Observation of the massive Lee-Fukuyama phason in a charge density wave insulator Soyeun Kim1 2Yinchuan Lv1 2Xiao-Qi Sun1Chengxi Zhao2 3Nina Bielinski1 2 Azel Murzabekova1 2Kejian Qu1 2Ryan A. Duncan4 5Quynh L. D. Nguyen4 5

2025-04-29 0 0 744.55KB 6 页 10玖币

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Observation of the massive Lee-Fukuyama phason in a charge density wave insulator

Soyeun Kim,1, 2 Yinchuan Lv,1, 2 Xiao-Qi Sun,1Chengxi Zhao,2, 3 Nina Bielinski,1, 2

Azel Murzabekova,1, 2 Kejian Qu,1, 2 Ryan A. Duncan,4, 5 Quynh L. D. Nguyen,4, 5

Mariano Trigo,4, 5 Daniel P. Shoemaker,2, 3 Barry Bradlyn,1and Fahad Mahmood1, 2, ∗

1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

2Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

3Materials Science and Engineering Department,

University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

4Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, United States

5Stanford Institute for Materials and Energy Sciences,

SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA

The lowest-lying fundamental excitation of an

incommensurate charge density wave (CDW) ma-

terial is widely believed to be a massless phason –

a collective modulation of the phase of the CDW

order parameter. However, as ﬁrst pointed out

by Lee and Fukuyama [1], long-range Coulomb

interactions should push the phason energy up to

the plasma energy of the CDW condensate, re-

sulting in a massive phason and a fully gapped

spectrum. Whether such behavior occurs in a

CDW system has been unresolved for more than

four decades. Using time-domain THz emission

spectroscopy, we investigate this issue in the ma-

terial (TaSe4)2I, a classical example of a quasi-

one-dimensional CDW insulator. Upon transient

photoexcitation at low temperatures, we ﬁnd the

material strikingly emits coherent, narrow-band

THz radiation. The frequency, polarization and

temperature-dependence of the emitted radiation

imply the existence of a phason that acquires

mass by coupling to long-range Coulomb interac-

tion. Our observations constitute the ﬁrst direct

evidence of the massive “Lee-Fukuyama” phason

and highlight the potential applicability of funda-

mental collective modes of correlated materials as

compact and robust sources of THz radiation.

The fundamental collective modes (amplitudon and

phason) of a broken symmetry ordered state (Fig. 1a)

have been key in establishing foundational theories across

various ﬁelds of physics, including gauge theories in par-

ticle physics; and superconductors, antiferromagnets and

charge-density wave (CDW) materials in condensed mat-

ter physics [2–4]. The phason is typically massless, in ac-

cordance with Goldstone’s theorem, which necessitates

the emergence of a massless boson for a broken sym-

metry in systems in which the ground or vacuum state

is continuously degenerate. A prominent exception oc-

curs in superconducting systems. Here, even though the

ground state is continuously degenerate, the long-range

Coulomb interaction pushes the longitudinal phason up

to the plasma frequency [5, 6], and so a massless Gold-

stone boson does not exist and the low-lying excitation

spectrum is fully gapped. This behavior is the celebrated

Anderson-Higgs mechanism which established the deep

connection between symmetry breaking and gauge ﬁelds,

and ultimately explained how all fundamental particles

acquire mass from interactions with the Higgs ﬁeld.

Unlike superconductivity, an incommensurate CDW is

believed to have a massless phason, typically understood

in terms of softening of a longitudinal acoustic phonon

branch around the CDW wavevector ~qCDW (Fig. 1b). Be-

low the CDW transition temperature (TCDW), this mode

softening results in the linear-in-wavevector, zero-gap dis-

persion of the phason, implying that the CDW can freely

slide for excitation wavevector ~q = 0. In any real ma-

terial, however, random impurities and disorder restrict

this sliding motion, leading to a small gap in the pha-

son dispersion (the pinning frequency) (Fig. 1b). Thus,

the sliding CDW motion can only be observed if a strong

enough electric ﬁeld is applied to ﬁrst depin the phason.

The resulting sliding motion of the CDW can then be

measured in DC transport experiments as has been done

in various systems [7].

However, the above phenomenology of a massless pha-

son (or disorder pinned phason at low frequency) as-

sumes the absence of long-range Coulomb interactions

(U). This assumption is believed to be valid because the

presence of normal electrons at a non-zero temperature

can screen U. However, if Uwere suﬃciently strong,

or if the density of normal electrons were suﬃciently

low, then the CDW phason at ~q = 0 should be pushed

to higher energies (even above the amplitudon energy)

(Fig. 1c). This behavior was highlighted in the seminal

work of Lee, Rice and Anderson (LRA) on CDW dynam-

ics [8, 9] and soon formalized by Lee and Fukuyama [1]

who noted the similarity of the emergence of the mas-

sive CDW phason with the Anderson-Higgs mechanism

in a superconductor. Later works [10, 11] predicted that

the massive (optical) phason could indeed dominate over

the massless (acoustic) phason at suﬃciently low temper-

atures where charged quasiparticles cannot suﬃciently

screen U[10, 11]. We note that in superconductors the

plasma frequency is much larger than the single parti-

cle gap, rendering the phase mode unobservable deep in

arXiv:2210.14207v1 [cond-mat.str-el] 25 Oct 2022

phason

amplitudon

ℱ

Re(Δ)

Im(Δ)

T ≪ TC

cCDW distortion (+U)

ωLF

qCDW 2qCDW

Phason ϕ(t)

T ≲TC

bCDW distortion (+screening)

qCDW 2qCDW

pinning massless (acoustic)

phasonfreq.

ωQ

LA phonon

massive (optical)

Amplitudon |Δ(t)|

FIG. 1. Collective modes of an incommensurate charge-density-wave (CDW) phase. (a) Ginzburg-Landau free energy (F)

and real space representation of the amplitudon (dashed arrow) and the phason (solid line arrow) for a CDW order parameter.

(b-c) Dispersion relations of the CDW collective modes. Below TCDW, the otherwise undistorted acoustic phonon (LA) softens

near ~qCDW and renormalizes into the amplitudon and phason bands. (b) At moderate T(.TCDW) the long-range Coulomb

repulsion Uis screened by quasiparticles. (c) When the system is cooled well below TCDW, the screening weakens and the

spectral weight from the massless (acoustic) phason is transferred to the massive (IR-active) phason of frequency ωLF.

the superconducting phase. In a CDW system, however,

the relevant scale is the plasma frequency of the conden-

sate, which can lie far below the single-particle gap. To

date, direct experimental evidence of the massive “Lee-

Fukuyama” phason in CDW systems has been elusive.

Here, we present evidence for the generation and de-

tection of a massive Lee-Fukuyama phason in the CDW

insulator (TaSe4)2I, a quasi-1D material [12] that under-

goes an incommensurate CDW transition below TCDW ∼

260 K [13–16] with a CDW gap for single particle exci-

tations of 2∆CDW ≈250 −300meV [17–20]. (TaSe4)2I

is unique among quasi-1D CDW systems due to its un-

usually high resistivity in the low temperature insulating

state [21], such that the long-range Coulomb interaction

can remain unscreened and the Lee-Fukuyama phason

can have have signiﬁcant spectral weight. To investigate

the collective modes of the CDW order in (TaSe4)2I, we

performed time-domain THz emission spectroscopy using

an ultrafast photoexcitation ‘pump’ pulse with an energy

of 1.2 eV (λ= 1030 nm) (See Fig. 2a for the experimental

geometry and [21] for further details of the experimen-

tal setup). Note that the photoexcitation energy here is

greater than 2∆CDW and so the pump pulse initially cre-

ates single-particle excitations across the CDW gap. As

(TaSe4)2I is structurally chiral (SG. 97) and lacks inver-

sion symmetry, this photoexciation generates a transient

current with a duration of a few picoseconds (ps). Such

phenomena is well-known as a photo-galvanic or a photo-

Dember eﬀect, both of which can occur in systems lacking

inversion symmetry [22, 23]. The transient current then

results in a short ps-duration burst of THz radiation in

the far-ﬁeld which we measure in the time-domain using

standard electro-optical sampling (EOS) [21].

Figure 2b shows the measured time proﬁle of the THz

electric ﬁeld (ETHz(t)) emitted from (TaSe4)2I upon pho-

toexcitation at T=7KTCDW. Here the pump

is p-polarized, with an electric ﬁeld component along

the quasi-1D chains of (TaSe4)2I. Two features are im-

mediately evident in ETHz(t): a transient peak around

tdelay = 0 ps followed by a long-lived coherent oscillation

that lasts over ∼80 ps. In the frequency domain (Fig. 2b

inset), the transient peak around tdelay ∼0 ps manifests

as a broad distribution over frequencies from 0.1 to 2

THz, while the long-lived coherent oscillation manifests

as a sharp peak centered at 0.23 THz. For the rest of this

work, we refer to the transient (tdelay ∼0 ps) peak as Etr

and the coherent oscillation as Eosc. As noted above, Etr

is what we typically expect from such an experiment due

to a photo-galvanic or a photo-Dember eﬀect. The tran-

sient current can be estimated from the measured Etr,

and is greater than the current necessary to depin the

dynamics of CDW order in (TaSe4)2I [21].

We focus on the observed narrow-band THz emission

Eosc since this aspect of the data is particularly striking.

Eosc lasts well over 80 ps – much longer than the typi-

cal few ps duration signal expected from semiconductors

[23] and semimetals [24–26] in THz emission experiments.

Another unusual feature of Eosc is the observed waveform

envelope in the time domain which appears to gradually

increase in magnitude starting at tdelay = 0 ps. In impul-

sive excitation ultrafast experiments, the signal is usually

peaked at tdelay = 0 from where it exponentially decays.

Additionally, while the measured transient peak Etr is

both horizontally and vertically polarized, the coherent

oscillation Eosc is only horizontally polarized (Fig. 2c).

In our experimental geometry, this corresponds to Eosc

being polarized along the quasi-1D chains of (TaSe4)2I

as shown in Fig. 2a.

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ObservationofthemassiveLee-FukuyamaphasoninachargedensitywaveinsulatorSoyeunKim,1,2YinchuanLv,1,2Xiao-QiSun,1ChengxiZhao,2,3NinaBielinski,1,2AzelMurzabekova,1,2KejianQu,1,2RyanA.Duncan,4,5QuynhL.D.Nguyen,4,5MarianoTrigo,4,5DanielP.Shoemaker,2,3BarryBradlyn,1andFahadMahmood1,2,1DepartmentofPhysics,U...

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Observation of the massive Lee-Fukuyama phason in a charge density wave insulator Soyeun Kim1 2Yinchuan Lv1 2Xiao-Qi Sun1Chengxi Zhao2 3Nina Bielinski1 2 Azel Murzabekova1 2Kejian Qu1 2Ryan A. Duncan4 5Quynh L. D. Nguyen4 5.pdf

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Observation of the massive Lee-Fukuyama phason in a charge density wave insulator Soyeun Kim1 2Yinchuan Lv1 2Xiao-Qi Sun1Chengxi Zhao2 3Nina Bielinski1 2 Azel Murzabekova1 2Kejian Qu1 2Ryan A. Duncan4 5Quynh L. D. Nguyen4 5

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