Transcript PL-sp06-m13-Superconductors

Superconductive Electronics
Lecture Overview
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Superconductors - basic principles
Josephson junctions
Rapid Single-Flux Quantum (RSFQ) circuits
Reversible parametric quantron
Superconducting quantum computers
Principles of Superconductivity
• Fermions & Bosons
• Coherent bosonic systems
• Cooper pairs & BCS theory
Particle Exchange
• Consider a quantum state of two identical particles in
single-particle states x and y, respectively.
– Amplitude given by wavefunction (x,y)
• Imagine any physical process (descibed by a unitary
matrix U) whose effect is just to exchange the locations
of the two particles.
– Because two such swaps gives the identical quantum state,
UU=1 (identity operation),
– One swap U must multiply the state vector by 1.
– There are only two square roots of 1: Namely, 1 and 1.
• Now, what happens if x=y?
Fermions & Bosons
• Fermions are simply those particles such that, when
they are swapped, the state vector is multiplied by 1.
–  (y,x)= (x,y), so if x=y then (y,x) = (x,x) = (x,x)
– But (x,x)(x,x) unless (x,x)=0,
• so, there is always 0 probability for two fermions to be in the same
state x. (Pauli exclusion principle.)
– Examples of some fundamental fermions:
• Electrons, Quarks, Neutrinos
• Bosons are those particles that when swapped, multiply
the state vector by 1.
– The quantum statistics of Bosons turns out actually to give a
statistical preference for them to occupy the same state.
– Examples of some fundamental bosons:
• Photons, W bosons, Gluons
Compound Bosons
• Note that exchanging two identical pairs of
fermions multiplies the state vector by
(1)2 = 1.
•  Two identical systems that each contain an
even number of fermions behave like bosons.
• If they contain an odd number of fermions, they
behave like fermions.
– Protons, Neutrons (3 quarks each) are fermions
– Atoms w. an even number of neutrons are bosons
• n protons + n electrons + 2k neutrons = even # of fermions
= boson
Coherent Bosonic Condensates
• Large numbers of bosons can occupy the same
quantum state and form a large, many-particle
system having a definite quantum state.
• Three (more or less) familiar examples:
– Laser beams - Bosonic condensates of photons.
– Supercurrents - Bosonic condensates of “Cooper
pairs” of conduction electrons.
– Bose-Einstein condensates - E.g. In 1995 Cornell
& Wieman cooled large numbers of 87Rb atoms (37
protons + 50 neutrons + 37 electrons = boson) to a
single quantum state at a temperature of ~20 nK.
History of Superconductivity
• Discovered by Kammerlingh-Onnes in 1911: In
solid mercury below 4.2 K resistance is 0!
– Superconducting loop currents can persist for years.
• Meissner & Oschenfeld discovered in 1933 that
superconductors exclude magnetic fields.
– Induced countercurrent sets up an opposing field.
• Electron-atom interactions shown to be
involved in 1950.
• Bardeen, Cooper, & Schrieffer proposed a
working theory of superconductivity in 1957
– BCS theory.
Electron-Lattice Interactions
• Electron moving through
lattice exerts an attractive
force on nearby + ions.
– Causes a lattice deformation
& local concentration of + charge.
• Positively charged “phonon”
(quantum of lattice distortion)
propagates as particle/wave
in “wake” of electron.
– Later, phonon may be absorbed
by a 2nd electron.
Cooper Pairs
• Two electrons exert a net
attractive force on each
other due to the exchange
of + phonons to which they
are both attracted.
– Repulsive below some distance.
– Typical separation: ~1 m
• Binding energy of pair = ~3kBTc
– Tc is critical superconducting temperature
• Note that phonon exchange doesn’t change total
momentum of pair.
Multiple overlapping pairs
• The lowest-energy state is when
each electron is paired with the
maximum number of neighbors.
• Most favored when all pairs have same total
momentum. - Wavefunctions in phase
• As a result, each electron’s momentum is
“locked” to its neighbors.
– All of the pairs move together.
• 3kBTc energy to break a given Cooper pair.
– This energy not thermally available if T<<Tc.
Josephson Junctions
Insulator (thin)
• Structure very simple:
– Thin insulator between
two superconductors.
• Current-controlled switch:
– Cooper pair wavefunctions
tunnel ballistically
I
through the barrier.
~10Å
Superconductive metal
• below critical current Ic
• Hysteretic I-V curve:
– After current exceeds Ic,
resistance stays “high”
• Till I drops back to 0.
Ic
Device has
built-in
“memory”
1.5 ps switching speed V
Leftovers from Last Lecture
• Most superconducting devices require very low
(<5K temperatures).
– However, “high-temperature” superconductors were
discovered in the 1980’s
• Tc ranging from ~90-130 K (compare 0°C = ~273 K).
• Electron pairing mechanism not well understood
– High-temperature Josephson junctions have also
been proposed
• 77K, liquid-N temp. deemed feasible (Braginski 1991)
• Discussion of BCS mechanism was very
oversimplified
– see van Duzer & Turner for details
Microstrip Transmission Lines
• Nice features:
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Short (ps) waveforms
Near c speeds
Low attenuation & dispersion
Dense layout with low crosstalk
• JJs can be impedance-matched w. TLs
– avoids wave reflection off of junction
– permits ballistic wave transfer
– 10  can be obtained, w. V < 3 mV
• Resistive state P = V2/R < 1 W.
• 100 Mjunctions  100 W?
Overview of JJ Logics
• Voltage-state logics
– IBM project in 1970s
• primarily dealt with magnetically-coupled gates
– Resistor-junction logic families (Japan, 1980s)
• RCJL (Resistor-Coupled Josephson Logic)
• 4JL (four-junction logic)
• MVTL (Modified Variable Threshold Logic)
– also used inductors & magnetic coupling
– These technologies not found to be practical...
• Better: Single-Flux-Quantum (SFQ) logics
– Encode bits using single quanta of magnetic flux!
 V (t ) dt = 0 : h/2qe = ~2 mV·ps
A Simple Element: Current Latch
• Bias current Ib slightly less than JJ critical Ic
• Incoming current pulse Iin(t)
– pushes JJ current over Ic, JJ switches to “off” state
• Part of bias current shunted into output TL
• JJ hysteresis means Iout is latched in high state
Ib < I c
current
Iout
Iin
Iout
(Ic)
Iin
time
How to turn JJ back on?
Overdamped Josephson Junctions
• Place resistor in parallel w. JJ
– Brings junction current back below Ic
when input pulse goes away
– Restores junction back to “on” state
waiting for another pulse
– Iout becomes another pulse similar to
input pulse
• Switching speeds up to 770
GHz have been measured!
current
– Voltage-state JJ logics were
limited to 1 GHz
• Were not competitive with modern CMOS
Iin
time
Iout
Problems w. superconductors
• Typical logic gates complex, hard to understand
– Simpler gates might yet be discovered
• Low temperatures increase total free-energy loss for a
given signal energy dissipated
– E.g. T=5 K: 60x worse than @ 300 K
• Superconducting effect may go away in nanoscale
wires (10 nm or less)
– Cooper pairs too big to fit
– Seems true for metal-based superconductors
– But, other nanoscale structures may take over!
• Superconductivity has been shown @<20K in carbon nanotubes
(Sheng, Tang et al. ‘01)
• Low temperatures imply lower maximum clock
frequencies, by Margolus-Levitin bound.
– E.g., 5 K circuits limited to a 300 GHz average frequency of
nbops