Quantum simulations can provide new insights into the physics of strongly correlated electronic systems. A well studied system, but still open in many regards, is the Hubbard-Holstein Hamiltonian, where electronic repulsion is in competition with attraction generated by the electron-phonon coupling. In this context we study the phase diagram of four quantum dots in a suspended carbon nanotube and coupled to its flexural degrees of freedom. The system is described by a Hamiltonian of the Hubbard-Holstein class, where electrons on different sites interact with the same phonon. We find that the system presents a transition from the Mott insulating state to a polaronic state, with the appearance of pairing correlations and the breaking of the translational symmetry. Our study shows that this system thus constitutes a relevant example of a correlated system that could be studied by experimental realization.
Quantum dots placed along a vibrating nanotube provide a quantum simulation platform that can directly address the electron-phonon interaction. This offers promising prospects for the search of new quantum materials and the study of strong correlation effects. As this platform is naturally operated by coupling the dots to an electronic reservoir, state preparation is straightforwardly achieved by driving into the steady state. Here we show that for intermediate electron-phonon coupling strength, the system with spin-polarized quantum dots undergoes a Peierls transition into an insulating regim…
We describe a quantum simulator for the Hubbard--Holstein model (HHM), comprising two dressed Rydberg atom species held in a monolayer by independent painted potentials, predicting that boson-mediated preformed pairing, and Berezinskii--Kosterlitz--Thouless (BKT) transition temperatures are experimentally accessible. The HHM is important for modeling the essential physics of unconventional superconductors. Experimentally realizable quantum simulators for HHMs are needed: (1) since HHMs are difficult to solve numerically and analytically, (2) to explore how competition between electron-phonon i…
Identifying the microscopic mechanism for superconductivity in magic-angle twisted bilayer graphene (MATBG) is an outstanding open problem. While MATBG exhibits a rich phase-diagram, driven partly by the strong interactions relative to the electronic bandwidth, its single-particle properties are unique and likely play an important role in some of the phenomenological complexity. Some of the salient features include an electronic bandwidth smaller than the characteristic phonon bandwidth and a non-trivial structure of the underlying Bloch wavefunctions. We perform a theoretical study of the coo…
Effects of short-range correlations on the Coulomb screening and the pairing interactions in electron-phonon systems - triplet pairing mediated by phonons
Density-matrix renormalization group study of pairing when electron-electron and electron-phonon interactions coexist: effect of the electronic band structure
We investigate formation and condensation of fermion pairs in cold-atom quantum simulators for extended Hubbard models ($UV$ models) with body-centered-cubic (BCC) optical lattices in the dilute limit, predicting small and light pairs. Pair mass, radius, and binding conditions are calculated, and used to compute transition temperatures. We predict that: (a) local pairs form in BCC optical lattices and binding energies can be large; (b) for particular cases where onsite $U$ and intersite $V$ are attractive with similar size, pairs are both small and light; and (c) pairs of $^6$Li atoms Bose--Ei…
A Unified Description of Superconductivity: Electron Density Dynamic's Response to Phonons at the Brillouin Zone Boundary Driven Real Space Electron-Hole Pairing Characterized by CP Symmetry
认为电子密度动力学对布里渊区边界声子的响应是MgB 2超导机制的关键因素，也是导致具有CP对称性的真实空间电子-空穴配对的所有超导化合物的关键因素（Charge and Parity symmetries）电子密度差的第一性原理计算是通过减去布里渊区边界处的纵向声学声子使晶体的电子密度与完美晶体的电子密度发生扭曲。从局域极化率和声子引起的电荷离域转移的角度讨论了这种电子密度动态响应这种扭曲的根源，这种扭曲导致了实空间中具有CP对称性特征的电子空穴配对。畸变驱动的轨道杂化动力学变化。这种方法也为寻找新的超导体提供了明确和快速的指导方针。
We propose a new Rashba-free mechanism to realize topological superconductivity with electron-phonon interaction. In the presence of a magnetic field, electron-phonon interaction with small momentum transfer is found to favor spin-triplet Cooper pairing. This process facilitates the formation of chiral topological superconductivity even when Rashba spin-orbital coupling is absent. As a proof of concept, we propose an experimentally feasible heterostructure to systematically study the entangled relationship among forward-phonon scatterings, Rashba spin-orbital couplings, pairing symmetries, and…
Starting from a continuum-model description, we develop a microscopic weak-coupling theory for superconductivity in twisted double-bilayer graphene. We study both electron-phonon and entirely electronic pairing mechanisms. In each case, the leading superconducting instability transforms under the trivial representation, $A$, of the point group $C_3$ of the system, while the subleading pairing phases belong to the $E$ channel. We explicitly compute the momentum dependence of the associated order parameters and find that the leading state has no nodal points for electron-phonon pairing but exhib…
Pairing interactions and pairing mechanism in high temperature copper oxide superconductors
在未掺杂的母体铜氧化物的极化子结合能E_{p}已被确定为约1.0 eV的反铁磁有序温度的非常规氧同位素效应。推导出的E_{p}值与由独立光学数据估计的值和由测量的介电常数理论估计的值在定量上是一致的。在最佳掺杂的铜酸盐中观察到的面内超载流子质量上的大量氧同位素效应表明极化子被束缚到库珀对中。我们还确定了声子模式，强烈耦合到传导电子的角度分辨的光电子能谱，隧穿光谱，和光学数据。我们一贯表明，有一个非常强的电子-声子耦合功能，在声子能量约20毫电子伏沿波腹方向，这种耦合变得越来越弱的对角方向。我们进一步指出，铜酸盐的高温超导电性是由强的电子-声子耦合、极化子效应以及与2 eV Cu-O电荷转移涨落的显著耦合引起的。
Odd-parity superconductivity from phonon-mediated pairing: Application to Cu$_x$Bi$_2$Se$_3$
受Cu $_x$ Bi $_2$ Se $_3$中提出的拓扑态的启发，我们研究了具有时间反转和反转对称性的自旋轨道耦合系统中声子介导奇宇称超导的可能性.对于这样的系统，我们表明，在一般情况下，纯电子-声子耦合永远不会导致一个三重态具有较高的临界温度比领先的单重态。库仑赝势是电子-电子相互作用的排斥部分，在弱关联系统中通常很小，因此对稳定三重态至关重要。我们引入了一个手征性量子数，它将最有利于三重态通道的电子-声子顶点相互作用确定为那些保持手征性的顶点相互作用。将这些结果应用于Cu $_x$ Bi $_2$ Se $_3$，我们发现，如果保持手征的电子-声子顶点比手征翻转的顶点强得多，则在弱电子关联下可以实现声子介导的奇宇称态.
Motivated by the observation of two distinct superconducting phases in the moiréless ABC-stacked rhombohedral trilayer graphene, we investigate the electron-acoustic-phonon coupling as a possible pairing mechanism. We predict the existence of superconductivity with the highest $T_c\sim 3$K near the Van Hove singularity. Away from the Van Hove singularity, $T_c$ remains finite in a wide range of doping. In our model, the $s$-wave spin-singlet and $f$-wave spin-triplet pairings yield the same $T_c$, while other pairing states have negligible $T_c$. Our theory provides a simple explanation for th…
Magic-angle twisted bilayer graphene exhibits a panoply of many-body phenomena that are intimately tied to the appearance of narrow and well-isolated electronic bands. The microscopic ingredients that are responsible for the complex experimental phenomenology include electron-electron (phonon) interactions and non-trivial Bloch wavefunctions associated with the narrow bands. Inspired by recent experiments, we focus on two independent quantities that are considerably modified by Coulomb interaction driven band renormalization, namely the density of states and the minimal spatial extent associat…
Programmable Polaron Models and Tomography in Trapped-Ion Quantum Simulators
Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；IBM Quantum, IBM Research – Zurich（IBM量子，IBM苏黎世研究中心）；Department of Physics and Astronomy and Smalley-Curl Institute, Rice University（莱斯大学天体物理学与天文系及Smalley-Curl研究所）；California Institute of Technology（加州理工学院）
A consistent microscopic theory of superconductivity for strongly correlated electronic systems is presented. The Dyson equation for the normal and anomalous Green functions for the projected (Hubbard) electronic operators is derived. To compare various mechanisms of pairing, the extended Hubbard model is considered where the intersite Coulomb repulsion and the electron-phonon interaction are taken into account. We obtain the $d$-wave pairing with high-$T_c$ induced by the strong kinematical interaction of electrons with spin fluctuations, while the Coulomb repulsion and the electron-phonon in…
