Theory of Slow NonEquilibrium Relaxation in Amorphous Solids at Low Temperature

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Theory of Slow Non-Equilibrium Relaxation in
Amorphous Solids at Low Temperature

• Alexander Burin
• Tulane, Chemistry

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Outline

• Experimental background and theory goals
• Pseudo-gap in the density of states (D.o.S.)
• Break of equilibrium and induced changes in
  D.o.S.
• Non-equilibrium dielectric constant and hopping
  conductivity within the TLS model
• Conclusions
• Other mechanisms of non-equilibrium dynamics

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Experimental background
EDC

ln(t)
??
??
Osheroff and coworkers (1993-2007)
??
ln(t)
Ovadyahu and coworkers (1990-2007), Grenet and
coworkers (2000-2007), Popovich and coworkers
(2005-2007)
??
ln(t)
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Goals

• Interpret experimental observations in terms of
  the non-equilibrium raise of the density of
  states of relevant excitations (TLS or conducting
  electrons) with its subsequent slow relaxation
  backwards
• The changes in the density of states are
  associated with the Coulomb gap effects induced
  by TLS TLS or TLS electron long-range
  interactions

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Non-equilibrium dynamics
External force raises density of states for
relevant excitations
Slow relaxation lowers D. o. S. back to
equilibrium
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Case of study TLS in glasses(Burin, 1995)
Two interacting TLS
Correction to the density of states (single TLS
excitations)
No interaction
With interaction
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Correction to TLS D. o. S.
No interaction
With interaction
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Change in D. o. S.
U12gtgtT ?
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Explanation of D. o. S. reduction (Efros,
Shklovskii, 1975)
E1E
E2?2
E12E?2-U12
0lt?2ltU12-E? Instability PIg0(U12-E),
?P -PPI
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Total correction to the D. o. S.
This correction should be averaged over TLS
statistics (Anderson, Halperin, Warma Phillips,
1972)
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Average correction to the D. o. S.
Since P0U010-3 we have ?P ltlt P.
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Change in D. o. S due to external DC field
application
Energy shift ?E -?FDC/?, ?3D, FDC10MV/cm,
?E7K gtgt TOnly TLS with Elt?E can be removed out
of equilibrium
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Time dependent D. o. S.
At time t only slow TLSs contributes
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Calculation of dielectric constant(adiabatic
response at low temperature)
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Non-equilibrium dielectric constant
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Non-equilibrium conductivity(Burin, Kozub,
Galperin, Vinokur, 2007)
EF
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Variable range hopping

• Defined by charges with energy ?hgtT (?hTa,
  a3/4, Mott a1/2, Efros, Shklovskii)
• Hopping to the distances rh1/(g?h)1/d (d
  problem dimension)
• Conductivity can be approximated as

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Non-equilibrium D. o. S. and conductivity
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Comparison with experiment

• Change in conductivity (logarithmic relaxation
  rate)

Estimate agrees with experiment !
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Width of the cusp VG
Estimate agrees with the experiment! (Vaknin,
Ovadyahu, Pollak, 2002)
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Suggestion

• Investigate glassy properties in related
  materials, i. e. temperature dependence of sound
  velocity and/or sound attenuation and dielectric
  constant temperature dependence at Tlt1K.

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Conclusions

• TLS model can be used to interpret
  non-equilibrium relaxation in glasses and doped
  semiconductors
• The non-equilibrium relaxation is associated with
  the evolution of the density of states affected
  by the long range interaction (Coulomb or
  dipolar gap)

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Acknowledgement

• Support by Louisiana Board of Regents, contract
  no. LEQSF (2005-08)-RD-A-29)
• Tulane University Research and Enhancement Funds
• To organizers of this extraordinary workshop for
  inviting me

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Interaction unrelated non-equilibrium dielectric
constant (Yu and coworkers, 1994 Burin 1995)
Theory predicts a huge non-equilibrium effect
comparable to the equilibrium one
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Time dependence
Power law relaxation is associated with
interaction stimulated dynamics (Burin, Kagan,
1994) only so one can study it. Better materials
are those which have no nuclear quadrupole, i. e.
mylar.