The  intriguing  physics  of  delafossite  metals  

Andy  Mackenzie    

Max  Planck  Ins,tute  for  Chemical  Physics  of  Solids,  Dresden,  Germany  

 School  of  Physics  &  Astronomy,  University  of  St  Andrews,  

Scotland    

University of St Andrews

University of St Andrews

Christoph  Geibel,  Alexandra  Gibbs,  Clifford  Hicks,  Phil  King,  Pallavi Kushwaha,  Yoshi  Maeno,  Philip  Moll,  Nabhanila  Nandi,  Burkhard  

Schmidt,  Veronika  Sunko,  Hiroshi  Takatsu  and  Ed  Yelland  

Collaborators

Max  Planck  InsJtute  for  Chemical  Physics  of  Solids,  Dresden    University  of  St  Andrews  

ETH  Zürich  Kyoto  University  

Tokyo  Metropolitan  University  

University of St Andrews

Contents

1. What are delafossites and why study them?

2. PdCoO2 as an ideal test material for modern FIB processing

3. Observation of ‘electron hydrodynamic’ effects

4. Future prospects

What are delafossites?

Pd

Co

O

PdCoO2  

R.D. Shannon, D.B. Rogers and C.T. Prewitt, Inorg. Chem. 10, 713 (1971); H. Takatsu et al., J. Phys. Soc. Jpn. 76, 104701 (2007)

Layered metals, magnets, semimetals and insulators

Of particular interest to us are the metals: PdCoO2, PtCoO2, PdRhO2, PdCrO2 and others.

PdRhO2  

e.g. K.P. Ong et al., Phys. Rev. B 81, 115120 (2010)

Why study delafossite metals?

•  The lowest room temperature resistivity per carrier of any known metal (PtCoO2 grown in Dresden)

•  The longest low temperature mean free path of any multi-component metal (up to 40 µm in PdCoO2)

•  The opportunity to study the interplay of this metallic physics with triangular lattice magnetism in a Mott insulating layer (PdCrO2)

Ultra-low momentum-relaxing scattering

H. Takatsu et al., PRL 105, 137201 (2010) C.W. Hicks et al. ArXiv:1504.08104

See poster by V. Sunko et al.

Amazingly clean photoemission spectra from PtCoO2

100  μm    

PdCoO2  

Delafossites  as  an  ideal  test-­‐bed  for  modern  Focussed  Ion  Beam  techniques  

Res

ista

nce

(mΩ

)

FIB-testing and probing a new regime of electronic behaviour

Experiment: Successively narrow the channel in factors of 2, measuring the magnetoresistance after every step.

P.J.W. Moll, P. Kushwaha, N. Nandi, B. Schmidt and A.P. Mackenzie

eBkr F

c!

=

Maximum when rc < W if boundary scattering is important.

Prefactor seen in semiconductors was 0.55; that in graphene was 0.9

0.00  

Boundary scattering therefore dominates the increase in resistivity as the channel is narrowed, but there is an extra twist….

ℓ   W

L

Electron  fluid  in  a  real  solid:  both  momentum-­‐conserving  and  momentum-­‐relaxing  scaAering  take  place    

Momentum-­‐relaxing  processes  Momentum-­‐conserving  processes  

Minimal  definiJon  of  a  ‘hydrodynamic’  metal:  momentum-­‐conserving  processes  are  more  rapid  than  momentum-­‐relaxing  ones.      

R.  Mahajan,  M.  Barkeshli  &  S.A.  Hartnoll,  Phys.  Rev.  B  88,  125107  (2013)  A.V.  Andreev,  S.A.  Kivelson  and  B.  Spivak,  Phys.  Rev.  LeS  106,  256804  (2011)  

In  99.9999%  of  known  metals,  momentum-­‐relaxing  sca^ering  dominates  completely.    In  fact,  standard  transport  theory  ignores  momentum-­‐conserving  sca^ering  altogether.    

R.N.  Gurzhi,  JETP  LeSs  44,  771-­‐772  (1963)  L.  W.  Molenkamp  and  M.  J.  M.  de  Jong,  Phys.  Rev.  B  49,  5038  (1994)  

Standard  Boltzmann  analysis    

C.W.J.  Beenakker  and  H.  van  Houten,  Solid  State  Physics,  44,  1-­‐228  (1991);  arXiv:cond-­‐mat/04122664  

PredicJon  from  a  theory  taking  hydrodynamic  effects  into  account.  M.J.M  de  Jong  &  L.W.  Molenkamp,  Phys.  Rev.  B  51,  13389  (1995)  

After a little more work with the theory..

Full numerical solution performed across the whole of its parameter space

.. we can make a rough calibration of the ‘hydrodynamically relevant’ parameters in PdCoO2

Result: 3 x 10-4 kg(ms)-1 < ηe < 6 x 10-3 kg(ms)-1

Comparison: η = 1 x 10-3 kg(ms)-1 for water at 300 K

η = 1 x 10-4 kg(ms)-1 for liquid N2 at 70 K

η = 5 x 10-2 kg(ms)-1 for liquid 3He at 2 mK

a) Momentum conserving scattering rate is approximately 10 times higher than the momentum relaxing one. This is consistent with the ratio of the mean free paths deduced from dHvA and resistivity.

b) Electronic viscosity ηe can also be estimated.

P.J.W. Moll, P. Kushwaha, N. Nandi, B. Schmidt and A.P. Mackenzie, preprint

Conclusions  

University of St Andrews

2) Experiments on the electron fluid in mesoscopically patterned single crystals of PdCoO2 provide evidence for hydrodynamic effects.

3) Technical significance: focussed ion beam processing caused no observable bulk damage even in channels 1 µm wide.

4) Hope that electronic turbulence and other hydrodynamic effects may be observable, in delafossites and other systems.

1) Delafossite metals combine simple electronic structure with ultra-high purity.