Electron transport over superconductor hopping insulator interface
This presentation is the property of its rightful owner.
Sponsored Links
1 / 20

Electron Transport over Superconductor - Hopping Insulator Interface PowerPoint PPT Presentation


  • 71 Views
  • Uploaded on
  • Presentation posted in: General

Electron Transport over Superconductor - Hopping Insulator Interface. A surprising and delicate interference-like cancellation phenomenon. Martin Kirkengen, Joakim Bergli, Yuri Galperin. Structure of presentation. Model presentation/the physics

Download Presentation

Electron Transport over Superconductor - Hopping Insulator Interface

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Electron transport over superconductor hopping insulator interface

Electron Transport over Superconductor -Hopping Insulator Interface

A surprising and delicate interference-like cancellation phenomenon

Martin Kirkengen, Joakim Bergli, Yuri Galperin


Structure of presentation

Structure of presentation

  • Model presentation/the physics

  • Results: what was expected, and what was not expected at all...

  • Origin of unexpected cancellations

  • Robustness of cancellations, three different attempts to avoid them

  • Relevance of problem and results


The model

The Model

SC

TB

HI

  • SC: Superconductor

  • TB: Tunneling Barrier

  • HI: Hopping Insulator

Typical situation: studying a hopping insulator using superconducting contacts


Superconductor

Superconductor

  • Cooper pairs – electrons dancing the Viennese Waltz

  • Energy gap D prevents single electron transport if D > kBT and D >eV

  • Coherence length, x

  • Fermi wave number, kF

  • Anomalous Greens Function:


Tunneling barrier

Tunneling Barrier

  • E.g. Shottky Barrier, due to band bending

  • Simplest case:- electrons enter and exit at same position- constant thickness&height

  • Various variations will be considered

SC

TB

HI


Hopping insulator

Hopping Insulator

  • Localized electron states centered on impurities (surface states are ignored)

  • Electrons may ”hop” between impurities

  • Hydrogen-like wavefunctions, but with radius a>>aH

  • IMPORTANT QUANTITY: kFa ~ 100

  • Resistance in insulator lower than in barrier

  • Greens Function:


Theoretical approach for the specially interested

Theoretical approach(for the specially interested)

  • Kubo Linear Response TheoryC=[H,I]/E

  • Hamiltonian: H = I A

  • Greens function formalism

  • Matsubara technique

  • Loads of contractions, complex integrations, Fourier transforms, analytical continuations +++

  • Following Kozub, Zyuzin, Galperin, VinokurPhys. Rev. Letters 96, 107004 (2006)


The problem

The Problem

  • What is the conductivity of such a barrier, if this is the dominant channel?

SC

TB

HI


Expected behaviour

Expected Behaviour

  • Transport function of distance (z) of impurities from barrier, e-z/a

  • Sufficient active impurities will allow us to ignore surface states’ contribution to transport

  • Maximum distance between contributing impurities limited by coherence length

  • Some fluctuation due to sin(kFr) from superconductor Greens function


Found behaviour

Found Behaviour

  • Maximum distance between contributing impurities limited by coherence length

  • Some fluctuation due to sin(kFr) from superconductor propagator

  • BUT:Transport determined by distance (z) of impurities from barrier as e-kFz , not e-z/a!

  • Only states VERY NEAR surface can contribute.


Where the error occured

Where the Error Occured...

  • Two sin(kFr) from the SC Greens function

  • Replaced by average of sin2(kFr) when integrated over space.

  • Integration extremely sensitive to phase


The essential integral

The Essential Integral

  • Positive area:

  • Negative area:

=

TB

HI

SC

HI

z=a, kFa=100

152.6689693731328496919146125035145839725143192401392

-152.6689693731328496919146125035145839725143192027575


How to kill cancellations

How to kill cancellations...

  • Effect of finite width of barrier

  • Different impurity wave function

  • Strong barrier fluctuations

  • Weak barrier fluctuations


Perfect barrier directional sensitivity

Perfect Barrier – Directional Sensitivity

  • Allow entry/exit coordinates to differ – Reduced transverse component of momentum

  • Integration over TB/HI-interface introduces polynomial correction to impurity wave function seen from SC/TB-interface

  • Essential behaviour remains e-kFz

SC

TB

HI


Importance of impurity shape

Importance of Impurity Shape

  • Square potential – hydrogen-like wave function: Strong cancellations, e-kFz

  • Parabolic potential – gaussian wave function: No cancellations, back to e-z/a


Deep barrier minimum

Deep Barrier Minimum

  • Gaussian behaviour near barrier minimum

  • Barrier variation rather than impurity variation determines transport

  • Back to e-z/a

Localisation length under barrier

TB

SC

HI

a


Shallow barrier minimum

SC

TB

HI

d

a

Shallow Barrier Minimum

  • r<a, positive accumulation

  • R>a, negative accumulation

  • Assume barrier T+ dq(r-a)

  • One part proportional to Te-kFz

  • Other part proportional tode-z/a


Conclusions barriers and conduction

Conclusions Barriers and Conduction

Hydrogen-like

Gaussian

Perfect barrier

VERY LOW (e-ka)

NORMAL

Deep minimum (of width ’w’)

LOW (w/a)

LOW (w/a)

Shallow minimumof length ’a’

LOW (d/T)

NORMAL


Macroscopic consequences

Macroscopic Consequences

  • Impurity pairs where barrier defects allow transport will dominate

  • Number of active impurities << total number of impurities

  • Surface states can maybe be ignored after all...


Possible relevance the quantum entangler

Possible Relevance – The Quantum Entangler

  • Idea – a Cooper pair is split, with one electron going to each electrode, their spins being entangled.

  • Choice of fabrication metod for quantum dots may be essential for success.

QD

SC

TB

I

QD


  • Login