Download Chiral Heat Wave in chiral fluids

Chiral Heat Wave in chiral fluids
(A review of “strange” anomalous transport effects in chiral media)
M. N. Chernodub
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Centre national de la recherche scientifique (CNRS)
University of Tours, France
Topics
(a review-style talk)
Anomalous transport phenomena in chiral fluids and gases.
Dissipationless transfer of charges and energy
Chiral Magnetic Effect (in magnetic field at finite chiral density)
Chiral Separation Effect (in magnetic field at finite fermion density)
Chiral Vortical Effects (in rotating medium at finite densities and temperature)
Transfer of energy (rotating hot system at finite densities and temperature)
Anomalous chiral waves:
Chiral Magnetic Wave
Chiral Vortical Wave
Chiral Alfvén Wave
Chiral Heat Wave
Dissipationless charge transfer: superconductivity
The London equation:
Wikipedia
Ballistic acceleration of the electric current J by the electric field E.
The electric current in a superconducting
wire will flow forever!
Properties:
1) no resistance = no dissipation;
2) superconducting condensate is needed!
Alternative(s) to superconductivity?
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Superconductivity emerges due to the presence of a
condensate of electrons pairs (the Cooper pairs).
The Cooper pairs are quite fragile: thermal fluctuations
destroy them quite effectively. That's why the roomtemperature superconductivity is not observed (yet).
May dissipationless charge transfer exist in the absence
of any kind of condensation? Do we have alternatives?
Yes, we do. The simplest example is
Chiral Magnetic Effect (CME)
The Chiral Magnetic Effect (CME)
Electric current is induced by applied magnetic field:
Spatial inversion (x → - x) symmetry (P-parity):
● Electric current is a vector (parity-even quantity);
● Magnetic field is a pseudovector (parity-odd quantity).
Thus, the CME medium should be parity-odd!
In other words, the spectrum of the medium which
supports the CME should not be invariant under
the spatial inversion transformation.
Non-dissipative nature of the current
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Time inversion:
Ohm conductivity (dissipative, loss of current):
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Superconductivity (non-dissipative, no losses):
Chiral Magnetic Effect (non-dissipative, no losses):
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An example of a parity-odd system?
Consider a massless fermion:
P-parity
Right handed
Left handed
The chirality (left/right) is a conserved number.
How to make a parity-odd system out of fermions?
Systems with equal number
of left- and right-handed
particles are P-invariant.
Examples of P-invariant systems in
the daily life: One right-handed particle
and one left-handed particle with
opposite momenta at IHEP, Beijing.
However, if we have a different number of left- and right-handed
particles (for example, in a gas) then this system is
not P-invariant. If these particles are electrically charged,
then we may expect that this system exhibits the CME:
[A. Vilenkin, '80; K. Fukushima, D. E. Kharzeev, H. J. Warringa, '08;
D. E. Kharzeev, L. D. McLerran and H. J. Warringa, '08]
The CME in quark-gluon plasma
1) The quark-gluon plasma
is created in heavy-ion
collisions (RHIC and LHC).
2) Typical energies of u and d
quarks are so high, that these
quarks may be considered
as massless fermions.
3) The imbalance in chirality is produced due to rapid
topological transitions mediated by QCD sphalerons:
a left quark may turn into a right quark (and vice versa)
due the axial QCD anomaly (→ the CME is “anomalous”)
4) Noncentral collisions create huge magnetic field (1016 Tesla).
The CME in heavy-ion collisions (I)
The induced electric current in the quark-gluon plasma is
proportional to the chiral chemical potential which controls
imbalance between left-handed and right-handed quarks.
[this formula is written for one
fermion with electric charge e]
The CME predicts that there
should be an asymmetric flow
of charged particles along the
normal to the reaction plane.
And such asymmetry was indeed
observed both at RHIC (USA)
and at LHC (Europe)!
J, B
The CME in heavy-ion collisions (II)
Visual picture:
Red: momentum
Blue: spin
Electric charges:
u-quark: q=+2e/3
d-quark: q= - e/3
P-invariant
plasma
of quarks
(and gluons)
Sphaleron
(instanton)
=
topological
charge
Role of topology:
uL → uR
dL → dR
P-odd
plasma
of quarks
(and gluons)
Chiral Magnetic Effect – experiment (Quark Gluon Plasma)
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Signatures of the Chiral Magnetic Effect in heavy-ion collisions
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Chiral Magnetic Effect – experiment (Solid State)
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Signatures of the Chiral Magnetic Effect in Dirac Semimetals
ArXiv:1412.6543
Why the CME is interesting?
1) Because it gives an equilibrium dissipationless current!
(similar to the electric current in superconductivity)
2) Because it exists in an interacting system: interactions cannot
destroy the CME if they do not wash out the chiral imbalance.
3) Because the CME does not need a presence of a condensate.
A) Thus, thermal fluctuations cannot destroy the CME.
B) Thus, the dissipationless electric current may exist at high
temperatures. BTW, the temperature of the quark-gluon
plasma is of the order of 1012 Kelvin (200 MeV and more)
4) … now, an analogue of the CME is under very active search
in condensed matter physics (in Dirac and Weyl semi-metals
discovered this and last years). Why? Because the CME is a
good alternative to the room-temperature superconductivity.
Examples of anomalous transport effects (I)
1) Chiral Magnetic Effect – the electric current is induced in
the direction of the magnetic field due to the chiral imbalance:
[all formulae are written
for one flavor of fermions]
2) Chiral Separation Effect – the axial current is induced in
the direction of the magnetic field:
Notes:
A) This effect is realized even if the plasma is chirally-trivial.
B) is the quark chemical potential (the plasma is dense)
C) The axial (chiral) current = the difference “right current”–“left current”.
Examples of anomalous transport effects (II)
3) Chiral Vortical Effect – the axial current is induced
in the rotating quark-gluon plasma along the axis of rotation:
angular velocity (vorticity)
4) Dissipationless energy transfer – the energy flow is
generated along the axis of magnetic field:
Energy current:
Note: All these effects will become more complicated (much richer) in a rotating,
chirally-imbalanced dense matter subjected to background magnetic fields.
Chiral Waves
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The chiral waves are massless excitations in the fluid
or plasma of chiral fermions.
There are four types of waves (disclaimer: status of August 18, 2015)
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Chiral Magnetic Wave (Dec '10) – reviewed in details
Chiral Vortical Wave (Apr '15) – reviewed
Chiral Alfvén Wave (May '15) – not covered, but interesting
Chiral Heat Wave (Aug '15, to appear) – discussed
These sound-like excitations correspond to coherent
propagation of charge density, axial (chiral) charge density,
and energy density waves in different combinations.
Chiral Magnetic Wave: currents and chemical potentials
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Chiral fluid/plasma (massless fermions of both chiralities)
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Currents:
vector
axial
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Right-handed and left-handed currents:
Chemical potentials:
vector
axial
Chiral Magnetic Wave: currents and density fluctuations
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Anomalous transport laws:
chiral magnetic effect
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chiral separation effect
Consider a neutral chiral system:
→ on average, all densities are zero
→ globally, all chemical potentials are zero
… but local fluctuations of densities may exist:
Magnetic Wave: couple densities and chemical potentials
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Anomalous transport laws:
What are these chemical potentials?
It is better to work with densities rather than with chemical potentials!
For small perturbations:
“susceptibility” (calculable)
Chiral Magnetic Wave: couple currents and densities
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Combine:
and
with the result:
Axial density induces vector current.
Vector density induces axial current.
Question: Are they married chained to each other?
Chiral Magnetic Wave: two current-density relations
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Anomalous current-density relation:
vector current
axial density
axial current
vector density
magnetic field B
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Usual current-density relation (conservation of charge):
[We do not consider external
electric field so that we have
no anomaly for the axial current.]
Chiral Magnetic Wave: relations between all densities
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Anomalous current-density relation
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Let B be along the z-axis, B=(0,0,B):
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Charge conservation:
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Exclude currents:
Chiral Magnetic Wave – wave equations
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Relations between densities:
Two first-order equations for two variables.
● Diagonalize them and get second order equations:
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Sound-like (“gapless”) wave propagation with velocity
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This is Chiral Magnetic Wave
Chiral Magnetic Wave – physical picture
(1) fluctuation in axial density
(2) creates fluctuation in vector current
magnetic field B
(3) which induces vector density
fluctuation at the next point
(4) which creates fluctuation
of the vector current
(5=1) which generates fluctuation
of the axial density at the next point
(6=2) creates fluctuation in vector current
(7=3) etc etc etc.
The Chiral Magnetic Wave is a chain-like process.
Chiral Magnetic Wave – velocity
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The wave propagates with velocity:
At weak magnetic field c is constant.
● At arbitrary field strength:
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Chiral Magnetic Wave – experiment
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Signatures of the Chiral Magnetic Wave in heavy-ion collisions
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Chiral Magnetic Wave – simplest signatures
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Can we see (“feel”) the existence of the Wave just from
anomalous relations without making all those steps?
Yes, we see the wave just from anomalous transport laws:
Signature: linear cross-coupling of chemical potentials
and the corresponding currents
In this particular example:
Vector current – Axial chemical potential
Axial current – Vector chemical potential
Other waves?
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We just discussed vector and axial currents for chiral fermions
in the background of magnetic field:
There are also anomalous effects due to rotation! Our plan:
➔ Switch off magnetic field, B = 0.
➔ Rotate the fluid or gas of chiral fermions!
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Anomalous currents in a rotating system:
Chiral Vortical Wave – feeling of existence
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Non-zero density, zero temperature, no magnetic field, rotation:
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Here we use d explicitly to stress that we have fluctuations.
➔ Coupling between vector/axial currents/densities!
➔ Chiral Vortical Wave!
Chiral Vortical Wave – physical picture
(1) fluctuation in axial density
(2) creates fluctuation in vector current
angular velocity W
(3) which induces vector density
fluctuation at the next point
(4) which creates fluctuation
of the vector current
(5=1) which generates fluctuation
of the axial density at the next point
(6=2) creates fluctuation in vector current
(7=3) etc etc etc.
The Chiral Vortical Wave is also a chain-like process.
Chiral Vortical Wave – results
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Velocity of wave propagation depends on angular velocity W:
ArXiv:1504.03201
Chiral Heat Wave – anomalous transport for energy
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Dissipationless energy transfer flow (energy current):
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Energy flow is defined by the stress-energy tensor:
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Anomalous conductivities:
Temperature
fluctuations:
We must consider
thermal fluctuations!
Chiral Heat Wave – finding its traces
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Finite temperature, zero density, no magnetic field, rotation:
fluctuations in vector (electric) current are negligible
fluctuations in axial current depend on temperature
fluctuations
fluctuations in energy (thermal) current depend
on fluctuations of the axial charge
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Conclusion: axial charge density and energy density are
together, the vector charge should leave does not participate
We have a wave of axial charge density and energy density!
Chiral Heat Wave
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Coupled axial and energy fluctuations:
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Sound waves of axial charge density and energy density:
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Velocity of propagation:
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This is Chiral Heat Wave (M.Ch., to appear soon)
Chiral Heat Wave – physical picture
(1) fluctuation in axial density
(2) creates fluctuation in energy flow (in energy current)
angular velocity W
(3) which induces thermal energy (4) which creates fluctuation
fluctuation (increase in
of the axial current
temperature) at the next point
(5=1) which generates fluctuation
of the axial density at the next point
(6=2) creates fluctuation in energy flow
(7=3) etc etc etc.
The Chiral Heat Wave is again a chain-like process.
Summary 1: anomalous transport
Chiral fermions form systems which exhibit various
dissipationless transport phenomena in equilibrium:
A) Chiral Magnetic Effect:
generation of the electric current by magnetic field
B) Chiral Separation Effect:
generation of the axial current by magnetic field
C) Chiral Vortical Effects: generation of the vector and
axial currents in rotating plasma
C) Energy flow in rotating plasma and in magnetic field
background
Summary 2: chiral waves
The same systems possess various massless excitations:
A) Chiral Magnetic Wave: coherent sound-like
propagation of vector and axial densities along
the axis of magnetic field
B) Chiral Vortical Wave: vector-axial density propagation
along the axis of rotation of the fluid
C) Chiral Heat Wave: axial-energy density waves
in rotating plasma
D) These waves may mix and lead to common
vector-axial-energy waves (not discussed in the talk)
Summary 3: experiment and applications
Some of these effects are already seen in:
1) High energy physics: heavy-Ion collisions (RHIC/LHC)
2) Solid state physics: Dirac semimetals
3) Our pocket: probably, consumer electronics in N years.
Intrinsic chiral magnetic effect in
Dirac semimetals
M. A. Zubkov
Institute of Theoretical and Experimental Physics, Moscow,
and Centre national de la recherche scientifique (CNRS)
University of Tours, France
M. N. Chernodub
CNRS, University of Tours, France
Arxiv:1508.03114
Previous Summary 3: experiment and applications
Some of the anomalous transport effects were seen in:
1) High energy physics: heavy-Ion collisions (RHIC/LHC)
2) Solid state physics: Weyl and Dirac semimetals
Soon: probably, consumer electronics in N years.
Very important!
What are Weyl and Dirac Semimetals?
Simplest ways to think about these materials:
1) A three-dimensional crystal which possesses
fermion quasiparticles in the electronic spectrum.
2) There are right-handed and left-handed quasiparticles.
3) The quasiparticles are electrically charged.
4) A three-dimensional version of graphene.
5) A very distant similarity to quark-gluon plasma
(light quarks are nearly massless particles
compared to their energies).
Semimetals: real crystal materials
ArXiv:1503.01304
ArXiv:1503.09188
1mm – 1 cm
● Good crystals
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Chiral fermionic quasiparticles
Energy spectrum of a Weyl semimetal
Energy
ArXiv:1503.09188
TaAs
Momentum
ArXiv:1503.01304
Dirac semimetal
ZrTe 5
ArXiv:1412.6543
Illustration: Chiral Magnetic Effect in a semimetal 1
Following ArXiv:1412.6543:
Illustration: Chiral Magnetic Effect in a semimetal 2
Consider a gas of free chiral fermions. The chiral density is
chiral chemical potential
temperature
usual chemical potential
velocity of fermions (“speed of light” for the fermion excitations) = Fermi velocity (v = c/300)
Evolution of chiral density (anomaly, the ideal case):
coming from the standard expression:
Following ArXiv:1412.6543
Illustration: Chiral Magnetic Effect in a semimetal 3
Evolution of chiral density (the real case):
axial anomaly
Equilibrium:
decay of chiral charge through
chirality-changing transitions
(expressed via the relaxation time)
equilibrium chiral density: the decay rate and production rate are the same:
Following ArXiv:1412.6543
Illustration: Chiral Magnetic Effect in a semimetal 4
Equilibrium chiral density:
from
and
small
Chiral Magnetic Effect:
Following ArXiv:1412.6543
Illustration: Chiral Magnetic Effect in a semimetal 5
Contribution to the current from anomaly and from the
Chiral Magnetic Effect:
Contribution to total conductivity depends on direction and
strength of magnetic field:
Experimentally measured, confirmed!
Following ArXiv:1412.6543
Dislocation in semimetals
The crystals of semimetals are not perfect, they may have
defects which are called “dislocations”
screw dislocation
edge dislocation
Burgers vector b: gives shifts of the atomic layers at the dislocation;
it is a constant vector for each dislocation
Intrinsic magnetic flux at a dislocation
Fermionic quasiparticles feel the dislocations as:
1) gravity (small for typical dislocations, ignore it)
2) magnetic field (large, we take it into account)
Total flux of the effective magnetic field:
total flux
Burgers vector (characterizes
the strength of the dislocation)
distance between Dirac nodes
in momentum space
internal, crystal-specific
parameter
direction of the dislocation
Fermion zero mode at the dislocation
Each dislocation carries a fermion zero mode which is
1) bound to the dislocation
2) propagates along the dislocation
3) has zero mass
4) appears due to magnetic flux
induced by the dislocation
Similar to a superconducting cosmic string.
Intrinsic Chiral Magnetic Effect (idea)
Each dislocation carries the magnetic flux.
So, we do not need an external magnetic flux for
1) anomaly
external (voltage)
intrinsic (internal, due to dislocation)
2) Chiral Magnetic Effect:
Thus, the external electric field generates anomalous
current at the dislocation: “Intrinsic Chiral Magnetic Effect”
Intrinsic Chiral Magnetic Effect (estimations)
Generation of the current due to anomalous processes at
the dislocation in the presence of external electric field:
E
anomalous contribution due
to dislocation (absent, if the
electric field is perpendicular
to the dislocation)
usual Ohm conductivity
Estimations:
Conclusions
1. Dislocations in the crystal structures of Dirac
semimetals carry effective magnetic field.
2. Dislocations behave as strings with magnetic flux.
3. In external electric field the effective magnetic field
leads to the axial anomaly, and generates a chiral
charge density around the dislocation.
4. Then, an intrinsic magnetic field of the dislocation
leads to an intrinsic Chiral Magnetic Effect which
generates an electric current along the dislocation.
5. The Intrinsic Chiral Magnetic Effect is proposed to be
experimentally measured in Dirac semimetals.