Mott Transition in the Two-Dimensional Hubbard Model

Kohno, Masanori

doi:10.1103/physrevlett.108.076401

Cited by 66 publications

(228 citation statements)

References 33 publications

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“…4. This agrees quantitatively with the previous results from ED [3], ED + cluster DMFT [35], and CPT [18] despite the fact that AFM order was not considered in these works. This shows that the appearance of AFM order doesn't affect total spectral weight transferred as the sum rule should be satisfied.…”

Section: Resultssupporting

confidence: 92%

Spectral evolution with doping of an antiferromagnetic Mott state

Lee

2017

Phys. Rev. B

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Since the discovery of half-filled cuprate to be a Mott insulator, the excitation spectra above the chemical potential for the unoccupied states has attracted many research attentions. There were many theoretical works using different numerical techniques to study this problem, but many have reached different conclusions. One of the reasons is the lack of very detailed high-resolution experimental results for the theories to be compared with. Recently, the scanning tunneling spectroscopy (STS)[1, 2] on lightly doped Mott insulator with an antiferromagnetic (AFM) order found the presence of in-gap states with energy of order half an eV above the chemical potential. The measured spectral properties with doping are not quite consistent with earlier theoretical works. In this paper we perform a diagonalization method on top of the variational Monte Carlo (VMC) calculation to study the evolution of AFM Mott state with doped hole concentration in the Hubbard model (HM). Our results found in-gap states that behave similarly with ones reported by STS. These in-gap states acquire a substantial amount of dynamical spectral weight transferred from the upper Hubbard band. The in-gap states move toward chemical potential with increasing spectral weight as doping increases. Our result also provides information about the energy scale of these in-gap states in relation with the coulomb coupling strength U.

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Section: Resultssupporting

confidence: 92%

Spectral evolution with doping of an antiferromagnetic Mott state

Lee

2017

Phys. Rev. B

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“…However, the precise origin of this phenomenon is not well understood due to the complex physics even in a minimal model used to describe the correlated nature of the electrons 1-3 : the 2D Hubbard model. It is often assumed that a first step in understanding the physics of this model is to study its spectral properties [4][5][6][7][8][9][10][11][12][13][14][15][16][17] in the simple undoped limit. The spectral function of the undoped 2D Hubbard model when the free electron bandwidth W is comparable to the Hubbard interaction U consists of two prominent features in the band structure, cf.…”

Section: Intorductionmentioning

confidence: 99%

Origin of strong dispersion in Hubbard insulators

et al. 2015

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Using cluster perturbation theory, we explain the origin of the strongly dispersive feature found at high binding energy in the spectral function of the Hubbard model. By comparing the Hubbard and t−J−3s model spectra, we show that this dispersion does not originate from either coupling to spin fluctuations (∝ J) or the free hopping (∝ t). Instead, it should be attributed to a long-range, correlated hopping ∝ t 2 /U , which allows an effectively free motion of the hole within the same antiferromagnetic sublattice. This origin explains both the formation of the high energy anomaly in the single-particle spectrum and the sensitivity of the high binding energy dispersion to the next-nearest-neighbor hopping t ′ .PACS numbers: 71.10. Fd, 74.72.Cj, I. INTORDUCTIONHigh-temperature superconductivity in the cuprate oxides has attracted significant attention over the past thirty years. However, the precise origin of this phenomenon is not well understood due to the complex physics even in a minimal model used to describe the correlated nature of the electrons [1][2][3] : the 2D Hubbard model. It is often assumed that a first step in understanding the physics of this model is to study its spectral properties 4-17 in the simple undoped limit. The spectral function of the undoped 2D Hubbard model when the free electron bandwidth W is comparable to the Hubbard interaction U consists of two prominent features in the band structure, cf. Fig. 1. At low binding energies (LBE), a sharply defined quasiparticle-like excitation disperses downward from (π/2, π/2) reaching an energy of the order of spin exchange J = 4t 2 /U near the Γ-point (0,0). This quasiparticle, often labeled the spin polaron (SP) 18 , represents a hole heavily dressed by spin excitations from the antiferromagnetic (AF) ground state with its bandwidth no longer governed by the free electron hopping t but by the spin exchange J 9,18-23 . At higher binding energies (HBE), another feature becomes prominent approaching the Γ-point. The delineation of the LBE spin polaron from the HBE feature has been widely associated with the "high energy anomaly" or "waterfall" seen in a number of cuprate photoemission results 11,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] . While the spin polaron is well understood, the characterization remains poor for the feature at higher energies. One may naively expect that a broad, non-dispersive Hubbard band should appear at the Γ-point. However, as shown in Fig. 1, it is clear that there is a sharp dispersion. Previous studies have attributed this feature to scenarios such as spin-charge separation 16,17,34,35,[41][42][43][44][45] or a weak-coupling spin-density wave 9,10,46 . However, these interpretations remain controversial.The aim of this paper is to understand the nature of the HBE feature and what separates it from the SP. Using cluster perturbation theory we examine both the Hubbard, t−J and t−J−3s models to provide an in-depth examination of what controls the quasiparticle dispersion and int...

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“…These moments serve to remove the time reversal symmetry, suppressing the coherent back-scattering of electrons. In 2D, the possibility of localized spin excitations at the Mott transition has been suggested theoretically [16,25], but without any experimental evidence so far.…”

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confidence: 99%

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confidence: 99%

“…Since each dopant P atom contributes one valence electron, the impurity band is intrinsically 'half filled' (schematic in Fig. 1a), which reinforces the interaction effects due to the inbuilt electron-hole symmetry, and forms an ideal platform to explore the rich phenomenology of the 2D MottHubbard model, ranging from Mott metal-insulator transition (MIT) to novel spin excitations and magnetic ordering [14][15][16][17].In this Letter we show evidence of spontaneously broken time reversal symmetry in 2D Si:P and Ge:P δ-layers as the on-site effective Coulomb interaction is increased by decreasing the doping density of P atoms. Quantum transport and noise experiments indicate a strong suppression of quantum interference effects at low doping densities.…”

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confidence: 99%

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Spontaneous Breaking of Time-Reversal Symmetry in Strongly Interacting Two-Dimensional Electron Layers in Silicon and Germanium

et al. 2014

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We report experimental evidence of a remarkable spontaneous time reversal symmetry breaking in two dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P δ−layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, providing a microscopic mechanism for spontaneous lifting of the time reversal symmetry. Our experiments suggest the emergence of a new many-body quantum state when two dimensional electrons are confined to narrow half-filled impurity bands.Invariance to time reversal is among the most fundamental and robust symmetries of nonmagnetic quantum systems. Its violation often leads to new and exotic phenomena, particularly in two dimensions (2D), such as the quantized Hall conductance in semiconductor heterostructures [1], the quantum anomalous Hall effect in topological insulators [2] or the predicted chiral superconductivity in graphene [3]. The breaking of time reversal invariance is experimentally achieved either by an external magnetic field or intentional magnetic doping. Here we show that strong Coulomb interactions can also lift the time reversal symmetry in nonmagnetic 2D systems at zero magnetic field.While bulk P-doped Si and Ge have been extensively studied in the context of electron localization in three dimensions [4][5][6][7][8][9], confining the dopants to one or few atomic planes (δ−layers) of the host semiconductor has recently led to a new class of 2D electron system [10][11][12][13]. Electron transport in these atomically confined 2D layers occurs within a 2D impurity band where the effective Coulomb interaction is parameterized in terms of U/γ, with U being the Coulomb energy required to add an additional electron to a dopant site, and γ, the hopping integral between adjacent dopants. Since each dopant P atom contributes one valence electron, the impurity band is intrinsically 'half filled' (schematic in Fig. 1a), which reinforces the interaction effects due to the inbuilt electron-hole symmetry, and forms an ideal platform to explore the rich phenomenology of the 2D MottHubbard model, ranging from Mott metal-insulator transition (MIT) to novel spin excitations and magnetic ordering [14][15][16][17].In this Letter we show evidence of spontaneously broken time reversal symmetry in 2D Si:P and Ge:P δ-layers as the on-site effective Coulomb interaction is increased by decreasing the doping density of P atoms. Quantum transport and noise experiments indicate a strong suppression of quantum interference effects at low doping densities. We could attribute this to a spontaneous breaking of time reversal symmetry which manifest in an unambiguous suppression of universal conductance fluctuations (UCF) at zero magnetic fiel...

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Mott Transition in the Two-Dimensional Hubbard Model

Cited by 66 publications

References 33 publications

Spectral evolution with doping of an antiferromagnetic Mott state

Spectral evolution with doping of an antiferromagnetic Mott state

Origin of strong dispersion in Hubbard insulators

Spontaneous Breaking of Time-Reversal Symmetry in Strongly Interacting Two-Dimensional Electron Layers in Silicon and Germanium

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