From 5244a55fe97ae9188b5a12d8f2822db0910cc67b Mon Sep 17 00:00:00 2001
From: "T. van der Sar" <t.vandersar@tudelft.nl>
Date: Sun, 3 Feb 2019 21:22:01 +0000
Subject: [PATCH] Update 3_drude_model.md - fix
---
src/3_drude_model.md | 10 +++++-----
1 file changed, 5 insertions(+), 5 deletions(-)
diff --git a/src/3_drude_model.md b/src/3_drude_model.md
index 05644aad..9bb975bf 100644
--- a/src/3_drude_model.md
+++ b/src/3_drude_model.md
@@ -106,15 +106,15 @@ We first consider an electron in free space, moving in a plane perpendicular to
3. The Drude model assumes that $\lambda$ is independent of temperature. How does the electrical resistivity $\rho$ depend on temperature under this assumption? Sketch $\rho(T)$.
5. Compare your sketch of $\rho(T)$ with that in the lecture notes. In what respect do they differ? Discuss possible reasons for differences.
-### Exercise 3: Hall resistivity and Hall coefficient
-We apply a magnetic field $\bf B$ perpendicular to a current carrying 2D sample. In this situation, the electric field $\mathbf{E}$ is related to the current density $\mathbf}J}$ by the resistivity matrix:
+### Exercise 3: The Hall conductivity matrix and the Hall coefficient
+We apply a magnetic field $\bf B$ perpendicular to a current carrying 2D sample. In this situation, the electric field $\mathbf{E}$ is related to the current density $\mathbf{J}$ by the resistivity matrix:
$$\mathbf{E} = \begin{pmatrix} \rho_{xx} & \rho_{xy} \\ \rho_{yx} & \rho_{yy} \end{pmatrix} \mathbf{J}$$
1. Sketch $\rho_{xx}$ and $\rho_{xy}$ as a function of the magnetic field $\bf B$.
- 2. Invert the resistivity matrix to obtain the conductivity matrix $\begin{pmatrix} \sigma_{xx} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} $ and express $\mathbf{J}$ as a function of $\mathbf{E}$.
- 3. Sketch $\sigma_{xx}$ and $\sigma_{xy}$ as a function of the magnetic field $\bf B$.
- 4. Define the Hall coefficient. What does the sign of the Hall coefficient signify?
+ 2. Invert the resistivity matrix to obtain the conductivity matrix $$\begin{pmatrix} \sigma_{xx} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} $$ and express $\mathbf{J}$ as a function of $\mathbf{E}$.
+ 3. Sketch $\sigma_{xx}$ and $\sigma_{xy}$ as a function of the magnetic field $\bf B$. Calculate the value of $\sigma_{xx}$ for $\rho_{xx}=0$. Discuss what is going on here.
+ 4. Give the definition of the Hall coefficient. What does the sign of the Hall coefficient indicate?
### Exercise 4: Drude model of thermal and electrical conductivity
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