# Presentation: 014193

##  or how to measure a single electron spinIvar Martin                                                        				   

***April  2006,***
***Los Alamos***

*This work is supported by the DOE and NSF *

**Single Spin Magnetic Resonance and Related **
**Phenomena in Si Field Effect Transistors  **

## Collaborators

*D. Mozyrsky (T-4)*
*M. Hastings (T-13)*
*A. Shnirman (Karlsruhe)*
*Experiment: H.W. Jiang’s group at UCLA*

- REFS:* **	**Phys. Rev. Lett. ***90**, 018301 (2003) 	- 	ESR - theoretical scheme
*	**Phys. Rev. Lett.* **91**, 078301 (2003) 	- 	experiment (B-dep)
- 	*Nature* **430**, 435 (2004)		- 	experiment (1 spin ESR)
*	**Phys. Rev. B* **71**, 165115 (2005) 		-	Kondo + lattice
- 	cond-mat/0312503 			- 	Fermi-edge + lattice
- 	*Phys. Rev. B ****73****, 035104 (2006)*  		-	polaronic molecular switch

## T-11 context(Balatsky, Bulaevskii, Martin, Ortiz, Smith)

*T-11 context**(Balatsky, Bulaevskii, Martin, Ortiz, Smith)*

*Physics of quantum computing*
*Qubit-meter interaction*
*Modeling environment influence*
*Nano-electromechanical systems*
*Sensitive measurement (quantum limited)*
*Ground-state cooling*
*Quantum-classical crossover*
*Inelastic noise spectroscopy*
*ESR-STM *
*DNA sequencing by STM*
*Spintronics*
*Local probes*

- TLS

- bath

## Outline

*Introduction: Single Spin Magnetic Resonance*
*Random Telegraph Noise in Field Effect Transistors*
*A scheme for Electron Spin Resonance: Theory*
*A scheme for Electron Spin Resonance: Experiment*
*Single Spin Detection *
*Inconsistency between expected and observed tunneling rates: Polaronic slowdown*
*Low temperature magnetic anomalies: Possible Kondo Effect*
*Summary and Open problems    *

## Applications of Spin measurement

- Magnetic Resonance Imaging
- (MRI)

- Spin – Effect Devices (Spin Transistors)

- Quantum Computing

- > 1010 spins

- > 103 spins

- 1 spin

## Electron Spin Resonance

- B0

**Ћ****ω****0 ****= g****μ****B****B****0**

## Single Spin Resonance: MRFM and Paramagnetic Traps in FETs 

- Rugar, Budakian, Mamin & Chui,
**Nature** **430**, 329 (2004)

- Magnetic Resonance Force
- 	Microscopy (MRFM)

- Electron Spin Resonance in a
- Field Effect Transistor (FET)

- Xiao, Martin, Yablonovitch & Jiang,
**Nature 430**, 435 (2004)

## Traps in Field Effect Transistors and Random Telegraph Signals 

- Vg>0

*I *> 0

- Field Effect Transistor (FET)

## Random Telegraph Signal (RTS) – experiment

- source-drain current

- Defects at Si - SiO2
- interface

## A Setup for Electron Spin Resonance(ESR) 

- At *T* = 0, *B*1 =0:
-      trap is filled if 	1/2 < 
-       trap is empty if 	1/2 > 

- No RTS

- At *T* = 0 and resonant *B*1(*t*):
-      trap can be filled if 	-1/2 < 
- e- is promoted1/2 -> -1/2
-       e- can escape if       	1/2 > 

- The trap occupation number is *modified* by resonant *B**1**(t)*

**trap**

## Quantum rate equations for ESR-RTS

*h.c.*

-  – rotating wave approx

- equations of motion
- for trap density matrix

- Average FET channel resistivity:

*I. Martin, D. Mozyrsky & H.-W.Jiang, Phys. Rev. Lett.* **90**, 018301 (2003)

## Resonance in average resistance

*t*

***e*

***f*

- Application of resonant rf *B*1(*t*) modifies the average channel resistivity by changing the RTS ***statistics***

- In presence of dephasing 1/*T*2’ >> 
- peak width:
-   peak height:

- 0

## ESR-RTS Experiment –averagecurrent (M. Xiao et al., Nature 430, 435, 2004)

- g = 2.02

## Traps for Quantum Computing A Readout Scheme

- |Ψ> = 0

**1.**

**Notes:**
The scheme is based on a possibility to shift  relative positions of energy levels and therefore is realizable in systems with electrostatic gates, such as quantum dots, FET, etc.  

## Single Spin Measurement in Quantum Dots

- Demonstrated Spin Measurement Efficiency ~ 65%

*Elzerman et al., Nature ****431****, 430 (2004)*

## The Readout Scheme: Experimental Facts

- The scheme works in quantum dots with 65% efficiency
- REF: J.M. Elzerman *etal.,* Nature **430**, 431(2004).

*So far in FET traps the scheme does not work – no RTS signal *
*WHY?** => spin is always in its ground state.*
*          **WHY? **=> fast spin relaxation => **WHY?*

*Maybe because of the exchange interaction with electrons*
*in the conduction channel ?! *
*Need to look at the microscopic structure of traps!*

## Outline

*Introduction: Single Spin Magnetic Resonance*
*Random Telegraph Noise in Field Effect Transistors*
*A scheme for Electron Spin Resonance: Theory*
*A scheme for Electron Spin Resonance: Experiment*
*Single spin Detection *
*Inconsistency between expected and observed tunneling rates: Polaronic slowdown*
*Low temperature magnetic anomalies: Possible Kondo Effect*
*Summary and Open problems*

## Determination of Defect’s Position. Surprise...

*Experimentalists can measure the location of the trap (x) with respect to the conduction channel. *
_*One finds x~1-3 Å.*_
*	**	**	** *

*Defect position determination:*

- Estimate for tunneling time yields ~ (ps – ns)

**Observed***** *****~ (ms – s) ****??? **

## Polaronic Slowdown 

- SiO2 is a polar crystal  strong coupling to optical phonons

**Empty Trap**

**Trap with an extra electron**

- 2DEG

- SiO2

## Estimate for Si Field Effect Transistor

*Estimate for Si Field Effect Transistor*

*Mozyrsky, Martin, Shnirman cond-mat/0312503 *

## Outline

*Introduction: Single Spin Magnetic Resonance*
*Random Telegraph Noise in Field Effect Transistors*
*A scheme for Electron Spin Resonance: Theory*
*A scheme for Electron Spin Resonance: Experiment*
*Single Spin Detection *
*Inconsistency between expected and observed tunneling rates: Polaronic slowdown*
*Low temperature magnetic anomalies: Possible Kondo Effect*
*Summary and Open problems*

## Magnetic field dependenceat low temperatures. Surprise II

*No agreement between simple model *
*and experiment at low T!**     *
***Kondo effect?***

- For a paramagnetic spin
- (τempty/τfull) ≈ exp(gμBB / kBT)

- gμBB

- μ

- B

- trap

- channel

## Kondo Effect

**Resistivity of metals doped with magnetic impurities **

**Magnetic impurity in a metal**

- A localized impurity spin is screened by spins of conduction electrons

- At low energy scale (below TK) the magnetic impurity creates a strong
- resonance at Fermi surface  => scattering => resistivity

## Kondo?

- TK ~ exp[-O(1) U/Γ ]

- For Γ ~ 1 s-1  => TK  0

- However, Γ is small only effectively – due to
- strong electron-lattice coupling! The “bare”
- hybridization (“bare” Γ0) may be strong!

- Large bare   relevant for Kondo if U > 0  finite TK

## Summary and Perspectives

***Single electron spin resonance in FET***
***Tunneling slowdown (due to strong electron-lattice coupling)***
***Kondo Effect in FET traps***

**What’s next?**

**A single nuclear spin?...**