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            <title xml:lang="en">Correlated Insulators, Density Wave States, and Their Nonlinear Optical Response in Magic-Angle Twisted Bilayer Graphene</title>
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                <forename type="first">Shihao</forename>
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                <forename type="first">Jianpeng</forename>
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            <funder>National Key Research and Development Program of China, NKRDPC, (2020YFA0309601)</funder>
            <funder>ShanghaiTech University</funder>
            <funder>National Natural Science Foundation of China, NSFC, (12174257)</funder>
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              <date type="whenSubmitted">2025-02-13 09:56:55</date>
              <date type="whenModified">2025-03-21 11:48:01</date>
              <date type="whenReleased">2025-02-13 09:56:55</date>
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                    <forename type="first">Jianpeng</forename>
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                <term xml:lang="en">Density waves</term>
                <term xml:lang="en">Graphene</term>
                <term xml:lang="en">Nonlinear optics</term>
                <term xml:lang="en">Probes</term>
                <term xml:lang="en">Bilayer Graphene</term>
                <term xml:lang="en">Chern numbers</term>
                <term xml:lang="en">Experimental probes</term>
                <term xml:lang="en">Optical conductivity</term>
                <term xml:lang="en">Wave state</term>
                <term xml:lang="en">Twisted bilayers</term>
                <term xml:lang="en">Research interests</term>
                <term xml:lang="en">Nonlinear optical response</term>
                <term xml:lang="en">Magic angle</term>
                <term xml:lang="en">Fractional filling</term>
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              <p>The correlated insulator (CI) states and the recently discovered density wave (DW) states in magic-angle twisted bilayer graphene (TBG) have stimulated intense research interest. However, to date, the nature of these "featureless"correlated states with zero Chern numbers are still elusive and lack a characteristic experimental signature. Thus, an experimental probe to identify the characters of these featureless CI and DW states is urgently needed. In this Letter, we theoretically study the correlated insulators and density wave states at different integer and fractional fillings of the flat bands in magic-angle TBG based on extended unrestricted Hartree-Fock calculations including the Coulomb screening effects from the remote bands. We further investigate the nonlinear optical response of the various correlated states and find that the nonlinear optical conductivities can be used to identify the nature of these CI and DW states at most of the fillings. Therefore, we propose that a nonlinear optical response can serve as a promising experimental probe for unveiling the nature of the CI and DW states observed in magic-angle TBG.</p>
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