arXiv subjects

Teemu Ojanen

Publications and source records attributed to Teemu Ojanen.

At least 55 records · Page 3Linked to original sources

arXiv2019

Engineering of Chern insulators and circuits of topological edge states

Impurities embedded in electronic systems induce bound states which under certain circumstances can hybridize and lead to impurity bands. Doping of insulators with impurities has been identified as a promising route towards engineering electronic topological states of matter. In this paper we show how to realize tuneable Chern insulators starting from a three dimensional topological insulator whose surface is gapped and intentionally doped with magnetic impurities. The main advantage of the protocol is that it is robust, and in particular not very sensitive to the impurity configuration. We explicitly demonstrate this for a square lattice of impurities as well as a random lattice. In both cases we show that it is possible to change the Chern number of the system by one through manipulating its topological state. We also discuss how this can be used to engineer circuits of edge channels.

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arXiv2019

Topological phase transitions in glassy quantum matter

Amorphous systems have rapidly gained promise as novel platforms for topological matter. In this work we establish a scaling theory of amorphous topological phase transitions driven by the density of lattice points in two dimensions. By carrying out a finite-size scaling analysis of topological invariants averaged over discrete and continuum random geometries, we discover unique critical properties of Chern and $\mathbb{Z}_2$ glass transitions. Even for short-range hopping models the Chern glass phase may persist down to the fundamental lower bound given by the classical percolation threshold. While the topological indices accurately satisfy the postulated one-parameter scaling, they do not generally flow to the closest integer value in the thermodynamic limit. Furthermore, the value of the critical exponent describing the diverging localization length varies continuously along the phase boundary and is not fixed by the symmetry class of the Hamiltonian. We conclude that the critical behaviour of amorphous topological systems exhibit characteristic features not observed in disordered systems, motivating a wealth of new research directions.

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arXiv2017

Amorphous topological superconductivity in a Shiba glass

Topological states of matter support quantized nondissipative responses and exotic quantum particles that cannot be accessed in common materials. The exceptional properties and application potential of topological materials have triggered a large-scale search for new realizations. Breaking away from the popular trend focusing almost exclusively on crystalline symmetries, we introduce the Shiba glass as a platform for amorphous topological quantum matter. This system consists of an ensemble of randomly distributed magnetic atoms on a superconducting surface. The collection of magnetic moments gives rise to subgap Yu-Shiba-Rusinov states that form a topological superconducting phase at critical density despite a complete absence of spatial order. Experimental signatures of the amorphous topological state can be obtained by STM measurements probing the topological edge mode. Our discovery demonstrates the physical feasibility of amorphous topological quantum matter and presents a concrete route to fabricating new topological systems from nontopological materials with random dopants.

cond-mat.mes-hall↗

arXiv2017

Coupled Yu-Shiba-Rusinov states in molecular dimers on NbSe$_2$

Magnetic impurities have a dramatic effect on superconductivity by breaking the time-reversal symmetry and inducing so-called Yu-Shiba-Rusinov (YSR) low energy bound states within the superconducting gap. The spatial extent of YSR states is greatly enhanced in 2D systems, which should facilitate the formation of coupled states. Here, we observe YSR states on single cobalt phthalocyanine (CoPC) molecules on a 2D superconductor NbSe$_2$ using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS). We use STM lateral manipulation to create controlled CoPc dimers and demonstrate the formation of coupled YSR states. The experimental results are corroborated by theoretical analysis of the coupled states in lattice and continuum models. Our work forms an important step towards the realization of exotic topological states in designer magnetic lattices.

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arXiv2017

Designer curved-space geometry for relativistic fermions in Weyl metamaterials

Weyl semimetals are recently discovered materials supporting emergent relativistic fermions in the vicinity of band-crossing points known as Weyl nodes. The positions of the nodes and the low-energy spectrum depend sensitively on the time-reversal (TR) and inversion (I) symmetry breaking in the system. We introduce the concept of Weyl metamaterials where the particles experience a 3d curved geometry and gauge fields emerging from smooth spatially varying TR and I breaking fields. The Weyl metamaterials can be fabricated from semimetal or insulator parent states where the geometry can be tuned, for example, through inhomogeneous magnetization. We derive an explicit connection between the effective geometry and the local symmetry-breaking configuration. This result opens the door for a systematic study of 3d designer geometries and gauge fields for relativistic carriers. The Weyl metamaterials provide a route to novel electronic devices as highlighted by a remarkable 3d electron lens effect.

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arXiv2017

Superlattice platform for chiral superconductivity with tuneable and high Chern numbers

Finding concrete realizations for topologically nontrivial chiral superconductivity has been a long-standing goal in quantum matter research. Here we propose a route to a systematic realization of chiral superconductivity with nonzero Chern numbers. This goal can be achieved in a nanomagnet lattice deposited on top of a spin-orbit coupled two-dimensional electron gas (2DEG) with proximity s-wave superconductivity. The proposed structure can be regarded as a universal platform for chiral superconductivity supporting a large variety of topological phases. The topological state of the system can be electrically controlled by, for example, tuning the density of the 2DEG.

cond-mat.mes-hall↗

arXiv2016

Engineering 1D topological phases on $p$-wave superconductors

In this work, we study how, with the aid of impurity engineering, two-dimensional $p$-wave superconductors can be employed as a platform for one-dimensional topological phases. We discover that, while chiral and helical parent states themselves are topologically nontrivial, a chain of scalar impurities on both systems support multiple topological phases and Majorana end states. We develop an approach which allows us to extract the topological invariants and subgap spectrum, even away from the center of the gap, for the representative cases of spinless, chiral and helical superconductors. We find that the magnitude of the topological gaps protecting the nontrivial phases may be a significant fraction of the gap of the underlying superconductor.

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arXiv2016

Topological states in engineered atomic lattices

Topological materials exhibit protected edge modes that have been proposed for applications in for example spintronics and quantum computation. While a number of such systems exist, it would be desirable to be able to test theoretical proposals in an artificial system that allows precise control over the key parameters of the model. The essential physics of several topological systems can be captured by tight-binding models, which can also be implemented in artificial lattices. Here, we show that this method can be realized in a vacancy lattice in a chlorine monolayer on a Cu(100) surface. We use low-temperature scanning tunneling microscopy (STM) to fabricate such lattices with atomic precision and probe the resulting local density of states (LDOS) with scanning tunneling spectroscopy (STS). We create analogues of two tight-binding models of fundamental importance: The polyacetylene (dimer) chain with topological domain wall states, and the Lieb lattice, featuring a lattice pseudospin 1 system with a flat electron band. These results provide the first steps in realizing designer quantum materials with tailored properties.

cond-mat.mes-hall↗

arXiv2016

Skyrmion-induced subgap states in p-wave superconductors

In s-wave systems, it has been theoretically shown that a ferromagnetic film hosting a skyrmion can induce a bound state embedded in the opposite-spin continuum. In this work, we consider a case of skyrmion-induced state in a p-wave superconductor. We find that the skyrmion induces a bound state that generally resides \emph{within} the spectral gap and is isolated from all other states, in contrast to the case of conventional superconductors. To this end, we derive an approximate expression for the $T$-matrix, through which we calculate the spin-polarized local density of states which is observable in scanning tunneling microscopy measurements. We find the unique spectroscopic features of the skyrmion-induced bound state and discuss how our predictions could be employed as novel experimental probes for p-wave superconducting states.

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arXiv2016

Topological state engineering by potential impurities on chiral superconductors

In this work we consider the influence of potential impurities deposited on top of two-dimensional chiral superconductors. As discovered recently, magnetic impurity lattices on an $s$-wave superconductor may give rise to a rich topological phase diagram. We show that similar mechanism takes place in chiral superconductors decorated by non-magnetic impurities, thus avoiding the delicate issue of magnetic ordering of adatoms. We illustrate the method by presenting the theory of potential impurity lattices embedded on chiral $p$-wave superconductors. While a prerequisite for the topological state engineering is a chiral superconductor, the proposed procedure results in vistas of nontrivial descendant phases with different Chern numbers.

cond-mat.mes-hall↗

arXiv2016

Topological superconductivity and anti-Shiba states in disordered chains of magnetic adatoms

Regular arrays of magnetic atoms on a superconductor provide a promising platform for topological superconductivity. In this work we study effects of disorder in these systems, focusing on vacancies realized by missing magnetic atoms. We develop approaches that allow treatment of ferromagnetic dense chains as well as long-range hopping ferromagnetic and helical Shiba chains at arbitrary subgap energies. Vacancies in magnetic chains play an analogous role to magnetic impurities in a clean $s$-wave superconductor. A single vacancy in a topological chain gives rise to a low-lying "anti-Shiba" state below the band edge of a regular magnetic chain. Proliferation of the anti-Shiba band formed by a finite density of hybridized vacancy states leads to deterioration of the topological phase, which exhibits unusual fragility in a particular parameter region in dilute chains. We also consider local fluctuation in the Shiba coupling and discuss how vacancy states could contribute to experimental verification of topological superconductivity.

cond-mat.mes-hall↗

arXiv2016

Ground state angular momentum, spectral asymmetry, and topology in chiral superfluids and superconductors

Recently it was discovered that the ground state orbital angular momentum in two-dimensional chiral superfluids with pairing symmetry $(p_x+ip_y)^ν$ depends on the winding number $ν$ in a striking manner. The ground state value for the $ν=1$ case is $L_z=\hbar N/2$ as expected by counting the Cooper pairs, while a dramatic cancellation takes place for $ν>1$. The origin of the cancellation is associated with the topological edge states that appear in a finite geometry and give rise to a spectral asymmetry. Here we study the reduction of orbital angular momentum for different potential profiles and pairing strengths, showing that the result $L_z=\hbar N/2$ is robust for $ν=1$ under all studied circumstances. We study how angular momentum depends on the gap size $Δ/E_F$ and obtain the result $L_z=\frac{\hbarν}{2} N(1-\fracμ{E_F})$ for $ν=2,3$. Thus, the gap-dependence of $L_z$ for $ν<4$ enters at most through the chemical potential while $ν\geq4$ is qualitatively different. In addition, we generalize the spectral asymmetry arguments to \emph{total} angular momentum in the ground state of triplet superfluids where due to a spin-orbit coupling $L_z$ is not a good quantum number. We find that the ground state total angular momentum also behaves very differently depending on total angular momentum of the Cooper pairs.

cond-mat.supr-con↗

arXiv2016

Chern mosaic - topology of chiral superconductivity on ferromagnetic adatom lattices

In this work we will explore the properties of superconducting surfaces decorated by two-dimensional ferromagnetic adatom lattices. As discovered recently [Röntynen and Ojanen, Phys. Rev. Lett. \textbf{114}, 236803 (2015)], in the presence of a Rashba spin-orbit coupling these systems may support topological superconductivity with complex phase diagrams and high Chern numbers. We show how the long-range hopping nature of the effective low-energy theory generically gives rise to a phase diagram covered by a \emph{Chern mosaic} -- a rich pattern of topological phases with large Chern numbers. We study different lattice geometries and the dependence of energy gaps and abundance of different phases as a function of system parameters. Our findings establish the studied system as one of the richest platforms for topological matter known to date.

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arXiv2015

Topological superconductivity in ferromagnetic atom chains beyond the deep-impurity regime

Recent developments in the search for topological superconductivity have brought lattices of magnetic adatoms on a superconductor into intense focus. In this work we will study ferromagnetic chains of adatoms on superconducting surfaces with Rashba spin-orbit coupling. Generalising the deep-impurity approach employed extensively in previous works to arbitrary subgap energies, we formulate the theory of the subgap spectrum as a nonlinear matrix eigenvalue problem. We obtain an essentially analytical description of the subgap spectrum, allowing an efficient study of the topological properties. Employing a flat-band Hamiltonian sharing the topological properties of the chain, we evaluate the $\mathbb{Z}$-valued winding number and discover five distinct topological phases. Our results also confirm that the topological band formation does not require the decoupled Shiba energies to be fine-tuned to the gap centre. We also study the properties of Majorana bound states in the system.

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arXiv2015

Visualizing the chiral anomaly in Dirac and Weyl semimetals with photoemission spectroscopy

Quantum anomalies are the breaking of a classical symmetry by quantum fluctuations. They dictate how physical systems of diverse nature, ranging from fundamental particles to crystalline materials, respond topologically to external perturbations, insensitive to local details. The anomaly paradigm was triggered by the discovery of the chiral anomaly that contributes to the decay of pions into photons and influences the motion of superfluid vortices in $^3$He-A. In the solid state, it also fundamentally affects the properties of topological Weyl and Dirac semimetals, recently realized experimentally in TaAs, Na$_3$Bi, Cd$_3$As$_2$, and ZrTe$_{5}$. In this work we propose that the most identifying consequence of the chiral anomaly, the charge density imbalance between fermions of different chirality induced by non-orthogonal electric and magnetic fields, can be directly observed in these materials with the existing technology of photoemission spectroscopy. With angle resolution, the chiral anomaly is identified by a characteristic note-shaped pattern of the emission spectra, originating from the imbalanced occupation of the bulk states and a previously unreported momentum dependent energy shift of the surface state Fermi arcs. We further demonstrate that the chiral anomaly likewise leaves an imprint in angle averaged emission spectra, facilitating its experimental detection. Thereby, our work provides essential theoretical input to foster the direct visualization of the chiral anomaly in condensed matter.

cond-mat.mes-hall↗

arXiv2014

Topological superconductivity and high Chern numbers in 2D ferromagnetic Shiba lattices

Inspired by the recent experimental observation of topological superconductivity in ferromagnetic chains, we consider a dilute 2D lattice of magnetic atoms deposited on top of a superconducting surface with a Rashba spin-orbit coupling. We show that the studied system supports a generalization of $p_x+ip_y$ superconductivity and that its topological phase diagram contains Chern numbers higher than $ξ/a$ $(\gg1)$, where $ξ$ is the superconducting coherence length and $a$ is the distance between the magnetic atoms. The signatures of nontrivial topology can be observed by STM spectroscopy in finite-size islands.

cond-mat.mes-hall↗

arXiv2014

Topological properties of helical Shiba chains with general impurity strength and hybridization

Recent experiments announced an observation of topological superconductivity and Majorana quasiparticles in Shiba chains, consisting of an array of magnetic atoms deposited on top of a superconductor. In this work we study helical Shiba chains and generalize the microscopic theory of subgap energy bands to a regime where the decoupled magnetic impurity energy and the hybridization of different impurity states can be significant compared to the superconducting gap of the host material. From exact solutions of the Bogoliubov-de Gennes equation we extract expressions for the topological phase boundaries for arbitrary values of the superconducting coherence length. The subgap spectral problem can be formulated as a nonlinear matrix eigenvalue problem from which we obtain an analytical solution for energy bands in the long coherence length limit. Physical consequences and departures from the previously obtained results in the deep-dilute impurity limit are discussed in detail.

cond-mat.mes-hall↗

arXiv2014

Ground state cooling of mechanical motion in the unresolved sideband regime by use of optomechanically induced transparency

We present a scheme for cooling mechanical motion to the ground state in an optomechanical system. Unlike standard sideband cooling, this scheme applies to the so-called unresolved sideband regime, where the resonance frequency of the mechanical mode is much smaller than the cavity linewidth. Ground state cooling becomes possible when assuming the presence of an additional, auxiliary mechanical mode and exploiting the effect of optomechanically induced transparency. We first consider a system where one optical cavity interacts with two mechanical modes, and show that ground state cooling of the unresolved mechanical mode is possible when the auxiliary mode is in the resolved sideband regime. We then present a modified setup involving two cavity modes, where both mechanical modes are allowed to be in the unresolved sideband regime.

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