Landau Fermi liquid model
m*
ρ = 2 ≡ AT 2
ne τ
Details: Stewart, Rev. Mod. Phys. 73, 797
(2001) & 78, 743 (2006)
C = γT
Often considered identifying features of Fermi Liquid (along with Pauli Paramagnetism)
Non-­‐Fermi Liquid (?)
High-­‐Tc related materials: strong interactions = highly correlated
Shibauchi, et al., PNAS 105, 7120 (2007)
“Cuprate” high-­‐Tc (e.g. YBa2Cu3O7)
Non-­‐Fermi liquid features
rho ~ T
C ~ T ln T
Generic phase diagram
See e.g. “Quantum Phase Transitions”, S. Sachdev,
Cambridge University Press, 2013.
Anissimova, Kravchenko, Punnoose,
Finkel'stein & Klapwijk
Nature Physics 3, 707 - 710 (2007)
Metal-­‐Insulator transitions:
General class of behavior now recognized as including transition near T = 0.
High-­Tc cuprates, Fe pnictides, and related superconducting materials.
Compound Tc (K)
Compound
Tc (K) 38
LaFeAs[O1-­‐xFx]
26
YBa2Cu3O7-­‐d (YBCO)
95
GdFeAsO1-­‐x
53
Bi2Sr2CaCu2O9 (BSCCO 2212)
110
BaFe2As2
38
Bi2Sr2Ca2Cu3O10 (BSCCO 2223)
110
FeSe
8.5
Hg2Sr2Ca2Cu3O8
134
LiFeAs
18
(Nd,Ce)2CuO4 (electron doped)
35
Sr2RuO4
0.93
(La,Sr)2CuO4-­‐d (LSCO)
(Nobel prize
Benorz, Muller)
Physics Today, Jan. 2001; Yoshiteru Maeno, T. Maurice Rice,
and Manfred Sigrist, "The Intriguing Superconductivity
of Strontium Ruthenate."; also see Evaluation of SpinTriplet Superconductivity in Sr2RuO4, Y. Maeno et al., J.
Phys. Soc. Jpn. 81 (2012) 011009.
More Pnictide Fermi surface images:
Ivanovskii, Platinum Metals Rev. 57, 87 (2013)
Ca10(Pt3As8) (Fe2–xPtxAs2)5
1st zone with KFe2Se2 superconductor
Fermi surface (Liu et al. Physica B 407, 1139,
Quasi 2-­‐D
metal
2012)
High-­Tc cuprates, Fe pnictides, and related superconducting materials.
Keimer et al. Nature
518, 179–186
(2015).
• Superconductivity from magnetic oxide ”bad metal” a surprise.
• Used in high-field magnets.
Nanoscale physics
• range of nanostructures considered to be 1 – 100 nm . (recall
electron energy levels tend to become discrete. Quantum
confinement effects.)
• Large investment, e.g. US National Nanotechnology Initiative
starting year 2000
• Development of technology; e.g. current microprocessor
feature size 14 nm ~ 100 atoms across.
• Nanostructured alloys: tailored strength and ductility;
produced by high-energy methods.
• Quantum confinement example: core-shell nanostructures.
• Quantum dots also built on 2DEG structures; coulomb
blockade.
Nanoscale physics
• Development of technology; e.g. current microprocessor
feature size 14 nm ~ 100 atoms across.
Some examples:
-­‐Lithography (electron-­‐beam systems) -­‐Patterning/contacts with Focused Ion Beam (few nm resolution)
-­‐Electron microscopy: now commercially available sub-­‐angstrom; can see atoms.
-­‐Scanning Tunneling Microscopy / Scanning Probe Microscopy (Nobel prize 1986 Binnig, Rohrer); also allows single atom manipulation
Carbon nanotube
IBM; early 90s
Scanning gate microscopy, quantized conductance in 2DEG constriction Westerveld
group Harvard
Nanoscale physics
•
•
•
•
Core-shell dot colors
Can be purchased
commercially, a number of
suppliers
Core of larger bandgap
material often used to protect
dot.
Much interest in
functionalizing for detection
applications etc…
D. Bera et al., Materials (2010), 3, 2260
Figure 7. Experimentally and theoretically determined band-gap as a function size of CdS
Qdots. Broken line: calculated parameters based on effective mass approximation, solid-line:
tight-bondingpcalculation;
Nanoscale hysics squares: experimental data (Reprinted with permission from [60].
Copyright 1991 American Chemical Society). Exciton confinement effects
Compared to the effective mass approximation, the LCAO-MO model provides a methodology to
calculate the electronic structure of much smaller Qdots. In contrast, this method cannot be used to
D. Bera et complexity
al., Materials
3, 2260
calculate the energy levels of large Qdots due to mathematical
and(2010),
limitations
of the
computing systems. Nevertheless, the degree of quantum confinement is determined by the ratio of the
Coulomb Blockade:
• As dot gets smaller, Coulomb charging energy for single electron progressively
larger.
electrons on the dot
0 and 1 and
the electron
numbersmall
can fluctuate
by one.
• Significant issue (and potential impediment)
foris between
integrated
circuits
with
device
Further away from the gate axis (green areas), the large bias (eV
> e /C ) allows
sizes.
for two electrons to tunnel at the same time. In a measurement of the di↵erential
conductance (@I/@V ) as a function of DC-bias V
and gate voltage the border
• May also be a basis for single-electron
transistors, or qubits and related
phenomena.
lines will show up as peaks since this is where the current through the dot changes
bias
2
⌃
bias
and a new transport channel opens/closes (cf. Fig. 5).
Bias Voltage (mV)
30
20
10
0
0
1
2
3
4
-10
-20
-30
-0.95
-0.85
-0.9
Gate Voltage (V)
-0.8
Figure 5: Measurement of Coulomb blockade diamonds in the di↵erential conductance
through a quantum dot. Blue(red) indicate regions of low(high) di↵erential conductance
@I/@Vbias respectively. The second diamond is a bit larger than it’s neighboring ones
indicating that the next orbital level is being occupied. The arrows at the top of the figure
show how the levels are being filled with spins.
Coulomb Blockade:
Lai et al. Scientific Reports 1, 110 (2011)
Spin blockade in double quantum dot.