Higher-Order Topological Mott Insulators

Kudo, K.; Yoshida, Tsuneya; Hatsugai, Yasuhiro

doi:10.1103/physrevlett.123.196402

Cited by 94 publications

(48 citation statements)

References 69 publications

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“…When the surface states of a 3DFOTI are gapped, the intersection of two surfaces of different topological classes, i.e., a hinge, has topologically nontrivial chiral hinge states, leading to a so-called 3D second-order topological insulator (3DSOTI). The well-accepted paradigm is that a d-dimensional material can be a (d − n)th-order topological insulator with 1 n d so that all states in submanifolds, whose dimensions are greater than (d − n + 1), are gapped whereas states are gapless on, at least, one submanifold of dimension (d − n) [19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Disorder-induced quantum phase transitions in three-dimensional second-order topological insulators

Wang

2020

Phys. Rev. Research

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Disorder effects on three-dimensional second-order topological insulators (3DSOTIs) are investigated numerically and analytically. The study is based on a tight-binding Hamiltonian for noninteracting electrons on a cubic lattice with a reflection symmetry that supports a 3DSOTI in the absence of disorder. Interestingly, unlike the disorder effects on a topological trivial system that can only be either a diffusive metal (DM) or an Anderson insulator (AI), disorders can sequentially induce four phases of 3DSOTIs, three-dimensional first-order topological insulators (3DFOTIs), DMs, and AIs. At a weak disorder when the on-site random potential of strength W is below a low critical value W c1 at which the gap of surface states closes while the bulk sates are still gapped, the system is a disordered 3DSOTI characterized by a constant density of states and a quantized integer conductance of e 2 /h through its chiral hinge states. The gap of the bulk states closes at a higher critical disorder W c2 , and the system is a disordered 3DFOTI in a lower intermediate disorder between W c1 and W c2 in which electron conduction is through the topological surface states. The system becomes a DM in a higher intermediate disorder between W c2 and W c3 above which the states at the Fermi level are localized. It undergoes a normal three-dimensional metal-to-insulator transition at W c3 and becomes the conventional AI for W > W c3. The self-consistent Born approximation allows one to see how the density of bulk states and the Dirac mass are modified by the on-site disorders.

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Section: Introductionmentioning

confidence: 99%

Disorder-induced quantum phase transitions in three-dimensional second-order topological insulators

Wang

2020

Phys. Rev. Research

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“…In a later influential paper[30], Qi et al pointed out that quantum anomalous Hall insulator (QAHI)/SC heterostructures provide a simple realization of 2d chiral TSCs which harbor not only vortex-core MZMs, but also chiral Majorana edge modes. These two theoretical works have triggered a lot of experimental works on TI(QAHI)/SC heterostructures [28,29,[31][32][33][34][35][36][37][38][39][40][41], and remarkable progress in detecting vortex-core MZMs has been witnessed in recent years [28,29,40,41].Very recently, TIs and TSCs have been generalized to include their higher-order counterparts [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Importantly, higher-order TIs (HOTIs) and TSCs (HOTSCs) have extended the conventional bulk-boundary correspondence.…”

mentioning

confidence: 99%

“…Very recently, TIs and TSCs have been generalized to include their higher-order counterparts [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Importantly, higher-order TIs (HOTIs) and TSCs (HOTSCs) have extended the conventional bulk-boundary correspondence.…”

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confidence: 99%

Majorana corner and hinge modes in second-order topological insulator/superconductor heterostructures

Yan

2019

Phys. Rev. B

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As platforms of Majorana modes, topological insulator (quantum anomalous Hall insulator)/superconductor (SC) heterostructures have attracted tremendous attention over the past decade. Here we substitute the topological insulator by its higher-order counterparts. Concretely, we consider second-order topological insulators (SOTIs) without time-reversal symmetry and investigate SOTI/SC heterostructures in both two and three dimensions. Remarkably, we find that such novel heterostructures provide natural realizations of second-order topological superconductors (SOTSCs) which host Majorana corner modes in two dimensions and chiral Majorana hinge modes in three dimensions. As here the realization of SOTSCs requires neither special pairings nor magnetic fields, such SOTI/SC heterostructures are outstanding platforms of Majorana modes and may have wide applications in future.Over the past decade, topological superconductors (TSCs) have attracted continuous and tremendous attention[1-9]. Among various TSCs, one-dimensional (1d) and twodimensional (2d) TSCs without time-reversal symmetry (TRS) have attracted particular interest as they harbor Majorana zero modes (MZMs) at their boundaries[10-12] and in the cores of vortices [13][14][15][16], respectively. Owing to their fractional nature, MZMs are ideal candidates to construct nonlocal qubits immune to local decoherence[10]. Moreover, owing to their non-Abelian statistics [17], their braiding operations are found to realize elementary quantum gates. Thus, MZMs are believed to be building blocks of topological quantum computation [18] and have been actively sought in experiments [19][20][21][22][23][24][25][26][27][28][29].As is known, odd-parity superconductors (SCs) provide natural realizations of TSCs, however, they are unfortunately rare in nature. In a seminal paper [14], Fu and Kane pointed out that topological insulator (TI)/SC heterostructures provide an effective realization of odd-parity superconductivity. Accordingly, in the presence of magnetic field, vortices emerging in such heterostructures are found to carry MZMs. In a later influential paper[30], Qi et al pointed out that quantum anomalous Hall insulator (QAHI)/SC heterostructures provide a simple realization of 2d chiral TSCs which harbor not only vortex-core MZMs, but also chiral Majorana edge modes. These two theoretical works have triggered a lot of experimental works on TI(QAHI)/SC heterostructures [28,29,[31][32][33][34][35][36][37][38][39][40][41], and remarkable progress in detecting vortex-core MZMs has been witnessed in recent years [28,29,40,41].Very recently, TIs and TSCs have been generalized to include their higher-order counterparts [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Importantly, higher-order TIs (HOTIs) and TSCs (HOTSCs) have extended the conventional bulk-boundary correspondence. Accordingly, an n-th order TI or TSC in d dimensions host (d − n)dimensional boundary modes. For instance, a second-order TI (SOTI) in 2d and 3d host zero-dimensional (0d) corner modes an...

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“…The studies of the HOTI have not always been material-oriented 23 – 28 , but also have covered a wide range of models 21 , 22 , 29 – 49 and experimental setups 50 – 57 . Among them, three of the present authors proposed a tailored model to investigate the correlation effects on the HOTI in and found a correlated topological state dubbed as a higher-order topological Mott insulator (HOTMI), in which gapless corner modes emerge only in spin excitations 45 .…”

Section: Introductionmentioning

confidence: 99%

Higher-order topological Mott insulator on the pyrochlore lattice

Otsuka

Yoshida

Kudo

et al. 2021

Sci Rep

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We provide the first unbiased evidence for a higher-order topological Mott insulator in three dimensions by numerically exact quantum Monte Carlo simulations. This insulating phase is adiabatically connected to a third-order topological insulator in the noninteracting limit, which features gapless modes around the corners of the pyrochlore lattice and is characterized by a $${\mathbb {Z}}_{4}$$ Z 4 spin-Berry phase. The difference between the correlated and non-correlated topological phases is that in the former phase the gapless corner modes emerge only in spin excitations being Mott-like. We also show that the topological phase transition from the third-order topological Mott insulator to the usual Mott insulator occurs when the bulk spin gap solely closes.

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Higher-Order Topological Mott Insulators

Cited by 94 publications

References 69 publications

Disorder-induced quantum phase transitions in three-dimensional second-order topological insulators

Disorder-induced quantum phase transitions in three-dimensional second-order topological insulators

Majorana corner and hinge modes in second-order topological insulator/superconductor heterostructures

Higher-order topological Mott insulator on the pyrochlore lattice

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