillation in the electronic band structure [28, 59, 60],which lasts as long as 2 ps in the iron-based superconduc-tor BaFe1.85Co0.15As2 and in its antiferromagnetic rela-tives BaFe2As2 and EuFe2As2. The oscillations were as-sociated with electron-phonon coupling.

Similar coherent phonon oscillations have been observedin Bi2212 [61], where the oscillation frequency has beenshown to be intriguingly close to an electron-phonon renor-malization kink in the band structure visible also throughequilibrium ARPES [62–64]. Interestingly, the ability toobserve electron-boson coupling interactions through ul-trafast coherent oscillations is complementary, and in cer-tain respects even superior to efforts to extract electron-boson coupling interactions by looking for band renormal-ization effects using equilibrium ARPES. The reason isthat in materials exhibiting significant three-dimensionalband dispersion (like many of the iron-based superconduc-tors), band positions become obscured by the absence ofout-of-plane momentum conservation in an ARPES exper-iment. Even in cases where band renormalization effectsare directly visible using equilibrium ARPES—as theyare in the cuprate superconductors—the ultrafast deter-mination of coupled bosonic mode energies can be muchmore sharply defined under ultrafast techniques than theycan under equilibrium techniques. Moreover, only specific

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Fig. 4: Pump-induced gap magnitude oscillations in the CDWmaterial 1T -TaS2. (a)–(b) Time- and energy-dependent pho-toemission spectral weight, integrated across a window in mo-mentum, following a near-infrared (1.5 eV) pump pulse. (c)Shift in the Hubbard peak, defined as the change in the peakenergy of the photoemission signal, as a function of pump-probe delay. Inset shows the result of applying a Fourier trans-form to the data. From Perfetti et al. [66]. Reprinted withpermission from the American Physical Society.

modes are excited, with coupling to different bands thatcan be mapped by studying the transient modulation ofthe band structure across momentum space.

In CDW systems, coherently driven oscillations appearas well. Early measurements of these oscillations in KMOby Demsar et al. using all-optical techniques [65] werereplicated in a wide variety of materials, ranging from 1T -TaS2 [57, 66] to TbTe3 [67]. One of the more prominentexamples of this type of oscillation in an ultrafast ARPESspectrum is displayed in Fig. 4, where it was demonstratedby Perfetti et al. [66] that a 1.5 eV pump pulse can inducegap oscillations in the CDW material 1T -TaS2 lasting aslong at 20 ps.

Dressed-state physics. – The strong light-matterinteraction between the electronic wavefunctions of a crys-talline solid and the coherent electric field of an intenselaser pulse can also result in novel modifications of theelectronic structure. Among the most intriguing develop-ments has been the observation of Floquet-Bloch states intopological insulators. Such states are a time-dependentextension of Bloch waves: Bloch waves are periodic incrystal momentum and result from a Hamiltonian thatcommutes with discrete translations in space, whereasFloquet-Bloch states are periodic in both crystal momen-tum and energy, and result from a Hamiltonian that com-mutes with discrete translations in space and time.

Recently, Wang et al. demonstrated experimental evi-dence of this effect [23], as shown in Fig. 5. Researchers

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performed pump-probe measurements on the topologicalinsulator Bi2Se3, and found that if the frequency of thepump pulse was reduced below the bulk band gap, andthe timing of the probe pulse was tuned to within the du-ration of the pump pulse, then a ladder of replica bandsbegins to appear with evenly spaced energies in the pho-toemission spectrum. Most interestingly, the surface statebands in Bi2Se3 are dispersive, leading to a number ofpoints where bands of different energy orders overlap. Forappropriately polarized light, band gaps open up at thesespecialized points, with the induced gap magnitude be-ing proportional to the strength of the applied electricfield [68]. This property separates Floquet-Bloch phenom-ena from more commonly observed laser-assisted photoe-mission (LAPE) [56,69,70], which is the result of photon-dressed electron states in vacuum. The effect may facili-tate device applications with ultrafast switching times.

Floquet-Bloch phenomena may also result in fascinat-ing new phenomena in other types of materials. Calcu-lations indicate that for sufficiently high pump pulse en-ergies, Floquet-Bloch phenomena in the form of a pump-induced band gap can be induced in graphene [71]. Forpulse energies approaching very high values, the gap mayeven begin to shrink again, leading to the possibility ofinteresting band gap tuning depending on pump fluence.

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Fig. 6: Unoccupied band structure of p-type Bi2Se3. (a) Tradi-tional ARPES (1PPE) is limited to occupied states (bottom),but 2PPE (top) reveals unoccupied band structure several eVbeyond the Fermi level, including Dirac cones in the unoccu-pied band structure that had not previously been observed.(b) Slab band structure calculation, which agrees well withexperiment. Adapted from Sobota et al. [72]. Reprinted withpermission from the American Physical Society.

Revealing unoccupied band structure. – Beyondits ability to create both novel nonequilibrium statesin both the coherent and incoherent regime, ultrafastARPES has opened up a number of possibilities for map-ping out the unoccupied band structure in solids, using 2-photon photoemission (2PPE) techniques. The ability toaccess these unoccupied bands is important, for example,to develop a better understanding of the conduction bandsof nanoscale materials for applications in opto-electronics,or of the energy-momentum dispersion of correlated quasi-particles in quantum materials. Strictly speaking, a time-delayed pump and probe pulse is not necessarily requiredto reveal unoccupied-state data. If the pulse energy is suf-ficiently intense, the same pulse can act both as pump andprobe. Still, the ability to isolate pump and probe signalsusing a variable delay can help isolate the signal of interestfrom background noise.

In topological insulators, ultrafast ARPES measure-ments of the unoccupied band structure are particularlystriking. It has been shown that it is possible, for exam-ple, to produce maps of the unoccupied surface-state bandstructure in Bi2Se3 extending even 6 eV above the chem-ical potential, as demonstrated by Sobota et al. [72] (seeFig. 6). More recently, Grubisic Cabo et al. have shownthat it is possible to use ultrafast ARPES to measure theconduction band of the transition metal dichalcogenide

MoS2 [73], and Ulstrup et al. have extended these stud-ies to a MoS2/graphene heterostructure [74], adding newinsight into the free carrier dispersion and band gap.

The future. – As ultrafast ARPES continues to ma-ture, completely new applications and directions are be-ginning to emerge. Among the most ambitious and ex-citing new directions include possibilities for optically en-hancing superconductivity in high-Tc materials, tailoringpump light in increasingly sophisticated ways to achievecoherent control of quantum phases, and developing theability to acquire simultaneous time-resolved, momentum-resolved, and spin-resolved ARPES data.

Tantalizing possibilities for ultrafast ARPES have to dowith the prospect of using optical means to access “hid-den” states of materials, which are thermodynamically in-accessible, but which can be accessed using intense opticalpulses. Two examples, which have already been exploredusing all-optical techniques, are the possibility of generat-ing a metastable conducting state in the CDW material1T -TaS2 [75], and that of generating photoinduced super-conductivity at temperatures above the equilibrium criti-cal temperature in cuprate superconductors [76–78].

Beyond this, there are intriguing nonlinear technicalpossibilities on the horizon for ultrafast ARPES. A partic-ular example is the prospect of incorporating increasinglysophisticated pump pulse sequences in ARPES experi-ments. At present, nearly all operational ultrafast ARPESexperiments can be understood in the regime of “linear”response: the pump pulse is understood to transfer quasi-particles from lower energies to higher energies in a man-ner that can be modeled using Fermi’s golden rule. Evenin cases where coherent oscillations are generated, the useof this single pulse has an only limited ability to con-trol these oscillations. In contrast, all-optical techniqueshave demonstrated that a great deal of increased controlcan be achieved if the pump pulse is divided into mul-tiple sub-pulses with variable time delays between pulses.One initial proof-of-principle demonstration of using thesetechniques was demonstrated by Aeschlimann et al. in2011 [79].

Finally, recent advances in spin-resolved ARPES [80,81]are opening up possibilities to establish an experiment ca-pable of simultaneous time, momentum, energy, and spinresolution in crystalline materials. This capability shouldprove useful in the generation and analysis of nonequilib-rium states in materials with spin-textured band struc-ture. Topological insulators are an obvious example.

As we have outlined in this perspective, ultrafastARPES has in recent years evolved into a powerful tech-nique enabling direct access to the dynamics of quasi-particles, electronic structure, and collective modes ofnanoscale and correlated quantum materials. While theinsight gained is already remarkable, we can expect therapid pace of progress to continue, portending insights intothe properties of solids in time, energy, and momentumspace that remain hidden in equilibrium.

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∗ ∗ ∗

This work was supported as part of the Ultrafast Mate-rials Program at Lawrence Berkeley National Laboratory,funded by the U.S. Department of Energy, Office of Sci-ence, Office of Basic Energy Sciences, Materials Sciencesand Engineering Division, under Contract No. DE-AC02-05CH11231. C.L.S. acknowledges support from an NRCResearch Associateship award at NIST.

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