Oxygen vacancy-driven orbital multichannel Kondo effect in Dirac nodal line metals IrO

Oxygen vacancy-driven orbital multichannel Kondo effect in Dirac nodal line metals IrO ₂ and RuO ₂

Juhn-Jong Lin 林志忠

Sheng-Shiuan Yeh 葉勝玄

Ta-Kang Su

An-Shao Lien Chao-Ching Liao

Stefan Kirchner Zhejiang University Hans Kroha

Farzaneh Zamani University of Bonn A Long Journey into Exotic Kondo Physics

International College of

Semiconductor Technology, NCTU

Sci. Adv. 3, e1700135 (2017)

We demonstrate theoretical conception and

experimental method to quantitatively characterize nanocrystallite motion in RuO₂ nanowires.

polycrystalline nanowire

Keywords:

Kondo physics

Magnetic spin-half Kondo effect

One-channel Kondo effect

Two-channel Kondo effect

Dynamic defects

Dynamic scattering centers Two-level systems

Fast two-level systems

A defect having two equivalent (nearby) sites in a solid An object switching in a double-well potential, modeled as a two-level system

crystallite (grain)

Noise due to atomic and granular dynamic defects

The motion of a large number of slow dynamic defects causes low- frequency (1/f) noise.

The motion of a single nanocrystallite leads to random telegraph noise.

Lorentzian behavior

“Strong electron correlations may give rise to an unconventional metallic state accompanying non-magnetic Kondo scattering. Here, the authors report signatures of orbital one- and two-channel Kondo physics in Dirac nodal line metals RuO₂ and IrO₂ nanowires.”

Vol. 11, 4749 (2020)

Experimental realization of non-Fermi liquid behavior at low temperatures!

A localized S = ½ magnetic impurity causes the standard Kondo effect

Experimental discovery in 1930s at Kamerlingh Onnes’ Lab. (Leiden) Theoretical explanation in 1960s

Comparison of experimental and theoretical ρ(T) curves for dilute AuFe alloys [J. Kondo, Prog. Theor.

Phys. 32, 37 (1964)]

Spin-half magnetic Kondo effect

W.J. de Haas and G.J. van den Berg (1936)

impure gold

Kondo resistivity: universal temperature dependence

Numerical renormalization group (NRG) calculations: one-channel Kondo (1CK) scaling form

T. A. Costi, A. C. Hewson & V. Zlatic JPCM 6, 2519 (1994)

Normalized Kondo resistivity vs.

reduced temperature T/T_K

(Taken from “Long Range Order in Solids”, by R. M. White and T. H.

Geballe, Fig. VII.14) 1960s

Scattering off a localized spin-half magnetic impurity

k k’ A nonmagnetic impurity (defect) in a metal

⇒ Elastic electron scattering

⇒ A constant, “residual resistivity” at low T

A localized magnetic impurity (S = ½) in a metal

⇒ Spin-spin coupling (s-d exchange interaction)

⇒ log(T) resistivity increase below a characteristic energy scale T_K

⇒ Fermi-liquid physics as T << T_K k ↓

S = 1/2

k’↑

S = −1/2

One conduction-electron band (a Fermi sea) couples with the localized spin-½ magnetic

moment, forming a spin-singlet ground state as T → 0 K.

†

, ,

,

k k k K c

k

H c c

J S s

σ

ε

= ∑ + ^{ } ⋅

A quantum impurity with internal degree of freedom

“We investigate a case where the interaction is of the Coulomb type, which may vary depending on the states of the localized system. The simplest of such a system may be an impurity atom, which can jump between two equivalent sites.”

( ) r s

( ), ( ) r

r

ψ ψ ψ

Ψ =   ⋅ ⇒  

Cf. Localized magnetic moments

A quantum impurity with internal degree of freedom

“The problem is similar to the s-d problem in that the conduction

electrons interact with an impurity system having an internal degree of freedom. In the present case, the relevant interaction is the

orbital-orbital interaction, since we are considering the Coulomb- type interaction.”

Two equivalent sites

Double-well potential ⇒ “Two-level system” model

“Impurity-spin flipping” vs. “Impurity-site switching”

⇒ Non-magnetic orbital Kondo effect !

J. Kondo (1976)

Spin multi-channel Kondo effect

The multichannel Kondo model:

A few conduction-electron bands interact with a localized quantum impurity which has internal degree of freedom.

One-channel Kondo effect

⇒ Fermi-liquid ground state

Multi- (two-) channel Kondo effect

⇒ a non-Fermi liquid ground state

⇒ Strange metal physics

“Over-screening” shall result in a non-Fermi-liquid ground state.

Orbital multi-channel Kondo effect

I. 18 pages II. 14 pages III. 17 pages

2

†

, , , ,

, , 1

M

i

k i k i k K c

i k i

H

J S s

σ

ε ψ ψ

=

= ∑ + ∑ ^{ } ⋅

M channels (M Fermi seas)

• Two-channel Kondo effect

• non-Fermi-liquid ground state

344 pages

(courtesy of S. Kirchner)

(courtesy of S. Kirchner)

PHYSICS WORLD, January 2001

A semiconductor quantum dot (∼ 100 nm) containing an odd number of electrons can act as a localized

spin- ½ magnetic impurity, giving rise to Kondo physics

⇒ Kondo “conductance” G(T)

Goldhaber-Gordon et al., Nature 391, 156 (1998)

QD

Drain Source

A quantum dot (S=1/2) coupled to source-drain

electrodes ^{metal quantum} _{dot device}

Source

Drain

K 0.2 K T 

two-channel

A suggested route to 2CK effect

( , ) ( , ) dI V T G V T

= dV 𝑇𝑇 temperature behavior A non-Fermi-liquid signature

Problems and difficulties:

1) Fine-tuning is required.

2) Implications for real solids and

topological quantum materials is unclear.

3) T_K value is very small.

Orbital two-channel Kondo effect in real materials

Experimental signature:

A 𝑇𝑇 resistivity increase at low temperatures (in the residual-resistivity regime). The resistivity increase is independent of an applied magnetic field.

2_CK

( , ) T B n

T ρ

∆ ∝ −

Altshuler & Aronov:

Electron-electron interaction (EEI) effect causes a 𝑇𝑇 resistivity increase at low temperatures in 3D weakly disordered metals.

2 2 0 0

( ) 0.915 4 3

4 3 2

k TB

T e

F D

ρ ρ

ρ π

∆ = −   −  

D: electron diffusion constant 0 ≤ F ≤ 1: a screening factor An ubiquitous effect in real conductors !

The presence of impurities cause multiple elastic scattering, leading to

quantum interference of electronic waves, which in turn results in enhanced e-e interaction. ⇒ The density of states at E_F is suppressed.

IrO

and RuO

crystalizes in the rutile structure

Ir: [Xe]4f

5d

6s

Ir

: [Xe]4f

5d

J. J. Lin et al., JPCM 16, 8035 (2004)

RuO₂ and IrO₂ single crystals

Good metals !

(300 K) (4 K) 100

ρ

ρ

RuO₂

IrO₂ Ir, Ru

O

5d orbitals are half-filled in IrO

R(T) below 10 K

Recent discovery: Dirac nodal line metals IrO

and RuO

Large spin Hall resistivity

•

IrO

nanowires were grown via MOCVD.

RuO

nanowires were grown via thermal evaporation.

•

Four-probe R(T) measurements down to 50 mK, in applied magnetic field up to 9 T.

•

Nanowires were measured as-grown, after annealing in vacuum, and after oxygenation.

•

Thermal annealing in vacuum generates oxygen vacancies which generate dynamic scattering defects, causing orbital Kondo effect.

•

The orbital Kondo effect is suppressed in (fully) oxygenated nanowires.

Low-temperature Kondo resistivity in rutile nanowires

nanowire diameter

≈ 50 – 190 nm

Nanowires were grown by Y.S.

Huang’s group (NTUST), and F.R.

Chen & J.J. Kai’s group (NTHU).

Resistivity vs. temperature for IrO

and RuO

nanowires

The overall resistivity curve ρ(T) reveals Boltzmann-transport behavior.

The low-T resistivity increase can be repeatedly introduced (suppressed) by thermal annealing in vacuum (oxygen).

Thermal annealing in vacuum

caused a low-T resistivity increase

Fully oxygenated Oxygen deficient Oxygen deficient

𝑇𝑇 resistivity increase in paramagnetic IrO

nanowires

• A 𝑇𝑇 resistivity increase is found after annealing in vacuum.

• The 𝑇𝑇 resistivity increase shows insensitivity to magnetic field.

• After aging in air, the 𝑇𝑇

behavior persists, but showing a smaller resistivity increase.

• Oxygenation reduces dynamic scattering defects, producing a smaller orbital Kondo effect.

• A deviation from the 𝑇𝑇

behavior occurs around 0.5 K !

Ruling out 3D electron-electron interaction effect

•

A deviation from the 𝑇𝑇 dependence at ∼0.5 K is incompatible with the 3D EEI effect.

•

The observed resistivity increase (

of magnitude as would be predicted by the 3D EEI effect (

•

The residual resistivities ρ

(B1) = 73.9 µΩ cm and ρ

(B2) = 75.0 µΩ cm differ by ≈1%. The 3D EEI effect predicts a ≈3% difference in resistivity increase. But, experiment shows ≈50% difference.

≈ 3×10^-4 in our MO₂ nanowires

( )

2

0 0

2 0

( ) 0.915 4 3 ( ) 4 3 2 ( )

kB

T e

F T T T

T D

ρ ρ

ρ π

∆ = −  −   −

 

Independence of applied magnetic field of the resistivity increase

is in accord with nonmagnetic orbital 2CK effect !

(courtesy of S. Kirchner)

Oxygen

(courtesy of S. Kirchner)

k k’

k ↓

S = 1/2

k’↑ S = −1/2

Heuristic picture for electron-quantum impurity scattering

Elastic electron-impurity scattering

⇒ “residual resistivity”

Magnetic spin-flip scattering

⇒ Standard 1CK effect

Electron-quantum impurity scattering:

The quantum impurity M⁺³ contains a defect electron which tunnels between the two-fold degenerate d_xz and d_yz

orbitals.

The spin-up and spin-down conduction electrons act as two independent and equivalent channels.

⇒ Nonmagnetic orbital 2CK effect ! S =±1/2 degenerate doublet states

k ↓ k ↑

d_xz

k’ ↓ k’ ↑ d_yz

(courtesy of S. Kirchner)

Lien et al., PRB 84, 155432 (2011)

The low-T resistance increase is insensitive to large magnetic fields !

Magnetoresistance for magnetic spin-1/2 Kondo effect by NRG calculations.

T. A. Costi, PRL 85, 1504 (2000)

K K

/ 1, 3.0 K

B B

g µ B k T ≥ T =

T_K ≈ 3.0 K

Temporal universal conductance fluctuations (UCFs) in RuO₂ wires

B = 3 T B = 5 T

Oxygenated NW 4

0.65%

ρ ρ

∆ 

(courtesy of S. Kirchner)

T_K values vary from 3 to 80 K. The Kondo resistivities conform to the universal 1CK scaling function !

Ruling out 3D electron-electron interaction effect

•

Conformation to the one-channel Kondo scaling form for three decades in T/T

rules out the 3D EEI effect

•

The observed resistivity increase is more than one order of magnitude as would be expected from the 3D EEI effect

≈ 3×10^-4 in our MO₂ nanowires

( )

2

0 0

2 0

( ) 0.915 4 3 ( ) 4 3 2 ( )

k

T e

F T T T

T D

ρ ρ

ρ π

∆ = −    −     −

 

The insensitivity to applied magnetic field indicates

nonmagnetic orbital one-channel Kondo effect !

Recent 2CK experiment of layered compound Zr-As-Se (?)

For the layered compound ZrAs_1.58Se_0.39, the authors argue that vacancies in the square nets of As give rise to the low-T transport anomaly in line with the nonmagnetic version of the 2CK effect.

in collaboration with MPI Dresden, Zhejiang University

Recent 2CK experiment of layered compound Zr-As-Se (?)

3D electron-electron interaction effect in Ti-Al alloys

Resistivity increase for Al-doped Ti alloys with ρ₀ = 143, 167 and 204 µm cm.

Phys. Rev B 48, 5021 (1993) δρ ∝ − T

吳至原副教授 (輔仁物理系)

PhD in 1996, NTU Physics

CONCLUSION

• IrO

and RuO

crystalize in the rutile structure, with approximate C

symmetry. Properties of the C

group imply two-fold degeneracy of the nonmagnetic impurity.

• In paramagnetic IrO

, the spin-degeneracy of the conduction bands is preserved. ⇒ Orbital 2CK effect !

• In

, the conduction band is (locally) spin- polarized. ⇒

• The symmetries that that enforces the existence of Dirac nodal lines also promote the formation of non-magnetic Kondo correlation.

• Both the emergence of the strange metallic state that accompanies unconventional superconductivity and the formation of the 2CK effect originate from strong electron interactions.

Kondo, 1976 Nozieres, 1980 Zawadowski, 1980s Many more ……

A quantum impurity (a localized spin, a moving electron or atom, etc.) with internal degree of freedom (two-fold degeneracy) generates the Kondo effect.