Magneto

oscillations in Underdoped Cuprates
Must be understood within the framework of
the other universal properties in the phasediagram
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 “fermiarcs”
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 Proc93, PRB97.
The Framework
Essential organizing feature is the Quantum Critical point,
consistent with a change of symmetry at the line T*(x).
T*
?
Magnetooscillations:
Primafacie, 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 QCﬂuctuations give the
MFL in Region I and promote dwave pairing.
Four fermipoint ground state
in the state with
loopcurrent order state suggested in PRL ’99.
1. Only thing which makes sense with the ARPES
results which see a Fermisurface ‘arc’ whose
length decreases with temperature, and with
2. Thermodynamic data.
3. Argument and a calculation which suggests that
the normal Fermisurface cannot be stable with
a loopcurrent ordered state.
I will not discuss this argument but instead show how
such a state has magnetooscillations 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.
“FermiArcs” 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.
Fermiarcs make sense only if the ground state has
four Fermipoints with a gap at chemical potential.
For T O( ), ﬁnite width gives the “Fermiarc”
Kanigel et al. (2006) plotted the angle of the “Fermiarc” 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 Fermipoints:
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 magnetooscillations periodic in 1/B?
Let us look at Graphene which has
N
(
E
)
!
E,i.e.
!
= 1
Some constant
energy contours
near chem. pot.
Magnetooscillations 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 magnetooscillations when the
H0 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 B0.
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 B0.
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
Magnetooscillations in Underdoped Cuprates
Must be understood within the framework of
the other universal properties in the phasediagram
of Cuprates.
The variation of the oscilaltions across xx_c
consistent only with a change of symmetry.
A pseudogap state with four fermipoint 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.
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