The second step (ii) is described by an effective mean-free path proportional to the probability of the electron to reach the surface with no change in momentum and energy, i.e without scattering. Inelastic processes are also possible, and result as a broad background in the ARPES spectrum which we can ignore in this discussion. The third step (iii) is related to the transmission probability for an electron to escape from the solid into vacuum. Hence, it is mainly the first step (i) that leads to the features of interest in the photoemission intensity. This step is described by Eq. A.5: $w_f$ measures the probability of the optical excitation of a bulk electron.

In order to connect the transition probability to the spectral function, and hence to the Green's function of the solid, $H_{int}$ may be re-written within second quantization:

$$ H_{int} = \sum_{\substack{f=\{m_f, \mathbf{k}_f\} \\ i=\{m, \mathbf{k}\}}} \mathbf{M}_{fi} c_f^\dagger c_i \\ \mathbf{M}_{fi} = -\frac{e}{m_e} \langle \phi_{m_f, \mathbf{k}_f} | \mathbf{A} \cdot \hat{\mathbf{p}} | \phi_{m, \mathbf{k}} \rangle \quad (A.6) $$

where $f = \{m_f, \mathbf{k}_f\}$ and $i = \{m, \mathbf{k}\}$ denote the orbital and momentum of the photoelectron $|\phi_{m_f, \mathbf{k}_f}\rangle$ and the initial electron $|\phi_{m, \mathbf{k}}\rangle$. Note that the $\{|\phi_{m, \mathbf{k}}\rangle\}$ are single-particle wavefunctions, and not many-body ones. Within the context of the effective Hubbard model that we use throughout this thesis, they can be thought of as the Fourier transformation of the localized Wannier orbitals [258] (i.e as Bloch bands):

$$ |\phi_{m, \mathbf{k}}\rangle = \sum_{\mathbf{R}} e^{i\mathbf{k}\mathbf{R}} |w_{m\mathbf{R}}\rangle. \quad (A.7) $$

This shows that the matrix elements $\mathbf{M}_{fi}$ are dependent on the symmetry of the material, and the orbital $m$ of the electron that absorbed the incoming photon. It is moreover a function of the light polarization and the angles $(\theta, \phi)$ due to the vector potential $\mathbf{A}$. Upon further transforming the transition probability, it will become clear that these matrix-elements lead to additional suppressions of the measured intensity not related to many-body effects [258].

Using the second quantized form of $H_{int}$, the transition probability now reads

$$ w_f = 2\pi \sum_{\substack{f'=\{m'_f, \mathbf{k}'_f\} \\ i=\{m, \mathbf{k}\}}} |\mathbf{M}_{f'i}|^2 |\langle \psi_f^N | c_{f',c_i}^\dagger | \psi_{GS}^N \rangle|^2 \delta(E_f^N - E_{GS}^N - \nu). \quad (A.8) $$

The final state $|\psi_f^N\rangle$ is a priori difficult to describe since it accounts for a many-body system of $N-1$ electrons plus a photoexcited electron, which may interact with the hole created via the photon absorption, and with the rest of the $N-1$ electrons. However, at the photon energies available in synchrotron facilities, roughly about 20-200eV, we can assume the optical excitation to be fast, and the energy of the photoelectron well separated from that of the bulk electrons, such that the final state can be written as a product state

$$ |\psi_f^N\rangle \approx c_{m_f, \mathbf{k}_f}^\dagger |\psi_n^{N-1}\rangle \quad (A.9) $$
where $|\psi_n^{N-1}\rangle$ is a $N-1$ electron state, and $c_{m_f, k_f}^\dagger$ is the creation operator of a photoelectron of orbital $m_f$ and momentum $k_f$. This is the so-called sudden approximation [24, 258]. For ARPES measurements using low-energy incident photons, like laser-ARPES, this assumption may break down. The energy of this product state can be conveniently written

$$E_f^N = E_{kin} + E_n^{N-1}, \qquad (A.10)$$

where $E_{kin}$ is the kinetic energy of the photoelectron and $E_n^{N-1}$ the energy of the $N-1$ many-body state $|\psi_n^{N-1}\rangle$. This form of the final state can now be injected in Eq. A.8 by summing over all the possible $N-1$ final states $\{|\psi_n^{N-1}\rangle\}$ [258]:

$$ \begin{aligned} w_f &= 2\pi \sum_{\substack{f'=\{m'_f, k'_f\} \\ i=\{m, k\}}} \sum_n |\mathbf{M}_{f'i}|^2 |\langle\psi_n^{N-1}|c_{m_f, k_f} c_{f'i}^\dagger c_i|\psi_{GS}^N\rangle|^2 \delta(E_n^{N-1} + E_{kin} - E_{GS}^N - \nu) \\ &= 2\pi \sum_{\substack{m, k \\ \{m_f, k_f\}}} \left|\mathbf{M}_{\{m_f, k_f\}}\right|^2 \sum_n |\langle\psi_n^{N-1}|c_{m, k}|\psi_{GS}^N\rangle|^2 \delta(E_n^{N-1} + E_{kin} - E_{GS}^N - \nu) \qquad (A.11) \\ &= 2\pi \sum_{\substack{m, k \\ \{m_f, k_f\}}} \left|\mathbf{M}_{\{m_f, k_f\}}\right|^2 A_{mm}^{-}(\mathbf{k}, \omega), \end{aligned} $$

where the $\{A_{mm}^{-}(\mathbf{k}, \omega)\}$ are the diagonal components of the one-electron removal spectral function corresponding to the orbital $m$ and momentum $\mathbf{k}$, and $\mathbf{M}_{\{m_f, k_f\}}$ are the matrix elements of the photoelectron of orbital $m_f$ and momentum $\mathbf{k}_f$. As mentioned above, these matrix elements lead to additional suppressions not linked to the many-body effects encoded in the spectral function $A_{mm}^{-}(\mathbf{k}, \omega)$. Although they could be naively viewed as a curse, the matrix elements can in fact be extremely useful to highlight some features in the spectrum [258], or for instance to determine the orbital character of certain unknown states [305]. For a more detailed discussion of matrix-elements effects, we refer the interested reader to the review of Moser [258].

So far, we have linked the transition probability, i.e the photocurrent measured in ARPES to the one-electron removal spectral function $A_{mm}^{-}(\mathbf{k}, \omega)$, which is defined as follows (at zero temperature):

$$A_{mm}^{-}(\mathbf{k}, \omega) = \sum_{n} |\langle \psi_{n}^{N-1} | c_{m, \mathbf{k}} | \psi_{GS}^{N} \rangle|^{2} \delta(E_{n}^{N-1} + E_{GS}^{N} - \omega) \qquad (A.12)$$

In order to directly see the connection to the Green's function calculated in CDMFT, it is convenient to write the retarded Green's function at zero temperature in Lehmann's representation

$$ \begin{aligned} G_{mm}(\mathbf{k}, \omega) &= G_{mm}^{-}(\mathbf{k}, \omega) + G_{mm}^{+}(\mathbf{k}, \omega) \\ &= \sum_{n} \frac{|\langle\psi_{n}^{N-1}|c_{m,\mathbf{k}}|\psi_{GS}^{N}\rangle|^2}{\omega + E_{n}^{N-1} - E_{GS}^{N} + i\eta} + \sum_{n} \frac{|\langle\psi_{n}^{N+1}|c_{m,\mathbf{k}}^{\dagger}|\psi_{GS}^{N}\rangle|^2}{\omega - E_{n}^{N+1} + E_{GS}^{N} + i\eta} \end{aligned} \qquad (A.13) $$
where $G_{mm}^{-}(\mathbf{k}, \omega)$, $G_{mm}^{+}(\mathbf{k}, \omega)$ are respectively the one-electron removal and addition Green's function, and $\eta$ is a small finite number. Using the relation

$$ \frac{1}{x + i\eta} \rightarrow_{\eta \to 0^+} \mathcal{P}\left(\frac{1}{x}\right) - i\pi\delta(x), \qquad (A.14) $$

one can relate the electron removal spectral function to $G_{mm}^{-}(\mathbf{k}, \omega)$:

$$ -\frac{1}{\pi} \mathrm{Im}[G_{mm}^{-}(\mathbf{k}, \omega)] = \sum_{n} |\langle\psi_{n}^{N-1}|c_{m,\mathbf{k}}|\psi_{GS}^{N}\rangle|^{2} \delta(\omega + E_{n}^{N-1} - E_{GS}). \qquad (A.15) $$

Therefore, the photocurrent measured in ARPES can be directly related to the occupied part of the CDMFT spectrum!

## A.2 FROM ANGLES TO MOMENTUM

While in the formalism above we related the transition probability to the momentum-dependent spectral function, in the experimental measurements one can only have a direct access to the emission angles $(\phi, \theta)$ of the photoelectrons. Therefore, we need to reconstruct the momentum dependence of the spectrum based on its angle dependence.

First, we can make the approximation that the momentum transfer from the electron is small, such that it can be neglected. This means that the photoelectron in the solid has the momentum $\mathbf{k}_f = \mathbf{k}$. When escaping from the material, the overall momentum of the electron is modified, i.e $\mathbf{k} \neq \mathbf{p}$, with $\mathbf{k}(\mathbf{p})$ the momentum inside (outside) the solid. Due to the conservation of the in-plane $(x, y)$ symmetry when crossing the solid/vacuum interface, the in-plane component of the momentum is conserved, i.e $\mathbf{k}_{\parallel} = \mathbf{p}_{\parallel}$ [24, 258]. However, the out-of plane component is not conserved since the photoelectron crosses a step-like potential when leaving the material:

$$ \begin{aligned} V(z) &= -V && \text{inside the solid} \\ &= 0 && \text{outside,} \end{aligned} \qquad (A.16) $$

where $V$ is the potential inside the solid. Within a simple free-electron picture, the non-conservation of the out-of-plane component can be written as [258]:

$$ \frac{\mathbf{k}_{\perp}^{2}}{2m_{e}} = \frac{\mathbf{p}_{\perp}^{2}}{2m_{e}} + V. \qquad (A.17) $$

The kinetic energy of the photoelectron in the vacuum, which is measured in the analyzer, is simply given by $E_{kin} = \frac{p^2}{2m_e}$. It is also related to the binding energy $E_B$ via $E_{kin} = \nu - E_B - \Phi$, with $\Phi$ the work function, i.e the energy necessary for the electron to escape into the vacuum. Hence, following the angle notations of Fig. A.1, we can relate the momentum $\mathbf{k}$ to the angle $\theta$ by the following relations [24, 258]:

$$ \begin{aligned} \mathbf{k}_{\parallel} &= \sqrt{2m_e E_{kin}} \sin(\theta) \\ \mathbf{k}_{\perp} &= \sqrt{2m(E_{kin} \cos(\theta)^2 + V)}. \end{aligned} \qquad (A.18) $$
<figure><img src="image_75.png" /><figcaption>Figure A.2: (a) Angle-dependent Fermi surface obtained by integrating the spectrum over a narrow region of frequency around the Fermi level, and (b) its transformation to momentum-space. (c1)-(c4) A series of fits for the determination of the Γ point from the angle-dependent spectrum in the specific regions highlighted in (a).</figcaption></figure>

Note that due to the *V* term in the expression of **k**⊥, the absolute value of the latter is not known *a priori*. One of the methods to determine **k**⊥ is to vary the photon energy and observe the periodicity of the spectrum at **k**‖ = 0 [24]. We notice also that as the angle θ varies, **k**⊥ changes accordingly. This means that, in principle, for a given angle-dependent spectral function map, the out-of-plane component **k**⊥ is not constant as a function of the angles (θ, φ). Since we have seen in the band structures of NaCCOC and t-CuO that the low-energy ZRS band displays a weak dispersion along **k**z, we can safely ignore this complication here.

With the relations of Eq. A.18, we can now transform a typical angle-dependent spectrum as shown in Fig. A.2(a), to its momentum counterpart shown in Fig. A.2(b). To perform such transformation, we used the pyARPES package [257] that the author adapted to import the data from SOLEIL synchrotron (for the Photon Factory data the Igor software was used). It is required to locate the Γ high-symmetry point, since it serves as a center of rotation to align the axis **k**<sub>x</sub> and **k**<sub>y</sub>. We find Γ from the Fermi surface, since it is in the middle of the four Fermi arcs that can be seen in Fig. A.2(a). Lorentzian fits can be used (see Fig. A.2(c)) to determine the precise position of each Fermi arc, from which Γ is then extracted. Once the Γ point is found as a function of the angles (φ, θ), the momentum-resolved spectrum can be obtained by estimating the rotation of the axis **k**<sub>x</sub> and **k**<sub>y</sub>, as shown in Fig. A.2(b). The data is then ready for further analysis and comparison to the theoretical momentum-resolved spectrum (albeit the matrix-element effects).
ACKNOWLEDGMENTS

As we have seen in this thesis, materials are cool. Guess what, humans too, especially colleagues,
friends, and family, with whom I spent quite some time in those last three years, and who deserve
at least a one-and-a-half special page here.

First things first, I would like to thank the secretaries of the lab, without whom we would not
do anything, as well as the computer support team.

I would like to thank Silke for welcoming me in her group, and offering me the opportunity to do
this thesis. I am more than happy to have learned so much about physics, research in general, as
well as singing techniques through our discussions. Benjamin (Lenz, not me), you deserve a few
lines in here for all the time you spent guiding and helping me with all the sorts of problem and
questions I had, although you were "slightly" busy with your new *Maître de Conférences* position.
I warmly thank you for all the knowledge you brought me, as well as the collaboration opportu-
nities that I'm glad I could participate to. And let's not forget about the many lunches at Jussieu!

Having mentioned collaborations, I would like to thank Matteo d'Astuto who kindly accepted
the dangerous task to embark theoreticians onto two ARPES beam times. These were probably
two of the best physics experiences of this PhD, which by the way almost convinced me to turn to
experimental physics. During the beam time in SOLEIL, it was the occasion to meet Chafic and
Hervé who I would like to thank for all the nice discussions. A special mention to Chafic for the
nights spent a SOLEIL with the photon flux going crazy, and who also saved us by ordering pizza
since the canteen had rejected us. Talking about food (would have been strange to not discuss
this topic in thesis written by a french), a second thank-you goes to both Chafic and Matteo, for
the nice libanese dessert and the amazing asparagus risotto.

We're not done with collaborators yet: thanks to Martin, Sebastian, and Max from whom I learned
a lot, both in terms of stories and physics. I have a special thought for Max, and all the nice writ-
ing sessions. I hope that you liked the *confit de canard*. And good luck to Sebastian, for taking
care of at least 14 bachelor students at the same time.

A warm thanks goes to Steffen: in fact you would deserve the title (officieux) of co-supervisor.
Thank you for all the time you spent answering my (often stupid) questions, helping me solving
all kinds of technical problems, as well as for the nice mushroom hunt during which we found
the nicest boletus I've ever eaten, and the amazing Christmas riddle. I hope that everything goes
well in Japan! Thanks also to all the nice people I met at the lab and who made life enjoyable
there: Jean-Baptiste, Louis, Julien who shared his writing experience that I can relate to right
now, Jakob, Sumanta, Marcello, Anna, Erik for bringing so much life to the group and especially
for the *caramel* tea, Adrian who should now enjoy the heatwave in France, Maria for the best (al-
most improvised) lecture on Feynman diagrams I attended to, Alaska for the sometimes heated
discussions, Jan for the coffee and language expertise, and Zhenya for destroying unintentionally
an innocent master's student presenting his results.

Life at the lab was not only about research, but also teaching. I must say that I was extremely
lucky to be asked to do the superconductivity *modal* with Yannis, Aurélien and Renaud. Thank
you to all three of you, for all the nice discussions about physics, flamenco, and others, as well as
our small end-of-modal parties. And also the lab visits to discover Yannis' and Aurélien's setups.

Enough with physics, it's now time to greet all my friends, from Cachan or before, with who I spent amazing times during these three years. They are too many of you and I would forget about some names, so to avoid any disrespectful omission I will simply give a warm thanks to all of you, since without all the good times we spent together I would not have made it to this point.

A special thanks goes to the militant association *Droit au logement*, with which I spent quite some time during these last two years to fight for housing rights. I am in debt with all the militants I met there, who taught me everything I know about housing, and with whom I walked a few kilometers in Paris' streets to fight against savage evictions, rental abuses, denied access to social housing, etc. *Un toit, c'est un droit!*

Finally, the last paragraph is devoted to my closest family, who brought me so much support and love. Marie, of course. My sister, you were always present when needed, and you paved me the way towards the PhD. My father, especially for your patience and help each time we moved in a new apartment, and finally my mother who, although she could not make it to read this, surely immensely contributed to provide me the chance to do this thesis.
ACRONYMS

<table><tr><td>μ-SR</td><td>muon spin resonance. 8, 121</td></tr><tr><td>2DEG</td><td>2D electron gas. 9, 10, 122–125, 131, 133, 136, 139, 145, 146</td></tr><tr><td>AIM</td><td>Anderson’s impurity model. 28, 32, 33</td></tr><tr><td>ARPES</td><td>angle-resolved photoemission spectroscopy. 6–9, 23, 40, 63, 65–67, 70, 71, 73–76, 87, 95, 98, 100, 104, 106, 108, 114, 119, 121, 137, 143, 144, 149–153</td></tr><tr><td>BZ</td><td>Brillouin zone. 4, 7, 25, 26, 38, 39, 58, 63, 66, 73, 76, 98, 100, 101, 106, 108, 109</td></tr><tr><td>CDMFT</td><td>cluster dynamical mean-field theory. 5–7, 9, 10, 22, 38–41, 44, 46, 51, 53, 55, 59, 64, 67–69, 71–73, 75–79, 83, 84, 86, 87, 89, 94–96, 98, 99, 101, 102, 104–106, 111–114, 117, 119, 121, 133, 143, 146, 152, 153</td></tr><tr><td>CDW</td><td>charge density wave. 4, 6, 38, 40, 63, 97, 146</td></tr><tr><td>CTQMC</td><td>continuous-time quantum Monte Carlo. 6, 9, 32, 41, 45, 46, 69, 98, 101, 111, 144</td></tr><tr><td>DCA</td><td>dynamical cluster approximation. 6, 7, 38, 64, 78, 92, 145, 146</td></tr><tr><td>DFT</td><td>density functional theory. 4, 8, 10, 13, 14, 17, 21–25, 27, 33, 67, 68, 97, 100, 101, 111, 121–123, 125, 139, 143, 145</td></tr><tr><td>DMFT</td><td>dynamical mean-field theory. 5–7, 10, 22, 24, 27, 28, 32, 34, 36–38, 41, 46, 55, 64, 110, 145, 146</td></tr><tr><td>DOS</td><td>density of states. 29, 40, 66, 67, 84, 86, 101, 123–127, 129–132, 135, 137–139</td></tr><tr><td>DSSF</td><td>dynamical spin structure factor. 8, 65, 69, 70, 87–96, 145</td></tr><tr><td>ED</td><td>exact diagonalization. 93</td></tr><tr><td>EDC</td><td>energy distribution curve. 75, 76, 78, 79, 86, 87</td></tr><tr><td>GGA</td><td>generalised gradient approximation. 18, 19</td></tr><tr><td>LDA</td><td>local density approximation. 4, 18–22, 24, 25, 38, 66–68, 100, 108, 123</td></tr></table>
<table>
  <tr>
    <td>LHB</td>
    <td>lower Hubbard band. 3, 71, 73, 74, 81, 114, 144</td>
  </tr>
  <tr>
    <td>LSDA</td>
    <td>local spin density approximation. 18–21</td>
  </tr>
  <tr>
    <td>MEM</td>
    <td>maximum entropy method. 48–54, 88</td>
  </tr>
  <tr>
    <td>MLWF</td>
    <td>maximally localized Wannier functions. 26, 27, 68</td>
  </tr>
  <tr>
    <td>MPS</td>
    <td>matrix-product state. 6, 9, 32, 98, 101, 103, 104, 106–112, 144</td>
  </tr>
  <tr>
    <td>MQEM</td>
    <td>maximum quantum entropy method. 48, 53, 54, 69, 71</td>
  </tr>
  <tr>
    <td>NaCCOC</td>
    <td>Ca<sub>2-x</sub>Na<sub>x</sub>CuO<sub>2</sub>Cl<sub>2</sub>. 3–8, 10, 14, 18, 19, 24, 25, 27, 44, 46, 57, 59, 63–69, 71, 73, 74, 76, 89, 95, 97, 99, 100, 143–146, 154</td>
  </tr>
  <tr>
    <td>NN</td>
    <td>nearest-neighbor. 5, 8, 24, 30, 54, 55, 57, 68, 80, 89–93, 98, 100, 104, 105, 126, 128, 129, 133, 135</td>
  </tr>
  <tr>
    <td>NNN</td>
    <td>next-NN. 8, 30, 58, 68, 88–93, 98, 100, 101, 104, 126, 133, 135, 144</td>
  </tr>
  <tr>
    <td>NNNN</td>
    <td>next-NNN. 27, 58, 68, 126</td>
  </tr>
  <tr>
    <td>PBE</td>
    <td>Perdew–Burke–Ernzerhof. 123, 124, 128, 137, 145</td>
  </tr>
  <tr>
    <td>PG</td>
    <td>pseudogap. 4, 6–8, 39, 63–65, 67–69, 71, 74–79, 81, 82, 84, 86, 87, 91–93, 95, 96, 143, 144, 146</td>
  </tr>
  <tr>
    <td>QMC</td>
    <td>quantum Monte Carlo. 7, 64, 145</td>
  </tr>
  <tr>
    <td>RIXS</td>
    <td>resonant inelastic x-ray scattering. 8, 65, 68, 80, 87–89, 98, 100, 121</td>
  </tr>
  <tr>
    <td>RVB</td>
    <td>resonating valence bond. 80, 83, 86, 96</td>
  </tr>
  <tr>
    <td>SCBA</td>
    <td>self-consistent Born approximation. 7, 9, 10, 56, 57, 59, 65, 72, 73, 75, 78, 82, 95, 108, 113, 114, 144</td>
  </tr>
  <tr>
    <td>SCOC</td>
    <td>Sr<sub>2</sub>CuCl<sub>2</sub>O<sub>2</sub>. 98</td>
  </tr>
  <tr>
    <td>SOC</td>
    <td>spin-orbit coupling. 121, 124, 128, 133</td>
  </tr>
  <tr>
    <td>STM</td>
    <td>scanning tunneling microscopy. 71, 137, 139</td>
  </tr>
  <tr>
    <td>STO</td>
    <td>SrTiO<sub>3</sub>. 8–10, 21, 97, 121–126, 133, 137, 139, 140, 145, 146</td>
  </tr>
  <tr>
    <td>t-CuO</td>
    <td>tetragonal CuO. 3, 5, 6, 8–10, 18, 19, 21, 39, 40, 46, 51, 53, 54, 57, 97–101, 104, 111, 114, 118–125, 137, 139, 140, 143–146, 154</td>
  </tr>
  <tr>
    <td>TB</td>
    <td>tight-binding. 23–25, 27, 67, 68</td>
  </tr>
  <tr>
    <td>TMO</td>
    <td>transition metal oxides. 8, 18–20, 23, 98</td>
  </tr>
  <tr>
    <td>UHB</td>
    <td>upper Hubbard band. 3, 114</td>
  </tr>
  <tr>
    <td>UHV</td>
    <td>ultra high vacuum. 70</td>
  </tr>
  <tr>
    <td>VASP</td>
    <td>Vienna ab initio simulation package. 67, 123–125</td>
  </tr>
</table>
<table><tr><td>VCA</td><td>variational cluster approximation. 6, 9, 99, 102, 118, 119, 146</td></tr><tr><td>XMCD</td><td>x-ray magnetic circular dichroïsm. 9, 10, 121–123, 125, 129, 131, 136, 137, 139, 145, 146</td></tr><tr><td>ZRS</td><td>Zhang-Rice singlets. 5, 23, 24, 27, 63, 67, 98, 108, 126, 143, 154</td></tr></table>
<figure><img src="image_76.png" /></figure>
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<figure><img src="image_77.png" /></figure>
**Titre** : Propriétés spectrales et magnétiques des oxydes de cuivre : vers une description théorique par les premiers principes

**Mots clés** : Cuprates, Système à électrons fortement corrélés, Théorie du Champ Moyen Dynamique, Théorie de la fonctionnelle de la densité, Spectroscopie par photoémission résolue en angle

**Résumé** : Si l'oxydation du cuivre peut être une malédiction pour les anciennes casseroles, c'est bénédiction pour le monde scientifique puisqu'elle est à l'origine de la famille des cuprates. Un champ entier de recherche s'est lancé pour comprendre pourquoi leur température critique supraconductrice est si élevée, découvrant au passage un diagramme de phase riche et complexe. Cependant, malgré les immenses efforts déployés par la communauté scientifique, un compréhension théorique globale fait toujours défaut. Dans cette thèse nous nous intéressons aux propriétés spectrales et magnétiques de deux oxydes de cuivres : $Ca_{2-x}Na_xCuO_2Cl_2$ (NaCCOC) et CuO tétragonal (t-CuO), en combinant la théorie fonctionnelle de la densité, la théorie du champ moyen dynamique appliquée aux amas (CDMFT), et la spectroscopie par photoémission résolue en angle.

Nous montrons d'abord le rôle essentiel des fluctuations antiferromagnétiques de spin dans les propriétés spectrales de NaCCOC non-dopé et dopé en trou. Le phénomène de "cascade" peut en effet être compris comme un

croisement entre une physique de polaron de spin et d'électrons localisés. Pour la gamme de dopage faible à intermédiaire, où nous observons un pseudogap, nous prouvons qu'il s'agit du produit de la suppression des excitations à basse énergie de l'amas dans le bain électronique auto-cohérent dû à des interférences destructives.

t-CuO est composé de plans CuO 2D, de symétrie tétragonal, qui se superposent au dessus d'un substrat de $SrTiO_3$ (STO). Nous démontrons que la forte répulsion de Coulomb locale est à l'origine du découplage des plans CuO en deux sous-réseaux $CuO_2$, phénomène observé expérimentalement mais encore inexpliqué. Dans le système dopé en trou, le découplage se traduit par un paramètre d'ordre supraconducteur ayant une symétrie $d_{xy}$ contrastant avec la symétrie $d_{x^2-y^2}$ usuelle pour les cuprates.

Enfin, nous montrons que la formation de lacunes en oxygène à l'interface t-CuO/STO peut expliquer les, a priori mystérieux, moments de spin paramagnétique et ceux orbitaux fixes observés en expérience.

**Title:** Spectral and magnetic properties of copper oxides: towards a theoretical description from first principles

**Keywords:** Cuprates, Strongly correlated systems, Dynamical Mean-Field Theory, Density Functional Theory, Angle-Resolved Photoemission Spectroscopy

**Abstract:** The oxidation of copper does not only lead to an unusable saucepan, but also to one of the most fascinating family of materials: the cuprates. Their large superconducting critical temperature first attracted the scientific community's attention, which led to the discovery of a rich and complex phase diagram. However a complete theoretical understanding is still missing. In this thesis, we investigate the spectral and magnetic properties of two copper oxide systems: $Ca_{2-x}Na_xCuO_2Cl_2$ (NaCCOC) and tetragonal CuO (t-CuO) using a combination of density functional theory, cellular dynamical mean-field theory (CDMFT) and angle-resolved photoemission spectroscopy.

We study the spectral properties of the undoped and hole-doped NaCCOC, and show that the antiferromagnetic spin fluctuations play a key role. We show that the waterfall feature observed experimentally and captured by our CDMFT calculations can be understood as a cross-over between a

spin-polaron and a localized electrons physics. At low to intermediate dopings, we argue that the pseudogap opens due to destructive interference of the low-energy excitations of the embedded cluster.

t-CuO is composed of two-dimensional CuO planes with a tetragonal symmetry, stacked above a $SrTiO_3$ (STO) substrate. We rationalize the experimentally observed decoupling of each of its CuO planes into two weakly-coupled $CuO_2$ sublattices as a consequence of the strong on-site Coulomb interaction. This translates upon doping into an unusual superconducting order parameter symmetry of type $d_{xy}$ instead of the usual $d_{x^2-y^2}$ found in cuprates.

Finally, we show that the formation of oxygen vacancies at the t-CuO/STO interface can explain the seemingly abnormal paramagnetic spin and pinned orbitals moments observed experimentally.