Magnetooscillations in Underdoped Cuprates Must be understood within the framework of the other universal properties in the phase-diagram of Cuprates.

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Nov 10, 2013 (3 years and 9 months ago)

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Magneto
-
oscillations in Underdoped Cuprates


Must be understood within the framework of
the other universal properties in the phase-diagram
of Cuprates.

Aim of this talk: To do this and in particular to
reconcile the observed oscillations with
deductions from ARPES about a state with “fermi-arcs”
shrinking with decreasing temperature,

and

To suggest unique predictions for experiments to
distinguish different possibilites.

Fermi liquid
T
x (doping)
QCP
I
II
SC
III
A
F
M
“Pseudo-
Gapped”
Marginal Fermi-
Liquid
Schematic Universal phase diagram of high-
T
c

superconductors
CMV- Los Alamos Proc-93, PRB-97.
The Framework
Essential organizing feature is the Quantum Critical point,
consistent with a change of symmetry at the line T*(x).
T*
?
Magneto-oscillations:
Prima-facie, it is not possible to get the
change observed between overdoped
and underdoped without a change of
symmetry between the two.
So what is this change in symmetry?
Change of Translational symmetry due to
CDW, SDW, DDW, STRIPES,....
can be ruled out, because
1. Not seen or not universally seen in direct experiments.
2. Do not explain observed properties
of the phase diagram.

III
T
x
I
II
S
A
F
T*
The only observed Change of Symmetry at T*(x) in four
different families of Cuprates is broken T and Inversion
without changing Translations. Its QC-fluctuations give the
MFL in Region I and promote d-wave pairing.
Four fermi-point ground state
in the state with
loop-current order state suggested in PRL ’99.
1. Only thing which makes sense with the ARPES
results which see a Fermi-surface ‘arc’ whose
length decreases with temperature, and with
2. Thermodynamic data.
3. Argument and a calculation which suggests that
the normal Fermi-surface cannot be stable with
a loop-current ordered state.
I will not discuss this argument but instead show how
such a state has magneto-oscillations periodic in 1/B
with period of the right order of magnitude and show that
some properties, discoverable by new experiments, differ
dramatically from the case of changed translational symmetry.
“Fermi-Arcs” in ARPES
: peak in spectral function does not reach
the chemical potential for any k in any angle except for T  T*(x).
shrinks with temperature: Consistent with T dependence of
specific heat and magnetic susceptibility below T*(x).
!
!
Norman et al.,
Damascelli et al.
Fermi-arcs make sense only if the ground state has
four Fermi-points with a gap at chemical potential.
For T  O( ), finite width gives the “Fermi-arc”
Kanigel et al. (2006) plotted the angle of the “Fermi-arc” for
5 different x of underdoped BISCCO to find scaling of the
angle of the arc with F(T/T*(x)) and extrapolation to 0 for
T to 0.
D
(
!
)
D
(
!
)
Kanigel et al. (2006)
Zhu and cmv (2006)
based on cmv (1999).
Damascelli et al. (2007): A sample of underdoped YBaCuO shows similar results.
M
State with Four Fermi-points:
Gap at the chemical potential, Density of
states near chemical potential varies as
N
(
E
)
!
E
!
,
!
"
= 0
.
!
= 1
/
2
proposed.
Does such a state have magneto-oscillations periodic in 1/B?
Let us look at Graphene which has
N
(
E
)
!
E,i.e.
!
= 1
Some constant
energy contours
near chem. pot.
Magneto-oscillations in Graphene: periodic in 1/B
Zhang et al. , Nature Physics ‘05
E
k
=
±
v
0
|
k
!
k
F
|
;
N
(
E
)
!
E
Energy of Landau levels :
E
n
!
±|
n
|
1
/
2
B
1
/
2
.
; Nernst Effect in Graphene!
Jiang et al. PRL ‘07
How can one tell by experiments that
while magneto oscillations are periodic in 1/B?
E
n
!
±|
n
|
1
/
2
B
1
/
2
.
Infrared Absorption in a field has resonances separated
by multiples of B(1/2).
Physics of magneto-oscillations when the
H0 density of states varies.
The degeneracy of any LL is fixed by quantization
condition to be
This is enough to make oscillations periodic in
1/B with a correction of O( ).
cmv(preprint)
B/
!
0
,
!
0
=
ch/e,the flux quantum.
!
B/B
I have calculated the oscillations for underdoped cuprate using
magnitude of pseudogap to deduce N(E) for B0.
Period too large by a factor of about 4 if planes alone are
included. About right when chains are included. Sign of Hall?
An important differences from the case of Graphene:
no closed orbits at constant energy near chem.-potl. for B0.
Predictions for future Experiments in a magnetic field:
1. Infrared absorption in a magnetic field: Peaks should
not be separated proportional to B.
Weaker prediction: Separation  B(2/3).
2. No oscillations if experiments are done at constant
chem. potential  0.
3. Oscillation period larger in crystals without chains.
4. Weak variation of period of oscillations with B:
Estimate at around B  50 T, 10% variation in
period for change of B by a factor of 2.
Please see preprint for how these predictions are arrived at.
Summary
:

III
T
x
I
II
S
A
F
Magneto-oscillations in Underdoped Cuprates

Must be understood within the framework of
the other universal properties in the phase-diagram
of Cuprates.
The variation of the oscilaltions across xx_c
consistent only with a change of symmetry.
A pseudogap state with four fermi-point ground state,
as inferred from ARPES does produce the magneto-
osc. periodic in 1/B.
Such a state is not definitely established. But the
proposed experiments can do so.
Such a state joins the list of new concepts introduced
into Physics by the cuprates because a gap tied to the
chemical potential without changing trans. symmetry
or superconductivity in a pure system is not
something we have seen before.