Comment on "Charge-parity symmetry observed through Friedel oscillations in chiral charge-density waves" by J. Ishioka et al

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by  Jasper van Wezel

Comment on “Charge-parity symmetry observed through Friedel oscillations in chiral
charge-density waves” by J. Ishioka et al.
Jasper van Wezel
Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA
Intheirpublication[Phys. RevB,84,245125(2011)],Ishiokaetal. discusstherecentlydiscovered
chiralchargedensitywavestatein1T-TiSe2 intermsofaparameterHCDW,whosesignissuggested
to correspond to the handedness of the chiral order. Here we point out that HCDW, as defined
by Ishioka et al., cannot be used to characterize chirality in that way. An alternative measure of
chirality for thespecific case of 1T-TiSe2 is suggested.
2
1
0 It has recently been suggested that the low tempera- Thesituationcanbeclarifiedbyconsideringthedefini-
2
ture ground state of the quasi two-dimensional, layered tionofthechiralchargedensitywavestateintroducedin

n material 1T-TiSe is a chiral charge ordered state.1–3 In Ref. 2. There, it is suggested that the electronic charge
2
a this state, the direction of the dominant component of a distribution of all phases of 1T-TiSe can be written in
2
J
triple-q charge density wave rotates as one progresses in the form

1
thedirectionperpendiculartotheatomiclayers. Intheir
2 recent publication,4 Ishioka et al. analyze scanning tun- ρ(r)=ρ +Aℜ eiq~j~r+ei(q~j+1~r+ϕ)+ei(q~j+2~r−ϕ) , (3)
0 n o
nelingmicroscopyimagesofthechiralphaseof1T-TiSe
] 2 where ρ is the uniform charge distribution in the high
l in terms of a parameter H , whose sign is suggested 0
e CDW temperature state, j is either 1, 2 or 3, and the other
- to reflect the handedness of the chiral state. Here we
r point out that the sign of this parameter is not well de- indices are defined modulo 3. The material undergoes a
st fined in 1T-TiSe , and that consequently H cannot transitionfromthe hightemperature uniformphase to a
. 2 CDW state with charge density modulations when A becomes
t be used as an order parameter for the chiral state.
a nonzero. Thischargedensitywaveisnon-chiralaslongas
m The chirality parameter is defined in Ref. 4 as:
ϕ=0. Nonzerophasedifferencesareexpectedtodevelop
d- HCDW =~q1·(~q2×~q3). (1) at a temperature Tchiral <TCDW, below which the chiral
sate prevails.2 The handedness of the chiral pattern is
n
o The vectors ~qj in this expression represent the propaga- determined by the sign of ϕ. This particular description
c tion vectors of the three components of the charge den- ofthe chiralchargedensity waveisinvokedby Ishiokaet
[ sity wave in 1T-TiSe . These are well known (see for al. in their equation (1).4
2
example equation (1) in Ref. 4) to be: ~q = 1(~a∗+~c∗), Becauseboththenon-chiralandthechiralchargeden-
1 1 2
v ~q = 1(~b∗+~c∗) and ~q = 1(−~a∗−~b∗+~c∗), with starred sity wave consist of a superposition of the same three
4 v2ector2s indicating the3 rec2iprocal lattice vectors of the propagation vectors, it is immediately clear that a pa-
8 rameter which only involves these vectors cannot distin-
original lattice. From their definitions, it is immedi-
4 guish between these states. Instead, it is essential to
ately clear that the propagationvectors differ from their
4
take into account the relative phase differences between
negated versions by precisely a reciprocal lattice vector.
.
1 the chargedensity wavecomponents. Defining the phase
0 ~q =−~q +~a∗+~c∗ relation between the components as in equation (3), the
2 1 1 sign of ϕ directly reflects the handedness of the chiral
1 ~q =−~q +~b∗+~c∗
2 2 state, and ϕ may be used as an order parameter to de-
:
v ~q3 =−~q3−~a∗−~b∗+~c∗. (2) scribe the emergence of the chiral order in 1T-TiSe2.
i Notice however that this definition of the chiral order
X
Sincetheelectronmomentumwithinthecrystallatticeis parameter is not universally applicable: in the related
ar definedonlyuptoareciprocallatticevector,wethusfind material 2H-TaS2, polar rather than chiral charge order
that ~q is equivalentto −~q for all j. Because the signof results from the charge distribution of equation (3), and
j j
the parameter H can be changed at will by adding in that case ϕ serves as a measure of the polarization.5,6
CDW
reciprocal lattice vectors to the propagation vectors, it Work at Argonne National Laboratory was supported
cannot have any physical meaning, and in particular it by the US DOE, Office of Science, under Contract No.
doesnotcorrespondtothehandednessofthechiralstate. DE-AC02-06CH11357.
1 J. Ishioka, et al., Phys. Rev. Lett. 105, 176401 (2010). 5 I.Guillamon, et al., New J. Phys. 13, 103020 (2011).
2 J. van Wezel, Europhys. Lett. 96, 67011 (2011). 6 J. van Wezel arxiv/cond-mat 1111.2035 (2011).
3 J. van Wezel and P. Littlewood, Physics 3, 87 (2010).
4 J. Ishioka, et al., Phys. Rev. B 84, 245125 (2011).