The break-up of Fermi
Liquid at Quantum Critical Point (QCP)
Presenter: Lee Wei Chuang
Course: Condensed Matter Physics PHY401 Date: 1 DEC 2020
Lecturer: Prof. Johan Chang
DOI:https://doi.org/10.1038/nature01774
Content
Brief catch-up of the Fermi liquid knowledge
Brief introduction of non-Fermi Liquid (NFL) & Quantum Critical Point (QCP) knowledge
The observation and the main figure of the paper
Results and discussions
Conclusion
Brief catch-up of FL
Fermi liquid theory is a theoretical model of interacting fermions that describes the normal state of most metals at sufficiently low
temperature.
“Adiabatically switching on” the interaction between electron…
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Fermi liquid theory - Wikip edia
Brief catch-up of FL
The most striking characteristic of Fermi Liquid, it the relationship of the resistivity and the temperature:
As what we have learnt before, due to the e-e interaction:
(compare to before and after interaction)
Fermi Surface doesn’t change
Electronic specific heat does change
the effective mass of the electron increases
DOI:
10.1103/PhysRevLett.111.027002
Non-Fermi Liquid
Non-fermi liquid behavior:
the n can be changed,
For example by doping level,
Quantum critical Point (QCP)
The quantum critical point is the point at
absolute zero where matter becomes unstable to new forms of order is called a QCP
The quantum fluctuations between order and disorder induced profound transformation in the electronic properties of materials in finite Temp.
Control parameter: Pressure, magnetic field…
Main figure & Background
Previous studies: Heavy-electron materials was studied near QCP by applying magnetic field, showed that the field induced QCP electrons move ever slowly and scatter with high probability…..
Question: Is this the artefact of the applied field? Or it is a general characteristic/effect of field-free QCP?
Goal: To understand whether the magnetic field matters at QCP…
Main figure
Material: Germanium-doped
Why doped? The critical field of QCP is getting closer to zero (0.027T)
Comparison:
Before: x=0, Bc=0.66T,
After: x=0.05, Bc=0.027T,
When B>Bc, field induced LFL state is established
When B→Bc, what happens?
Δ � = � � �
Observation and Main figure
When B→Bc, the coefficient A(B)∝1/(B-Bc), A(B) diverges!
Therefore, by considering the ratio outside the QCP for LFL, which is small than Kadowaki-Woods ratio, seems to shows the trends of having divergence of m* when B→Bc
The Neel Temperature gets closer to zero!
Δ � = � � �
Ratio between
It found to be constant for Transition metals
&
Heavy-fermion compounds (with different value)
Result
The slightly-doped material is essentially identical to the undoped material, still probing same QCP.
Doped case, the QCP is essentially located at Bc=0T.
The Neel temperature (still a tiny trend of AFM), and large effective moment per
a figure shows a logarithmic divergence between 0.3K to 10K, and an upturn below 0.3K for undoped case
B figure shows how the change of the applied field affect the trend of the upturn
Result
B figure shows how the change of the applied field affect the trend of the upturn
When B>0.1T, is temperature independent (expected for FL)
When the B is lowered, the suddenly surges and diverges
This type of upturn of at zero-field is somehow related to the characteristic of the electron (in zero-field) and the intrinsic specific heat at QCP!
Result
From the A figure, two samples were studies
When , the (stronger than logarithmic scale)
From B figure, the values for the electronic specific-heat coefficient shown in A figure, ) of either interpolation or extrapolation.
For 2D SDW (black dashed)
Therefore, again, this characteristic of QCP is an intrinsic property of QCP, irrelevant to magnetic field
Result and discussion
This result of the specific heat at zero-field is also supported by electrical resistivity data. (Both data collapse into a single set of scaling relations)
And and ,
For NFL (), where is constant and and field tuned LFL is described by the limit of these equations.
If there are residual pockets of LFL that were left unaffected by the QCP, we would still expect a residual quadratic component in the resistivity, however, the data collapse in the observed fashion.
Therefore, The break-up of the LFL involves the entire FS!
Conclusion
This type characteristic is neither three, two or even one-dimensional, but local! The critical fluctuations are fundamentally “zero-dimension” in character.
Slightly-doped material will have a Bc which is shifted closer zero, (goal achieved)
The electronic specific heat coefficient deviate towards larger values for small B
They ascribe this intrinsically electronic feature to the critical fluctuation associated with the zero-field quantum phase transition that exists at a slightly Ge concentration.
The break-up of Fermi liquid involves the entire fermi surface!
