Science - USA (2020-01-17)

the slow long-wavelength fluctuations of the
order parameter alone describe a Gaussian
fixed point, wherew/Tscaling is violated. The
incorporation of the single-electron excitations
in the quantum criticalspectrum not only makes
charge fluctuations part of the quantum crit-

icality but also turns the fixed point into an

interacting one ( 24 ), leading tow/Tscaling.

Dynamical scaling of the optical conductiv-

ity in the region ofT-linear resistivity has also

been analyzed in an optimally doped Bi-2212

cuprate ( 27 ). There, different scaling functions

are needed in differentw/Tranges, leaving

open the question of how the fluctuations of

the charge carriers connect with the robust

linear-in-temperature resistivity of the cuprate

superconductors. By contrast, in the present

study of YbRh 2 Si 2 , a singlew/Tscaling form

Prochaskaet al.,Science 367 , 285–288 (2020) 17 January 2020 2of3

Fig. 1. YbRh 2 Si 2 thin films grown by means of

MBE.(A) Visualization of the lattice matching

between YbRh 2 Si 2 (blue circles and black lines)

and Ge (green circles and red lines), with the

crystallographiccdirections pointing out of

the plane. For the Yb atoms to associate

with the Ge atoms, the respective unit cells

(thick lines) [(C), right] are rotated by 45° with

respect to each other around thecdirection.

(B) High-resolution x-ray diffraction pattern, with

all peaks identified as due to the (about 40 nm

thick) film or the Ge substrate, confirming that

the film is phase-pure YbRh 2 Si 2 .(C) Atomic-

resolution high-angle annular dark field scanning

transmission electron microscopy (HAADF-STEM)

image of the interface between film (top left)

and substrate (bottom left), representative

enlarged views with simulated overlays (center),

and the corresponding unit cells (right).

(D) Intensity profiles along the red dotted lines

in (C). The left and right panels correspond

to the top red dotted line within the film and the

bottom red dotted line across the interface,

respectively.

0.0 0.5 1.0 1.5 2.0

HAADF Intensity (arb. unit)

Position (nm)

Yb Yb

Rh

Rh

Rh

Yb

Rh

Si

Si

0.0 0.5 1.0 1.5 2.0

HAADF Intensity (arb. unit)

Position (nm)

Yb

Rh-Si

Ge

GeGe

GeGe

A B

C

D

Fig. 2. Electrical resistivity of MBE-grown YbRh 2 Si 2.

(A) Normalized resistance of an MBE-grown YbRh 2 Si 2

film and a bulk single crystal with currentjwithin

the tetragonalaaplane ( 15 ) for comparison. The film

was measured by using the van der Pauw technique.

(B) Corresponding low-temperature resistivities, with

the residual resistivities [r 0 = 11.6 and 2.45 microhm cm

for the MBE and bulk ( 15 ) samples, respectively,

determined by linear-in-Tfits to the data below 1 K]

subtracted, displaying non–Fermi liquid behavior (lines

representr–r 0 =A′Tafits with a constant exponent

ato the data below 12 K; the temperature dependence

ofais provided in fig. S1).

1 10 100

0.0

0.2

0.4

0.6

0.8

1.0 MBE film

bulk #1 jZc

R/R

max

T(K)

024681012

0

5

10

15

20

25

MBE film

bulk #1 jZc

0

(μΩ

cm)

T(K)

AB

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