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Abolhassan Vaezi

Publications and source records attributed to Abolhassan Vaezi.

At least 37 records · Page 2Linked to original sources
arXiv2017

Numerical Observation of Parafermion Zero Modes and their Stability in 2D Topological States

The possibility of realizing non-Abelian excitations (non-Abelions) in two-dimensional (2D) Abelian states of matter has generated a lot of interest recently. A well-known example of such non-Abelions are parafermion zeros modes (PFZMs) which can be realized at the endpoints of the so called genons in fractional quantum Hall (FQH) states or fractional Chern insulators (FCIs). In this letter, we discuss some known signatures of PFZMs and also introduce some novel ones. In particular, we show that the topological entanglement entropy (TEE) shifts by a quantized value after crossing PFZMs. Utilizing those signatures, we present the first large scale numerical study of PFZMs and their stability against perturbations in both FQH states and FCIs within the density-Matrix-Renormalization-Group (DMRG) framework. Our results can help build a closer connection with future experiments on FQH states with genons.

cond-mat.str-el↗
arXiv2017

Topological superconductivity in monolayer transition metal dichalcogenides

Theoretically it has been known that breaking spin-degeneracy and effectively realizing 'spinless fermions' is a promising path to topological superconductors. Yet, topological superconductors are rare to date. Here, we propose to realize spinless fermions by splitting the spin-degeneracy in momentum space. Specifically, we identify monolayer hole-doped transition metal dichalcogenide (TMD)s as candidates for topological superconductors out of such momentum-space-split spinless fermions. Although electron-doped TMDs have recently been found superconducting, the observed superconductivity is unlikely topological due to the near spin-degeneracy. Meanwhile, hole-doped TMDs with momentum-space-split spinless fermions remain unexplored. Employing a renormalization group analysis, we propose that the unusual spin-valley locking in hole-doped TMDs together with repulsive interactions selectively favors two topological superconducting states: inter-pocket paired state with Chern number 2 and intra-pocket paired state with finite pair-momentum. A confirmation of our predictions will open up possibilities for manipulating topological superconductors on the device friendly platform of monolayer TMDs.

cond-mat.supr-con↗
arXiv2016

Spin-Torque Generation in Topological-Insulator-Based Heterostructures

Heterostructures utilizing topological insulators exhibit a remarkable spin-torque efficiency. However, the exact origin of the strong torque, in particular whether it stems from the spin-momentum locking of the topological surface states or rather from spin-Hall physics of the topological-insulator bulk remains unclear. Here, we explore a mechanism of spin-torque generation purely based on the topological surface states. We consider topological-insulator-based bilayers involving ferromagnetic metal (TI/FM) and magnetically doped topological insulators (TI/mdTI), respectively. By ascribing the key theoretical differences between the two setups to location and number of active surface states, we describe both setups within the same framework of spin diffusion of the non-equilibrium spin density of the topological surface states. For the TI/FM bilayer, we find large spin-torque efficiencies of roughly equal magnitude for both in-plane and out-of-plane spin torques. For the TI/mdTI bilayer, we elucidate the dominance of the spin-transfer-like torque. However, we cannot explain the orders of magnitude enhancement reported. Nevertheless, our model gives an intuitive picture of spin-torque generation in topological-insulator-based bilayers and provides theoretical constraints on spin-torque generation due to topological surface states.

cond-mat.mes-hall↗
arXiv2016

Measurement of topological invariants in a 2D photonic system

A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting quantum Hall model, edge modes manifest as mid-gap states between two topologically distinct bulk bands. The bulk-boundary correspondence dictates that the number of chiral edge modes, a topological invariant called the winding number, is completely determined by the bulk topological invariant, the Chern number. Here, for the first time, we measure the winding number in a 2D photonic system. By inserting a unit flux quantum at the edge, we show that the edge spectrum resonances shift by the winding number. This experiment provides a new approach for unambiguous measurement of topological invariants, independent of the microscopic details, and could possibly be extended to probe strongly correlated topological orders.

cond-mat.mes-hall↗
arXiv2015

Phase diagram of $ν=\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings

We present the quantitative phase diagram of the bilayer bosonic fractional quantum Hall system on the torus geometry at total filling factor $ν=1$ in the lowest Landau level. We consider short-range interactions within and between the two layers, as well as the inter-layer tunneling. In the fully polarized regime, we provide an updated detailed numerical analysis to establish the presence of the Moore-Read phase of both even and odd numbers of particles. In the actual bilayer situation, we find that both inter-layer interactions and tunneling can provide the physical mechanism necessary for the low-energy physics to be driven by the fully polarized regime, thus leading to the emergence of the Moore-Read phase. Inter-layer interactions favor a ferromagnetic phase when the system is $SU(2)$ symmetric, while the inter-layer tunneling acts as a Zeeman field polarizing the system. Besides the Moore-Read phase, the $(220)$ Halperin state and the coupled Moore-Read state are also realized in this model. We study their stability against each other.

cond-mat.str-el↗
arXiv2015

Non-Abelian phases in two-component $ν=2/3$ fractional quantum Hall states: Emergence of Fibonacci anyons

Recent theoretical insights into the possibility of non-Abelian phases in $ν=2/3$ fractional quantum Hall states revived the interest in the numerical phase diagram of the problem. We investigate the effect of various kinds of two-body interlayer couplings on the $(330)$ bilayer state and exactly solve the Hamiltonian for up to $14$ electrons on sphere and torus geometries. We consider interlayer tunneling, short-ranged repulsive/attractive pseudopotential interactions and Coulomb repulsion. We find a 6-fold ground-state degeneracy on the torus when the interlayer hollow-core interaction is dominant. To identify the topological nature of this phase we measure the orbital-cut entanglement spectrum, quasihole counting, topological entanglement entropy, and wave-function overlap. Comparing the numerical results to the theoretical predictions, we interpret this 6-fold ground-state degeneracy phase to be the non-Abelian bilayer Fibonacci state.

cond-mat.str-el↗
arXiv2014

Superconducting proximity effect in topological metals

Much interest in the superconducting proximity effect in three-dimensional (3D) topological insulators (TIs) has been driven by the potential to induce Majorana bound states at the interface. Most candidate materials for 3D TI, however, are bulk metals, with bulk states at the Fermi level coexisting with well-defined surface states exhibiting spin-momentum locking. In such topological metals, the proximity effect can differ qualitatively from that in TIs. By studying a model topological metal-superconductor (TM-SC) heterostructure within the Bogoliubov-de Gennes formalism, we show that the pair amplitude reaches the naked surface, unlike in a topological insulator-superconductor (TI-SC) heterostructure where it is confined to the interface. Furthermore, we predict vortex-bound-state spectra to contain a Majorana zero-mode localized at the naked surface, separated from the bulk vortex-bound-state spectra by a finite energy gap in such a TM-SC heterostructure. These naked-surface-bound modes are amenable to experimental observation and manipulation, presenting advantages of TM-SC over TI-SC.

cond-mat.supr-con↗
arXiv2014

Fibonacci Anyons From Abelian Bilayer Quantum Hall States

The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this paper, we consider a simple bilayer fractional quantum Hall (FQH) system with the $1/3$ Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous `Fibonacci'anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at $ν= 2/3$ in bilayers, as past experiments may not have definitively ruled them out.

cond-mat.str-el↗
arXiv2014

$Z_3$ generalization of the Kitaev's spin-1/2 model

We generalize the Kitaev's spin-1/2 model on the honeycomb by introducing a two-dimensional $Z_3$ clock model on the triangular lattice with three body interaction. We discuss various properties of this model and show that the low energy theory of the $Z_3$ generalized Kitaev model (GKM) is described by a single $Z_3$ parafermion per lattice site coupled to a $Z_3$ gauge field. We also introduce a slave-fermion approach for this GKM, treat the resulting fermionic Hamiltonian at the mean-field level, solve the mean field parameters self-consistently, and obtain the low energy effective Chern-Simons (CS) gauge theory. The resulting CS gauge theory is identical to that of a (221) fractional quantum Hall state. We then go beyond the mean-field approximation and demonstrate that fluctuations generate a uniform interlayer pairing for the dual (221) bilayer state. We argue that this perturbed system can undergo a phase transition to the Fibonacci phase by tuning the interlayer pairing strength.

cond-mat.str-el↗
arXiv2014

Superconducting analogue of the parafermion fractional quantum Hall states

Read and Rezayi $Z_k$ parafermion wavefunctions describe $ν=2+\frac{k}{kM+2}$ fractional quantum Hall (FQH) states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this paper, we study the $ν=2/k$ FQH-superconductor heterostructure and find the superconducting analogue of the $Z_k$ parafermion FQH state. Our main tool is the mapping of the FQH into coupled one-dimensional (1D) chains each with a pair of counter-propagating modes. We show that by inducing intra-chain pairing and charge preserving backscattering with identical couplings, the 1D chains flow into gapless $Z_{k}$ parafermions when $k< 4$. By studying the effect of inter-chain coupling, we show that every parafermion mode becomes massive except for the two outermost ones. Thus, we achieve a fractional topological superconductor whose chiral edge state is described by a $Z_k$ parafermion conformal field theory. For instance, we find that a $ν=2/3$ FQH in proximity to a superconductor produces a $Z_3$ parafermion superconducting state. This state is topologically indistinguishable from the non-Abelian part of the $ν=12/5$ Read-Rezay state. Both of these systems can host Fibonacci anyons capable of performing universal quantum computation through braiding operations.

cond-mat.str-el↗
arXiv2013

UV-IR transmutation for hybrid realizations of Z_k parafermion systems

Recent experiments brought Majorana particles closer to reality and raised interest in realizing $\mathbb{Z}_k$ parafermions for general value of $k$ in hybrid structures. Of particular interest is the prospect of realizing a two dimensional system with the edge states described by $\mathbb{Z}_k$ parafermion conformal field theory (CFT) by coupling one dimensional hybrid systems. However in order to understand the effective perturbation due to local inter-wire coupling, it is crucial to relate short distance ultra-violet (UV) degrees of freedom to primary fields of the CFT describing long distance infra-red (IR) physics. Here we consider two recent proposals for realizing a one dimensional system described by $\mathbb{Z}_k$ parafermion CFT upon tuning to quantum critical points: a parafermion chain and a pair of $ν=2/k$ quantum Hall chiral edge states under uniform backscattering and pairing, where the latter is represented by self-dual sine-Gordon model. We explicitly derive the relation between distinct UV degrees of freedom relevant for each proposals and the primary fields of $\mathbb{Z}_3$ parafermion CFT. Our results point to a marked difference in the effect of local coupling between wires represented by each proposals, regarding robustness of the edge states in the resulting two dimensional systems.

cond-mat.str-el↗
arXiv2013

Topological kink states at a tilt boundary in gated multi-layer graphene

The search for new realization of topologically protected edge states is an active area of research. We show that a tilt boundary in gated multi-layer graphene supports topologically protected gapless kink states, associated with quantum valley Hall insulator (QVH). We investigate such kink states from two perspectives: the microscopic perspective of a tight-binding model and an ab-initio calculation on bilayer, and the perspective of symmetry protected topological (SPT) states for general multi-layer. We show that a AB-BA bilayer tilt boundary supports gapless kink states that are undeterred by strain concentrated at the boundary. Further, we establish the kink states as concrete examples of edge states of {\it time-reversal symmetric} ${\mathbb Z}$-type SPT, protected by no valley mixing, electron number conservation, and time reversal $T$ symmetries. This allows us to discuss possible phase transitions upon symmetry changes from the SPT perspective. Recent experimental observations of a network of such tilt boundaries suggest that transport through these novel topological kink states might explain the long standing puzzle of sub-gap conductance. Further, recent observation of gap closing and re-opening in gated bi-layer might be the first example of a transition between two distinct SPT's: QVH and LAF.

cond-mat.mes-hall↗
arXiv2013

Fractional topological superconductors with fractionalized Majorana fermions

In this paper, we introduce a two-dimensional fractional topological superconductor (FTSC) as a strongly correlated topological state which can be achieved by inducing superconductivity into an Abelian fractional quantum Hall state, through the proximity effect. When the proximity coupling is weak, the FTSC has the same topological order as its parent state and is thus Abelian. However, upon increasing the proximity coupling, the bulk gap of such an Abelian FTSC closes and reopens resulting in a new topological order: a non-Abelian FTSC. Using several arguments we will conjecture that the conformal field theory (CFT) that describes the edge state of the non-Abelian FTSC is $U(1)/Z_2$ orbifold theory and use this to write down the ground-state wave function. Further, we predict FTSC based on the Laughlin state at $ν=1/m$ filling to host fractionalized Majorana zero modes bound to superconducting vortices. These zero modes are non-Abelian quasiparticles which is evident in their quantum dimension of $d_m=\sqrt{2m}$. Using the multi-quasi-particle wave function based on the edge CFT, we derive the projective braid matrix for the zero modes. Finally, the connection between the non-Abelian FTSCs and the $Z_{2m}$ rotor model with a similar topological order is illustrated.

cond-mat.str-el↗
arXiv2011

Slave-spin approach to the strongly correlated systems

In this paper, we develop a new type of slave particle method which is similar to the slave rotor model except that the quantum rotor is substituted by a spin one slave particle. The spin-one slave particle itself can be represented in terms of Schwinger bosons/fermions. This approach is more conveniently applicable to the strongly correlated Hamiltonians with on-site Hubbard interaction and resolves the limitations of using the slave rotor model as well as the Anderson-Zou slave particle technique. For instance, the mean-field parameters of the slave spin method do not vanish above the Mott transition and this approach is smoothly connected to the non-interacting limit. As an example, we study the phase diagram of the Kane-Mele-Hubbard model using our current approach. In the absence of the spin-orbit interaction, the Mott transition occurs at $U_c ~ 3 t_1$. Several aspects of the slave spin method, its gauge theory and various possible mean-field states associated with this approach have been discussed.

cond-mat.str-el↗
arXiv2011

Doping the Kane-Mele-Hubbard model: A Slave-Boson Approach

We study the Kane-Mele-Hubbard model both at half-filling and away from half-filling using a slave-boson mean-field approach at zero temperature. We obtain a phase diagram at half-filling and discuss its connection to recent results from quantum Monte Carlo, slave-rotor, and $Z_2$ mean-field studies. In particular, we find a small window in parameter space where a spin liquid phase with gapped spin and charge excitations reside. Upon doping, we show the spin liquid state becomes a superconducting state by explicitly calculating the singlet pairing order parameters. Interestingly, we find an "optimal" doping for such superconductivity. Our work reveals some of the phenomenology associated with doping an interacting system with strong spin-orbit coupling.

cond-mat.str-el↗
arXiv2011

Electron-phonon interaction in the strongly correlated systems and its implications on the high Tc cuprates

The theory of electron-phonon interaction in the presence of strong correlation has been investigated in the present work. Due to the so called spin-charge separation, it is argued that the electron-phonon interaction in the strongly interacting systems is fundamentally different from the weakly interacting counterparts. Both spinons and holons are shown to carry electric charge and couple to the electromagnetic field and consequently to phonons. A systematic approach to calculate the dynamical charge of spinons and holons is presented, followed by a discussion of implications of this model for the high temperature superconductors. It is demonstrated that the unusual oxygen isotope effect in high Tc materials can be easily understood within this framework.

cond-mat.str-el↗
arXiv2011

Cooperative Electronic and Phononic Mechanism of the High Temperature Superconductivity in Cuprates

In conventional superconductors, phonons glue two electrons with opposite spins to form Cooper pairs and condensation of these pairs leads to the superconductivity. Identifying the underlying mechanism of the high temperature superconductivity in cuprates is among the most important problems in physics. Even quarter of a century after the first report of high temperature superconductor by Bednorz and Muller in 1986, there is still no general consensus on the pairing mechanism of superconductivity in these materials. So far, many theories have been developed to explain the exotic properties of cuprates, but they can explain only a limited number of experiments. In this article, we present a new pairing mechanism that incorporates both strong correlation and phonon mediated interaction on an equal footing to produce superconductivity. In this framework, strong correlation and anti-ferromagnetic interaction between electrons, create RVB pairs and phonons provide the phase coherence between these RVB pairs. Both of these are required in this approach to obtain the superconductivity. This approach resolves three limitations of the U(1) slave boson method. We achieve a better estimation of $T_c$, we only predict $\frac{h}{2ec}$ vortices and the linear $T$ coefficient of the superfluid is not sensitive to the doping. This formalism provides a framework that connects Anderson's idea of preformed Cooper pairs and phonon based theories.

cond-mat.supr-con↗