TOPOLOGICAL MATTER

Observation of chiral phononsHanyu Zhu,1,2 Jun Yi,1 Ming-Yang Li,3 Jun Xiao,1 Lifa Zhang,4 Chih-Wen Yang,3

Robert A. Kaindl,2 Lain-Jong Li,3 Yuan Wang,1,2* Xiang Zhang1,2*

Chirality reveals symmetry breaking of the fundamental interaction of elementaryparticles. In condensed matter, for example, the chirality of electrons governs manyunconventional transport phenomena such as the quantum Hall effect. Here we show thatphonons can exhibit intrinsic chirality in monolayer tungsten diselenide. The brokeninversion symmetry of the lattice lifts the degeneracy of clockwise and counterclockwisephonon modes at the corners of the Brillouin zone. We identified the phonons by theintervalley transfer of holes through hole-phonon interactions during the indirect infraredabsorption, and we confirmed their chirality by the infrared circular dichroism arising frompseudoangular momentum conservation. The chiral phonons are important for electron-phonon coupling in solids, phonon-driven topological states, and energy-efficientinformation processing.

Chirality is a fundamental property of anobject not identical to itsmirror image. Forelementary and quasiparticles, it is an im-portant quantum concept at the heart ofmodernphysics. For example, the discovered

handedness of neutrinos in electroweak interac-tion revolutionized our understanding of the uni-versal parity conservation law. Chiral fermionswith spin-momentum locking can emerge in solid-state systems such as the recently observed Weylsemimetals with inversion symmetry–breakinglattices (1). Electron chirality in graphene definedthrough pseudospin was found to cause distinc-tive transport properties such as unconventionalLandau quantization and Klein tunneling (2, 3).Meanwhile, electrons in monolayer transitionmetal dichalcogenides with broken inversion sym-metry display optical helicity, which opens thefield of valleytronics (4). The outstanding ques-tion is whether bosonic collective excitations suchas phonons can attain chirality. Recently, theintrinsic chirality of phonons without appliedexternal magnetic fields in an atomic latticewas predicted theoretically at the corners of theBrillouin zone of an asymmetric two-dimensional(2D) hexagonal lattice (5). Because of the three-fold rotational symmetry of the crystal and themomentum vectors, the vibrational plane wave iscomposed of unidirectional atomic circular ro-tation. Because the phonons in the same valleyhave distinct energy levels, the rotation is notthe superposition of linearmodes, in contrast to thecircular motion in nonchiral cases (6). The hy-pothetical chiral phonons are potentially im-portant for the control of intervalley scattering(7, 8), lattice modulation–driven electronic phasetransitions (9, 10) and topological states (11), aswell as information carriers that can be robust

against decoherence for solid-state quantum in-formation applications (12).Here we report the observation of intrinsic

chiral phonons via transient infrared (IR) spec-troscopy in the atomic lattice ofmonolayer WSe2.A particle’s angular momentum is calculatedby the phase change under a rotational trans-formation. This definition can be extended forquasiparticles in solid lattices with discrete spa-tial symmetry, as long as the rotation is in thecrystalline symmetry group (13). For an inversionsymmetry–breaking 2D hexagonal lattice suchasmonolayerWSe2 (Fig. 1A), phonons with well-defined pseudoangular momentum (PAM) arelocated at the G, K, and K′ points in the recip-rocal space (5). Because the phonons inherit thethreefold rotational (C3) symmetry of the lattice,their function of motion must be C3 invariantexcept for a phase difference (i.e., circular) (14).The K and K′ phonons are particularly notablebecause there is no reflection line that preservesboth the lattice and their momentum (fig. S5).Therefore, the atomic rotation cannot be reversedwithout changing its momentum or energy. Forexample, if we attempt to reverse the rotationaldirection of the Se atoms in a longitudinal op-tical phonon LO(K) while keeping the relativephase determined by the q =Kmomentum, themode changes to a longitudinal acoustic pho-non LA(K) that oscillates at a different frequen-cy. Thus, unlike the G phonon, such a rotationcannot be decomposed into orthogonal linearvibrations with a ±p/2 phase shift. On the otherhand, to maintain the same mode, the relativephase must be reversed, resulting in a phonon atthe K′ point.We deduce the phonon PAM l for each mode

from the phase change after counterclockwise120° rotation:Ĉ3(uk) = e−i(2p/3)luk, where uk is thefunction of atomicmotion (fig. S6). Because LA(K)is always C3 symmetric, it has l = 0; in con-trast, LO(K) gains negative phase after rota-tion (becomes ahead of time) and thus l = 1.The K phonons with different PAM are com-pletely nondegenerate because of the mass differ-ence betweenW and Se. The lifting of degeneracy

guarantees that each mode has a distinctiveselection rule for the electron-phonon and op-tical scattering (table S1). These features differ-entiate the intrinsically chiral phonons from anypreviously investigated phonons where circularatomic motion results from superposing linearpolarized eigenmodes (6, 15, 16). Chirality in theabsence of an external magnetic flux is also dis-tinguished from themagnetic field–induced splitof degenerate superposition modes (17). Finally,both the physical origin and properties of theatomic chiral phonons are fundamentally dif-ferent from previous phononic crystal–based chi-rality from geometric engineering or topologicaledge states (18–20).We use an optical pump-probe technique to

identify the chiral phonon by its scattering withholes (Fig. 1B and fig. S2). The linearmomentum,PAM, and energy of the respective phononmodesare determined by characterizing all of the otherparticles involved in the intervalence band tran-sition (IVBT) process (14). First, we inject holes atthe K valley by a left–circularly polarized (LCP)optical pump pulse. The K valley–polarized holerelaxes to the valence band edge with initial lin-ear momentum pi = −K. It can transit to the K′point (pf =K) by emitting aKphonon (q=pi−pf =−2K = K), but the intermediate state is virtualbecause the spin-conserving state has much high-er energy due to large spin-orbit coupling. Wethen send an IR pulse to satisfy the energy con-servation and place the hole in the spin-split bandat K′. Because the hole states have zero PAM, thePAM of the phonon must be equal to the spinangular momentum of the absorbed IR photon.Therefore, the LCP pulse controls the creation ofonly LO(K) phonons. Eventually, we recognize thefinal spin-split state in the opposite valley by theenergy and right circular polarization of its radi-ative decay. The selection rule of phonon crea-tion will be identical if the hole first absorbs an IRphoton, transits to an intermediate state withinthe valley, and then emits a phonon, as long as thefinal state is the same. The phonon annihilationis negligible because the population is very lowfor all phonon modes at the K or K′ points at abase temperature of 82 K. The selection is alsonot affected by a small momentum distribu-tion of the initial and final holes (14) due tofinite thermal energy or the strong many-bodyinteraction (21). This is because, like the opticalvalley-selectivity, the contrast of electron-phononcoupling strength remains large in the vicinityof K and K′, even if the PAM is only defined onthese points.To determine the linear momentum of the

involved phonon, wemeasure the linearmomen-tum of the initial and final holes. Under circu-larly polarized pump excitation, the majority ofholes maintain their linear momentum near theoriginal valley, as shown by the positive helicityof the photoluminescence. The final linear mo-mentum of the spin-split states is read out by thepolarization of their luminescence at higher en-ergy than the original pump photon (Fig. 2A).We measure the difference of luminescence withthe same polarization as the pump light (Isame)

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1Nanoscale Science and Engineering Center, University ofCalifornia, Berkeley, CA 94720, USA. 2Materials SciencesDivision, Lawrence Berkeley National Laboratory, Berkeley,CA 94720, USA. 3Physical Sciences and Engineering Division,King Abdullah University of Science and Technology, Thuwal23955-6900, Kingdom of Saudi Arabia. 4Department of Physics,Nanjing Normal University, Nanjing, Jiangsu 210023, China.*Corresponding author. Email: xzhang@me.berkeley.edu (X.Z.);yuanwang@berkeley.edu (Y.W.)

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LO(K)

= 1

LA(K)

= 0

00

4π/3 2π/3 4π/3 2π/3

=

LO(K) phonon creation

= 1

luminescence detection

Infrared probeabsorption

= 1

optical pump excitation

++

+

KK

Fig. 1. Nondegenerate chiral phonons in monolayer WSe2 and the selec-tion rule of hole-phonon interactions. (A) The atomic motion of W and Seatoms (blue and yellow spheres, respectively) in the real space is intrinsicallycircular for the chiral phonons residing at the K point (red dot) in the reciprocallattice (array of black dots), due to the threefold rotational symmetry. Becausethe momentum vector determines the relative phase of the Se motion,opposite rotations correspond to completely different modes.The two modes

have distinct PAM with respect to the center of the hexagon. (B) In theintervalley optical transition of holes, the PAM of the K phonon is equal to thespin of the IR photon due to angular momentum conservation. A hole injectedby the LCP optical pump moves from the K to the K′ valley through virtualscattering with a LO(K) phonon.Owing to the spin and energymismatch, a realphonon is created only if the hole simultaneously absorbs an IR probe photonand transits to the spin-split state, which is signaled by the RCP luminescence.

2.05 2.10 2.15 2.200.0

-0.5

-1.0

-1.5

Emission energy (eV)

Pol

ariz

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lum

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cenc

e (a

.u.)

0 1 2 3-10

-5

0

5

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ariz

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lum

ine s

cen c

e (a

. u.)

Delay (ps)

Data Deconvolution fitting

Data B-exciton PL

spin-allowedindirect

transition

++

+

KK

+

spin-forbiddentransition

+

Fig. 2. Chiral phonon creation from the intervalley transition of holesmeasured by polarized luminescence. (A) The spin-allowed intervalleytransition of holes from the K point creates a K phonon, yet the spin-forbiddentransition within the same valley does not.The two processes are distinguishedby the polarized luminescence signal. (B) The observed initial positivepolarization indicates a spin-flipping transition of nonequilibrium holes, with alifetime of ~0.2 ps. After that, the negative polarization shows a prevailing

phonon-creating intervalley transition for valley-polarized holes, with a lifetimeof ~2 ps at 82 K.The pump and probe energies are tuned to 1.97 and 0.51 eV,respectively, whereas the signal is integrated from 2.05 to 2.19 eV. (C) Thespectrum of the polarized luminescence taken at t = 0.8 ps agrees with theB-exciton photoluminescence (PL) and confirms its spin-split hole origin.The error bars in (B) and (C) indicate SE calculated from multiple measure-ments. a.u., arbitrary units.

0 1 2 3 4

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Data Fitting

hA(K)

hB(K )

LO(K)

TA(K)

hB(K )

hA(K)

photon

photon

time

space

Fig. 3. Chirality of phonons measured by transient IR CD. (A) Thephonons participating in the indirect optical transition are different for theLCP and RCP IR photons because of the conservation of linear and angularmomentum. Their distinct electron-phonon scattering strengths dictatethat the two processes have different amplitudes, leading to polarizedIR absorption. hA(K), hole at the valence band edge of the K valley;hB(K′), hole in the spin-split band of the K′ valley. (B) The measured CD at82 K (black squares and red fitting curve) is positive for both the initialintravalley spin-flipping transition and the later intervalley phonon-creating

transition. It not only proves the chirality of phonons but also indicatesthat the LO phonon process is dominant. (C) The spectrum of thetransient CD acquired at t = 0.8 ps shows a photonic energy thresholdof 0.448 ± 0.002 eV. Its step shape is expected from the 2D excitonicdensity of states. Subtracting the energy difference between the initial andfinal hole states, a phonon energy of 29 ± 8 meV is deduced, in agreementwith that of the LO mode. The error bars denote SE calculated frommultiple measurements, and the threshold uncertainty indicates the SEof the fitting parameter.

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and the opposite polarization (Ioppo) as a func-tion of the probe delay time t (Fig. 2B). We findthat the polarized luminescence (Isame − Ioppo) ispositive for t < 0.2 ps, indicating that the spin-flipping intravalley IVBT has a higher probabilitywhen the IR probe arrives immediately after theexcitation of holes. This is because spin is notstrictly conserved for optical transitions awayfrom the high-symmetry points. However, theprocess is forbidden at the valley center withincident light perpendicular to the lattice plane,so its magnitude decays with a lifetime of 0.2 psas the nonequilibrium carriers thermalize to theband edge (22, 23). After that, the luminescenceswitches polarization as a result of the dominantspin-conserving intervalley IVBT. It shows thatthe majority of final holes have a linear momen-tum opposite that of the initial holes. The mo-mentummust have been transferred to phononsinstead of defects, as seen from the comparisonof the second-order Raman scattering throughthe defect-assisted one-phonon process with thatof the two-phonon process, which is an order ofmagnitude stronger (fig. S7). Directional inter-valley transfer through electron-electron interac-tions (24) is excluded because the pump is not inresonance with the A exciton, and the signal islinearly proportional to the hole density (fig. S8).The exchange interaction reduces the polariza-tion of the holes but should not create an oppo-site polarization (25). Finally, the depolarizationplus the decay of the hole population yields ajoint lifetime of ~2 ps for the polarized lumi-nescence, in agreement with previous excitonstudies (26). To further verify the nature of thefinal holes, we measure the polarized lumines-cence at different collection energies with t =0.8 ps. The emission spectra obtained with dif-ferent IR photon energies are all close to the B-exciton photoluminescence (Fig. 2C and fig. S12),which proves that the emission is the radiativedecay of a real state near the edge of the spin-split band, rather than a virtual state. Therefore,we use the luminescence from 2.05 to 2.19 eV toquantify the indirect IR absorption and the pho-non creation.The PAM of valley phonons is determined

by measuring the polarization selection of theabsorbed IR photon, resulting from the chiralelectron-phonon interaction. With LCP excita-tion, the intervalley transition of holes from theK valley can either absorb an LCP IR photon toproduce LO phonons or absorb a right–circularlypolarized (RCP) IR photon to produce TA/A1

phonons (Fig. 3A). We observe different IR ab-sorption when the probe has the same polar-ization as the pump light (asame) versus when ithas the opposite polarization (aoppo). This IRcircular dichroism (CD = asame − aoppo) dem-onstrates that scattering cross sections of thetwo processes are not equal, owing to the dif-ference of electron-phonon coupling strength.As shown in Fig. 3B, the CD at 82 K is alwayspositive for valley-polarized holes. Because theholes have zero PAM regardless of valley indexor spin-split bands, the angular momentum of

the IR photon is transferred to either the spinor the phonon. The initial intravalley IVBT pro-duces positive CD because the electronic spinflips from −1/2 in the spin-split band to +1/2at the valence band edge at the K point. How-ever, this contribution decays fast as a functionof IR delay in accordance with Fig. 2B. Thus,the intervalley phonon-creating transition isthe dominant source of positive CD for t ≥ 0.8 ps.It indicates that the LO branch contributes mostto the indirect IR absorption. For nonchiral sys-tems, although photons with opposite circularpolarization may interact with different par-ticles, the probabilities are always equal. There-fore, the CD is the signature of intrinsic phononchirality.The energy of this phonon mode is measured

according to energy conservation: The energysum of the incoming particles, the IR photon,and the initial holes must be equal to that of theoutgoing particles, the chiral phonon, and thefinal holes (14).We observe that the CD spectrumat t = 0.8 ps (Fig. 3C) is a step function with aclear threshold near 0.448 ± 0.002 eV, broad-ened by the spectral width of the IR pulse. Theshape corresponds to a transition from a hole atthe valence edge to a band with parabolic dis-persion in two dimensions (fig. S9). This value isdistinguished from either the intra-excitonic tran-sition (27) or the exciton dissociation energy (21).Next, we find that the ground-state configurationof the initial holes is the darkA trion atEi = 1.671 ±0.006 eV (fig. S11) (28) based on the dominantbright A-trion photoluminescence (fig. S1). Weverify that the dark trions are near thermalequilibrium because the IR spectrum is very dif-ferent from that of nonequilibrium carriers withexcessive energy at t = 0 ps (fig. S10). The finalstate is the bright B trion at Ef = 2.090 ± 0.005 eV,as measured through its emission (fig. S12). Sum-marizing these values, we deduce the phononenergyEphonon =Ephoton +Ei−Ef = 29 ± 8meV, inagreement with the first-principles calculationand the Raman spectrum for the LO(K) mode(figs. S7 and S9). The uncertaintymay be reducedin the future by improving the uniformity ofthe sample and the spectral resolution of theB-exciton emission. Better spectroscopy will alsopotentially reveal details about the chiral phonon-exciton coupling—such as the contribution fromLA phonons and the various pathways of theindirect transition—that are not resolvable withthe current signal-to-noise ratio.Our findings of chiral phonons are fundamen-

tally important for potential experimental testsof quantum theories with chiral bosons (29) inthe solid state. Our work also provides a possi-ble route for controlling valley and spin throughelectron-phonon scattering and strong spin-phonon interactions (16). Furthermore, the lift-ing of degeneracy by chirality offers robust PAMinformation against decoherence and long-rangeperturbation and offers a new degree of freedomto the design and implementation of phononiccircuitry (30) at the atomic scale without mag-netic fields.

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ACKNOWLEDGMENTS

We thank F. Wang and Q. Niu for helpful discussions. This workwas primarily supported by the U.S. Department of Energy, Officeof Science, Basic Energy Sciences, Materials Sciences andEngineering Division under contract no. DE-AC02-05-CH11231within the van der Waals Heterostructures program (KCWF16)for sample preparation and theory and data analysis, and withinthe Subwavelength Metamaterials Program (KC12XZ) foroptical design and measurement. R.A.K. was supported under thesame contract within the Ultrafast Materials Science program(KC2203) for mid-IR frequency conversion. J.Y. acknowledges ascholarship from the China Scholarship Council (CSC) undergrant no. 201606310094. L.Z. thanks M. Gao for helpfulcalculation and discussion and acknowledges support from theNational Natural Science Foundation of China (grant no.11574154). L.-J.L. acknowledges support from the King AbdullahUniversity of Science and Technology through a CompetitiveResearch Grant (CRG5) for monolayer WSe2 synthesis. Alldata needed to evaluate the conclusions in the paperare present in the paper and the supplementary materials.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/359/6375/579/suppl/DC1Materials and MethodsFigs. S1 to S12Table S1References (31–46)Movies S1 and S2

20 October 2017; accepted 19 December 201710.1126/science.aar2711

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Observation of chiral phonons

Xiang ZhangHanyu Zhu, Jun Yi, Ming-Yang Li, Jun Xiao, Lifa Zhang, Chih-Wen Yang, Robert A. Kaindl, Lain-Jong Li, Yuan Wang and

DOI: 10.1126/science.aar2711 (6375), 579-582.359Science 

, this issue p. 579Sciencesolids.Phonon chirality could be used to control the electron-phonon coupling and/or the phonon-driven topological states of

, detected spectroscopically as the circular dichroism of the phonon-assisted transition of holes.2dichalcogenide WSe observed a chiral phonon mode in a monolayer of the transition metalet al.particular chemical species. Zhu

asymmetry can be seen, for example, in the electronic responses of particular materials or the reactions between Chirality is associated with the breaking of symmetry, often described as left- or right-handed behavior. Such

A phonon merry-go-round

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