diff --git a/SolidState/ElectronBands.ipynb b/SolidState/ElectronBands.ipynb index 4442cb87d4e9b0201c692c677d6b8d99732df19e..f92a37dfe6b4e1aec4518e62be4c9a87c9fb83fb 100644 --- a/SolidState/ElectronBands.ipynb +++ b/SolidState/ElectronBands.ipynb @@ -40,7 +40,7 @@ }, { "cell_type": "code", - "execution_count": 107, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -53,6 +53,7 @@ "plt.rcParams['xtick.labelsize'] = 10\n", "plt.rcParams['ytick.labelsize'] = 10\n", "plt.rcParams['font.size'] = 15\n", + "from scipy.optimize import root_scalar\n", "\n", "# Definimos los vectores de la red cúbica simple\n", "a = 5e-10 # parámetro de red en metros (Ã…)\n", @@ -62,9 +63,10 @@ "# Definimos los vectores de la base de átomos\n", "tA = np.array([0,0,0]) # posición del átomo A\n", "tB = a*np.array([1/2,1/2,1/2]) # posición del átomo B\n", - "tO1 = a*np.array([1/2,1/2,0]) # posición del átomo O1\n", - "tO2 = a*np.array([1/2,0,1/2]) # posición del átomo O2\n", - "tO3 = a*np.array([0,1/2,1/2]) # posición del átomo O3\n", + "tO1 = a*np.array([1/2,1/2,0]) # posición del átomo Oxy\n", + "tO2 = a*np.array([1/2,0,1/2]) # posición del átomo Oxz\n", + "tO3 = a*np.array([0,1/2,1/2]) # posición del átomo Oyz\n", + "ts = np.array([tA,tB,tO1,tO2,tO3]) # posiciones de los átomos\n", "\n", "# Definimos los puntos del camino en el espacio recÃproco\n", "GAMMA = np.array([0,0,0]) # punto \\Gamma\n", @@ -105,7 +107,7 @@ }, { "cell_type": "code", - "execution_count": 108, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -161,18 +163,78 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 3. Tight Binding\n", - "\n" + "## 2. Tight Binding\n", + "\n", + "En este modelo, consideramos que las funciones de onda de los electrones en la red son una superposición de funciones de onda atómicas, cuya base es de la forma:\n", + "\n", + "\\begin{equation*}\n", + "\\chi_{\\mathbf{k} l i} = \\sum_{\\mathbf{R}} e^{i \\mathbf{k} \\cdot \\mathbf{R}} \\phi_l (\\mathbf{r} - \\mathbf{t}_i - \\mathbf{R}),\n", + "\\end{equation*}\n", + "\n", + "donde $l$ es el orbital atómico, $i$ es el átomo en la celda primitiva y $\\phi_l$ es la función de onda atómica del átomo $l$ en la posición $\\mathbf{t}_i$. La expansión de la función de onda en esta base es entonces:\n", + "\n", + "\\begin{equation*}\n", + "\\psi_{\\mathbf{k}} (\\mathbf{r}) = \\sum_{l i} c_{\\mathbf{k} l i} \\chi_{\\mathbf{k} l i} (\\mathbf{r}),\n", + "\\end{equation*}\n", + "\n", + "entonces, solo queda encontrar los valores propios del Hamiltoniano de la red, que se puede escribir como:\n", + "\n", + "\\begin{equation*}\n", + "\\left<\\chi_{\\mathbf{k} m j} | \\hat{H} | \\chi_{\\mathbf{k} l i}\\right> = \\hat{H}_{mjli} = \\sum_{\\mathbf{R}} e^{i \\mathbf{k} \\cdot \\mathbf{R}} \\left<\\phi_m (\\mathbf{r} - \\mathbf{t}_j) | \\hat{H} | \\phi_l(\\mathbf{r} - \\mathbf{t}_i- \\mathbf{R})\\right>.\n", + "\\end{equation*}\n", + "\n", + "\n", + "\n", + "Para nuestro caso, consideramos únicamente el orbital $s$ de los átomos, de modo que podemos omitir el Ãndice $l$ y, además, los valores esperados para los orbitales atómicos del hamiltoniano no serán calculados, y serán tomados como constantes de la forma:\n", + "\n", + "\\begin{equation*}\n", + "t_{ij} = -\\left<\\phi (\\mathbf{r} - \\mathbf{t}_j) | \\hat{H} | \\phi(\\mathbf{r} - \\mathbf{t}_i)\\right>,\n", + "\\end{equation*}\n", + "\n", + "siendo $t_{ii}$ la energÃa de los electrones en el orbital $s$ del átomo $i$ (\"autointeracción\"), y $t_{ij}$ con $i \\neq j$ la energÃa de interacción (términos de hopping) entre los orbitales $s$ de los átomos $i$ y $j$. Además, tomaremos únicamente los primeros vecinos de los átomos A (12 átomos O) y B (6 átomos O), y los segundos vecinos de los átomos O (2 átomos B y 4 átomos A).\n", + "\n", + "Con estas consideraciones, las ecuaciones para cada $i=$\\{A, B, $O_{xz}$, $O_{xy}$, $O_{yz}$\\} son, con $H_{i}=\\sum_{j} H_{ij}$:\n", + "\n", + "\\begin{align*}\n", + "H_A &= -t_{AA} - t_{AO}[3 + 2(e^{-ia\\mathbf{k}\\cdot \\hat{x}}+e^{-ia\\mathbf{k}\\cdot \\hat{y}}+e^{-ia\\mathbf{k}\\cdot \\hat{z}}) + (e^{-ia\\mathbf{k}\\cdot (\\hat{x}+\\hat{y})}+e^{-ia\\mathbf{k}\\cdot (\\hat{x}+\\hat{z})}+e^{-ia\\mathbf{k}\\cdot (\\hat{y}+\\hat{z})})], \\\\\n", + "H_B &= -t_{BB} - t_{BO}(3 + e^{-ia\\mathbf{k}\\cdot \\hat{x}}+e^{-ia\\mathbf{k}\\cdot \\hat{y}}+e^{-ia\\mathbf{k}\\cdot \\hat{z}}), \\\\\n", + "H_{O_{xz}} &= -t_{OO} - t_{OA}(e^{-ia\\mathbf{k}\\cdot \\hat{y}}), \\\\\n", + "H_{O_{xy}} &= -t_{OO} - t_{OA}(e^{-ia\\mathbf{k}\\cdot \\hat{z}}), \\\\\n", + "H_{O_{yz}} &= -t_{OO} - t_{OA}(e^{-ia\\mathbf{k}\\cdot \\hat{x}}).\n", + "\\end{align*}\n", + "\n", + "De modo que la matriz se puede escribir de la forma:\n", + "\n", + "$$\n", + "H = \\begin{pmatrix}\n", + "-t_{AA} & 0 & H_{02} & H_{03} & H_{04} \\\\\n", + "0 & -t_{BB} & H_{12} & H_{13} & H_{14} \\\\\n", + "H_{20} & H_{21} & -t_{OO} & 0 & 0 \\\\\n", + "H_{30} & H_{31} & 0 & -t_{OO} & 0 \\\\\n", + "H_{40} & H_{41} & 0 & 0 & -t_{OO}\n", + "\\end{pmatrix}\n", + "$$\n", + "\n", + "Donde:\n", + "\n", + "- $H_{02} = -t_{AO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{x}} + e^{-i a \\vec{k} \\cdot \\vec{z}} + e^{-i a \\vec{k} \\cdot (\\vec{x} + \\vec{z})}\\right) = H_{20}^*$\n", + "- $H_{03} = -t_{AO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{x}} + e^{-i a \\vec{k} \\cdot \\vec{y}} + e^{-i a \\vec{k} \\cdot (\\vec{x} + \\vec{y})}\\right) = H_{30}^*$\n", + "- $H_{04} = -t_{AO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{z}} + e^{-i a \\vec{k} \\cdot \\vec{y}} + e^{-i a \\vec{k} \\cdot (\\vec{z} + \\vec{y})}\\right) = H_{40}^*$\n", + "- $H_{12} = -t_{BO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{y}}\\right) = H_{21}^*$\n", + "- $H_{13} = -t_{BO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{z}}\\right) = H_{31}^*$\n", + "- $H_{14} = -t_{BO}\\left(1 + e^{-i a \\vec{k} \\cdot \\vec{x}}\\right) = H_{41}^*$\n", + "\n", + "Al ser una matriz hermÃtica $5 \\times 5$, obtendremos valores 5 valores propios reales para cada $\\vec{k}$, que serán las bandas de energÃa de los electrones en la red. Ahora, procedemos a calcular estas bandas de energÃa con la implementación numérica." ] }, { "cell_type": "code", - "execution_count": 120, + "execution_count": 3, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", "text/plain": [ "<Figure size 800x600 with 1 Axes>" ] @@ -183,11 +245,11 @@ ], "source": [ "# Definimos las constantes de hopping\n", - "tAA = 0 # eV\n", - "tBB = 15.8 # eV\n", - "tOO = 10.0 # eV\n", - "tAO = 19.7 # eV\n", - "tBO = 17.5 # eV\n", + "tAA = 7 # eV\n", + "tBB = 8 # eV\n", + "tOO = 5 # eV\n", + "tAO = 2.1 # eV\n", + "tBO = 1.0 # eV\n", "\n", "# Definimos la base cartesiana\n", "x = np.array([1,0,0])\n", @@ -196,14 +258,14 @@ "\n", "\n", "# Definimos las componentes de la matriz hamiltoniana como función de k\n", - "def Hamiltoniano(k):\n", + "def HamiltonianoTB(k):\n", " # El orden de los Ãndices 5x5 es: A, B, Oxz, Oxy, Oyz\n", " H = np.zeros((5,5),dtype=complex)\n", - " H[0,0] = -2*tAA\n", - " H[1,1] = -2*tBB\n", - " H[2,2] = -2*tOO\n", - " H[3,3] = -2*tOO\n", - " H[4,4] = -2*tOO\n", + " H[0,0] = -tAA\n", + " H[1,1] = -tBB\n", + " H[2,2] = -tOO\n", + " H[3,3] = -tOO\n", + " H[4,4] = -tOO\n", " H[0,2] = -tAO*(1+np.exp(-1j*a*np.dot(k, x))+np.exp(-1j*a*np.dot(k, z)) + np.exp(-1j*a*np.dot(k, x+z)))\n", " H[0,3] = -tAO*(1+np.exp(-1j*a*np.dot(k, x))+np.exp(-1j*a*np.dot(k, y)) + np.exp(-1j*a*np.dot(k, x+y)))\n", " H[0,4] = -tAO*(1+np.exp(-1j*a*np.dot(k, z))+np.exp(-1j*a*np.dot(k, y)) + np.exp(-1j*a*np.dot(k, z+y)))\n", @@ -219,10 +281,7 @@ " return H\n", "\n", "# Obtenemos las bandas de energÃa\n", - "bands_TB = np.array([np.linalg.eigvalsh(Hamiltoniano(k)) for k in k_path]).T\n", - "\n", - "# Quitamos algunas bandas para mejorar la visualización\n", - "# bands_full = np.delete(bands_full, [18,17,13], axis=0) # eliminamos las bandas 19, 18 y 14\n", + "bands_TB = np.array([np.linalg.eigvalsh(HamiltonianoTB(k)) for k in k_path]).T\n", "\n", "# Graficamos las bandas de energÃa\n", "color = 'darkorchid'\n", @@ -239,33 +298,203 @@ "\n" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. Modelo Kronig-Penney\n", + "\n", + "La extensión a tres dimensiones del modelo presentado en Kittel representa una gran dificultad al tratar de considerar deltas de dirac como potenciales, pues para representar cada sitio, la forma del potencial deberÃa ser como $V(x,y,z) = \\delta (x-x_0) \\delta (y-y_0) \\delta (z-z_0)$, de modo que la ecuación de Schrödinger\n", + "\n", + "$$\n", + "\\left[ -\\frac{\\hbar^2}{2m} \\nabla^2 + V(x,y,z) \\right] \\psi(x,y,z) = E \\psi(x,y,z)\n", + "$$\n", + "\n", + "no es separable. Además, muy poco se dice en la literatura sobre este modelo aplicado a sistemas tridimensionales.\n", + "\n", + "Para generalizar el modelo a un cristal tridimensional nos basamos entonces en el trabajo [*Berezin, A. A. (1986). Two-and three-dimensional Kronig-Penney model with δ-function-potential wells of zero binding energy. Physical Review B, 33(4), 2122.*](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.33.2122?__cf_chl_tk=LgIZGYFThFthgKAXGyH87iqGLrzzJdHheOzxE08lD_A-1734019083-1.0.1.1-cVBnznyzNCq.4R_4S4LPWHkT4ySaHsfjK0K7qevsOro).\n", + "\n", + "El potencial de Hulthen se define como:\n", + "\n", + "$$\n", + "V(r) = -\\frac{b}{\\exp(ar) - 1}.\n", + "$$\n", + "\n", + "Para modelar un pozo de potencial tipo delta ($\\delta$), el radio efectivo de acción de la fuerza se hace tender a cero. Este proceso se logra haciendo que los parámetros $a$ y $b$ del potencial de Hulthen tiendan a infinito de manera que el cociente $b/a^2 = 1/2$ se mantenga. Este procedimiento está detallado en las referencias del artÃculo.\n", + "\n", + "En un único potencial delta, la función de onda del estado base del sistema toma la forma:\n", + "\n", + "$$\n", + "\\psi(r) = \\sqrt{\\frac{\\gamma}{2\\pi}} \\frac{\\exp(-\\gamma r)}{r},\n", + "$$\n", + "\n", + "donde $\\gamma$ representa la \"fuerza\" o \"profundidad efectiva\" del potencial delta. Para un sistema de múltiples potenciales delta ubicados en posiciones $\\mathbf{R}_j$, la función de onda se expresa como:\n", + "\n", + "$$\n", + "\\psi(\\mathbf{r}) = \\sum_{j} A_j \\frac{\\exp(-\\alpha |\\mathbf{r} - \\mathbf{R}_j|)}{|\\mathbf{r} - \\mathbf{R}_j|},\n", + "$$\n", + "\n", + "donde $\\alpha$ se relaciona con los valores de energÃa posibles $E = \\alpha^2/2$ (unidades atómicas), y los coeficientes $A_j$ dependen de las condiciones del sistema, en este caso periódicos y de continuidad en las fronteras de las celdas unitarias.\n", + "\n", + "El sistema de condiciones de frontera conduce a la ecuación secular trascendental para $\\alpha$:\n", + "\n", + "$$\n", + "\\det \\left[ (\\gamma - \\alpha) \\delta_{ij} + (1 - \\delta_{ij}) \\frac{\\exp(-\\alpha |\\mathbf{R}_i - \\mathbf{R}_j|)}{|\\mathbf{R}_i - \\mathbf{R}_j|} \\right] = 0,\n", + "$$\n", + "\n", + "esta ecuación determina los niveles de energÃa discretos para un sistema con $N$ pozos delta de la celda.\n", + "\n", + "Consideremos ahora una red cúbica infinita de pozos delta periódicos con fuerza $\\gamma$. En este caso, los coeficientes $A_j$ en la función de onda satisfacen la condición de Bloch:\n", + "\n", + "$$\n", + "A_j = A \\exp(i \\mathbf{k} \\cdot \\mathbf{R}_j),\n", + "$$\n", + "\n", + "y la función de onda puede representarse como:\n", + "\n", + "$$\n", + "\\psi(\\mathbf{r}) = A \\sum_{\\mathbf{R}_j} \\exp(i \\mathbf{k} \\cdot \\mathbf{R}_j) \\frac{\\exp(-\\alpha |\\mathbf{r} - \\mathbf{R}_j|)}{|\\mathbf{r} - \\mathbf{R}_j|}.\n", + "$$\n", + "\n", + "Aplicando la condición de frontera en cualquier sitio $\\mathbf{R}_0$, se llega a la ecuación trascendental:\n", + "\n", + "$$\n", + "\\alpha - \\gamma = \\sum_{\\mathbf{R}_j \\neq \\mathbf{R}_0} \\frac{\\exp(-\\alpha |\\mathbf{R}_j - \\mathbf{R}_0|)}{|\\mathbf{R}_j - \\mathbf{R}_0|} \\exp(i \\mathbf{k} \\cdot \\mathbf{R}_j),\n", + "$$\n", + "\n", + "la cual se puede resolver numéricamente para obtener los valores de $\\alpha$." + ] + }, { "cell_type": "code", - "execution_count": 110, + "execution_count": 58, "metadata": {}, "outputs": [ { "data": { + "image/png": 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", "text/plain": [ - "array([-179.06647307, -33.01113561, -20. , -20. ,\n", - " 120.27760868])" + "<Figure size 800x600 with 1 Axes>" ] }, - "execution_count": 110, "metadata": {}, - "output_type": "execute_result" + "output_type": "display_data" } ], "source": [ - "bands_TB.T[0]" + "# Definimos las constantes fÃsicas\n", + "gammaA = -1000 # eV\n", + "gammaB = 1500 # eV\n", + "gammaO = 0 # eV\n", + "\n", + "# Definimos las ecuaciones para cada sitio\n", + "def SitioA(alpha,k):\n", + " suma_fin = 0\n", + " for t in np.delete(ts,0,axis=0):\n", + " suma_fin += np.exp(1j*np.dot(k,t))*np.exp(-alpha*np.linalg.norm(t-ts[0]))/np.linalg.norm(t-ts[0])\n", + " return suma_fin.real + gammaA - alpha\n", + "def SitioB(alpha,k):\n", + " suma_fin = 0\n", + " for t in np.delete(ts,1,axis=0):\n", + " suma_fin += np.exp(1j*np.dot(k,t))*np.exp(-alpha*np.linalg.norm(t-ts[1]))/np.linalg.norm(t-ts[1])\n", + " return suma_fin.real + gammaB - alpha\n", + "def SitioOxy(alpha,k):\n", + " suma_fin = 0\n", + " for t in np.delete(ts,2,axis=0):\n", + " suma_fin += np.exp(1j*np.dot(k,t))*np.exp(-alpha*np.linalg.norm(t-ts[2]))/np.linalg.norm(t-ts[2])\n", + " return suma_fin.real + gammaO - alpha\n", + "def SitioOxz(alpha,k):\n", + " suma_fin = 0\n", + " for t in np.delete(ts,3,axis=0):\n", + " suma_fin += np.exp(1j*np.dot(k,t))*np.exp(-alpha*np.linalg.norm(t-ts[3]))/np.linalg.norm(t-ts[3])\n", + " return suma_fin.real + gammaO - alpha\n", + "def SitioOyz(alpha,k):\n", + " suma_fin = 0\n", + " for t in np.delete(ts,4,axis=0):\n", + " suma_fin += np.exp(1j*np.dot(k,t))*np.exp(-alpha*np.linalg.norm(t-ts[4]))/np.linalg.norm(t-ts[4])\n", + " return suma_fin.real + gammaO - alpha\n", + " \n", + "# Definimos la energÃa a partir del alpha\n", + "def E_alpha(alpha):\n", + " return hbar**2*alpha**2/(2*m*e)\n", + "\n", + "# Encontramos las raices para los diferentes valores de k\n", + "# path = k_GX\n", + "path = k_path\n", + "bands_KP = []\t\n", + "root_range = [0,10]\n", + "for k in path:\n", + " try:\n", + " alphaA = root_scalar(SitioA,args=(k),method='brentq',bracket=[1,1e10]).root\n", + " except:\n", + " alphaA = 0\n", + " try:\n", + " alphaB = root_scalar(SitioB,args=(k),method='brentq',bracket=[1,1e10]).root\n", + " except:\n", + " alphaB = 0\n", + " try:\n", + " alphaOxy = root_scalar(SitioOxy,args=(k),method='brentq',bracket=[1,1e10]).root\n", + " except:\n", + " alphaOxy = 0\n", + " try:\n", + " alphaOxz = root_scalar(SitioOxz,args=(k),method='brentq',bracket=[1,1e10]).root\n", + " except:\n", + " alphaOxz = 0\n", + " try:\n", + " alphaOyz = root_scalar(SitioOyz,args=(k),method='brentq',bracket=[1,1e10]).root\n", + " except:\n", + " alphaOyz = 0\n", + " bands_KP.append(list(map(E_alpha,[alphaA,alphaB,alphaOxy,alphaOxz,alphaOyz])))\n", + "\n", + "# Graficamos las bandas de energÃa\n", + "bands_KP = np.array(bands_KP).T\n", + "n_graf = len(bands_KP) # número de bandas a graficar\n", + "for i in range(n_graf):\n", + " plt.plot(np.arange(len(path)), bands_KP[i], '.', markersize=3)\n", + "plt.xticks([0,N,2*N,3*N,4*N],['$\\\\Gamma$','X','M','$\\\\Gamma$','R'])\n", + "plt.xlabel('Camino en el espacio recÃproco')\n", + "plt.ylabel('EnergÃa (eV)')\n", + "# plt.ylim(0,400)\n", + "plt.title('Bandas de energÃa mediante Kronig-Penney')\n", + "plt.grid()\n", + "plt.show()" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 50, "metadata": {}, - "outputs": [], - "source": [] + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 800x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Ploteamos SitioOxy para todos los valores de alpha con un k fijo\n", + "k = X\n", + "alpha = np.logspace(0,10,100)\n", + "plt.semilogx(alpha, [SitioA(a,k) for a in alpha])\n", + "plt.xlabel('alpha')\n", + "plt.ylabel('Sitio Oxy')\n", + "plt.title('Sitio Oxy')\n", + "plt.grid()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4. Análisis\n", + "\n" + ] } ], "metadata": {