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---+ Lab Assignment: Quantized Conductance Lab

Quantum mechanics states that electrons behave like waves. Howver, in macroscopic systems, we rarely observe their wavelike properties. For example, the electron transport in bulk metal can be well-expalined by the classical [[https://en.wikipedia.org/wiki/Drude_model][Drude's model]]. As the system becomes smaller and the temperature goes down, Drude’s model no longer explains the electronic transport. the wave properties of electroan appear.

In this lab, you will explore the phenomena of quantized conductance in a gold quantum point contact repeatedly created at room temperature. From the experiment, you will understand the importance of quantum mechanics at the nanoscale. You will also learn the typical electrical characterization techniques in condensed matter Physics and nano science fields.
---++ Theory

Please read the references(see the three attachments at the bottom of this page) to understand the quantized conductance through classical Physics (Drude model) and Quantum Physics.

Quantum conductance, denoted by the symbol G<sub>0,</sub> is the *quantized* unit of electrical *conductance*. It is defined by the elementary charge e and Planck constant h as G0=2e^2/h=7.7480917310(18)×10<sup>&minus;</sup><sup>5</sup> S&asymp;1/13 k&Omega;

More information can refer to Wikipedia: https://en.wikipedia.org/wiki/Conductance_quantum

You should also read refs about [[https://en.wikipedia.org/wiki/Quantum_tunnelling][quantum tunneling]]. Quantum tunneling happens when the two metal electrodes are in a distance of a few nanometers. You will observe the quantum tunneling current right after the breakage of the gold point contact. Based on quantum tunnleing, [[https://en.wikipedia.org/wiki/Scanning_tunneling_microscope][Scanning Tunneling Microscope]] (STM) was invented and STM can help us to see individual atoms at real space.

---++ Setup and calibration

Before the experiment, you need to understand the theory and principle of the experiment.

You will be supervised by a graduate student to use the experimental setup and collect data. Please follow the instruction of the graduate student.

You will learn:

1. How to prepare sharp(a few nanometer at the tip) gold tip and clean both gold tip and gold substrate

2. How the experimental setup works (electric circuit, noise reduction...).

3. Data acquisition using DAQ card (from national instrument) and customed labview programs

4. How to repeatedly acquire a large number of the conductance-distance (I-d) curves.

5. Statistical data analysis, build histogram, perform Gaussian fits to the histogram.

6. Develop understanding of quantum mechanics

<img alt="setup.PNG" height="418" src="%ATTACHURL%/setup.PNG" title="setup.PNG" width="546" />

<img alt="" src="%ATTACHURL%/Z:\jinhe\class\2019 spring senior lab\setup.png" />
---++ Part A: Data Collection

Observe quantum steps in the current vs distance (I-d) curve. You should be able to see at least one conductance (conductance=current/voltage) step at G0=2e^2/h&asymp;77.5 microsiemen (uS) or R0=1/G0=12.9 k&Omega;, There are typically more than 1 steps, appearing at 1G0, 2G0, ...

Learn how to optimize the experimental conditions, i.e., tip approach and withdraw speed of the tip, applied bias, environment (in air and in solution).

Build histograms from 50, 100 and 200 I-d curves at 0.1V bias. Compare the shape of peaks and understand how the statistics play the role.

Collect about 200 withdraw conductance curves (more is better) at different biases, 0.05V, 0.1V, 0.2V.
---++ Part B: Data Analysis

You will use the labview programs to build conductance histograms from hundreds of I-d curves you collected. You need to understand how to covert the current unit Amper to quantume conductance unit G0 and how to convert individual I-d curves to G-d curves, then to a conductance histogram (pay attention to the bin size). After buding conductance histograms, you will perform Gaussian fits to the conductance peaks in the histograms. You will discuss the goodness of fit using reduced chi-square.
---++ Materials and Equipment:

The list of necessary equipment is:
   * Current amplifier for small current measurement (understand pA, nA and uA current scales)
   * Stepper motor for low precision movement of gold tip (about 100 nm resolution).
   * Piezo driver and piezo actuator to control the high precision movement of gold tip (about 0.1 nm resolution).
   * Data acquisition setup, labview program to control the hardware
   * Electrical and Mechanical noise reduction setup. Also read this [[https://dberard.com/home-built-stm/][link]].
Write Up

You need to explain the experiment principle and theory, quantum conductance, quantum tunneling.

The experimental setup: Simple diagram of electrical circuit of electrical measurement. How the gold point contact was repeatedly formed, the Piezoelectric effect. The precise control of distance by Piezo actuator.

Results and discussions:

The cleanness of the tip and substrate is important to achieve better results. The size of gold atom? Why the electron transport through the gold wire with the width of one or a few gold atoms be limited?

For individual conductance curve (or G-d cruve), explain why the current decrease with the withdraw of the tip. Explain the quantum steps, the sharp drop of the conductance after the step, also the quantum tunneling current between two nanoscale electrodes after the point contact is broken.

Other interesting discovers in your experiments.
---++ Comments

<br />%COMMENT%
   * [[%ATTACHURL%/1.4765331-Quantum_step_ref1.pdf][1.4765331-Quantum_step_ref1.pdf]]: ref 1

   * [[%ATTACHURL%/Quantized_Conductance_ref_2.pdf][Quantized_Conductance_ref_2.pdf]]: ref 2

   * [[%ATTACHURL%/laetitia-report_ref_3.pdf][laetitia-report_ref_3.pdf]]: ref 3
Attachments
Topic attachments
I	Attachment	History	Action	Size	Date	Who	Comment
pdf	1.4765331-Quantum_step_ref1.pdf	r1	manage	3330.3 K	2018-01-09 - 01:26	JinHe	ref 1
pdf	Quantized_Conductance_ref_2.pdf	r1	manage	103.6 K	2018-01-09 - 01:26	JinHe	ref 1
pdf	laetitia-report_ref_3.pdf	r1	manage	574.3 K	2018-01-09 - 01:26	JinHe	ref 1
PNG	setup.PNG	r1	manage	33.4 K	2019-01-28 - 19:41	JinHe
Topic revision: r9 - 2019-01-28 - JinHe