arXiv subjects

A. Alexandradinata

Publications and source records attributed to A. Alexandradinata.

At least 19 recordsLinked to original sources

arXiv2026

Vortex-enhanced photovoltaic current in disordered topological materials

In disordered topological materials, real-space crystalline defects interplay with momentum-space wave function singularities to \textit{enhance} the bulk photovoltaic current. What's singular is the interband Berry phase, or equivalently the phase of the \textit{optical} dipole matrix element, which has a \textit{vortex} structure in momentum space. Such \textit{optical vorticity} is guaranteed to exist in all topological materials associated with nontrivial Chern numbers. These vortices enhance electron-impurity skew scattering, which manifests as a ballistic photovoltaic current that is sensitive to (a) the topological material class, (b) the symmetry class of crystalline defects, and (c) the light polarization. This sensitivity manifests in two ways: firstly, by (a-c)-dependent frequency exponents for the photovoltaic current $\propto ω^{\text{exponent}}$ in topological semimetals, with $ω$ the frequency of the light source. Secondly, by (a-c)-dependent constraints of the bulk photovoltaic tensor, which are explainable only by emergent, \textit{magnetic} symmetries of \textit{time-reversal-invariant} topological materials. These ideas are concretized by case studies on multifold fermions, 3D $m$-order Weyl semimetals and 2D $n$-order Dirac systems, which include $n$-layer rhombohedral graphene, transition metal dichalcogenides, and topological surface states. Theoretical guidance is provided for a tri-pronged experimental program that combines frequency-tuned photoconductivity measurements, defect characterization and defect engineering.

cond-mat.str-el↗

arXiv2025

Anomalous shift and optical vorticity in the steady photovoltaic current

Steady illumination of a non-centrosymmetric semiconductor results in a bulk photovoltaic current, which is contributed by real-space displacements (`shifts') of charged quasiparticles as they transit between Bloch states. The shift induced by interband excitation via absorption of photons has received the prevailing attention. However, this excitation-induced shift can be far outweighed ($\ll$) by the shift induced by intraband relaxation, or by the shift induced by radiative recombination of electron-hole pairs. This outweighing ($\ll$) is attributed to (i) time-reversal-symmetric, intraband Berry curvature, which results in an anomalous shift of quasiparticles as they scatter with phonons, as well as to (ii) topological singularities in the interband Berry phase (`optical vortices'), which makes the photovoltaic current extraordinarily sensitive to the linear polarization vector of the light source. Both (i-ii) potentially lead to nonlinear conductivities of order $mAV^{-2}$, without finetuning of the incident radiation frequency, band gap, or joint density of states. A case study of BiTeI showcases the anomalous shift and optical vorticity in a realistic material.

cond-mat.mes-hall↗

arXiv2025

The Future of the Correlated Electron Problem

A central problem in modern condensed matter physics is the understanding of materials with strong electron correlations. Despite extensive work, the essential physics of many of these systems is not understood and there is very little ability to make predictions in this class of materials. In this manuscript we share our personal views on the major open problems in the field of correlated electron systems. We discuss some possible routes to make progress in this rich and fascinating field. This manuscript is the result of the vigorous discussions and deliberations that took place at Johns Hopkins University during a three-day workshop January 27, 28, and 29, 2020 that brought together six senior scientists and 46 more junior scientists. Our hope, is that the topics we have presented will provide inspiration for others working in this field and motivation for the idea that significant progress can be made on very hard problems if we focus our collective energies.

cond-mat.str-el↗

arXiv2024

Quantization of intra- and inter-band Berry phases in the shift current

The theory of the shift current is thus far geometrical without being topological. This means that the real-space displacement/shift of a photoexcited quasiparticle depends on the geometric Berry phase, but the Berry phase is not quantized to a rational multiple of $2π$. I rectify this status quo by introducing a new class of topological insulators whose band topology is \textit{only} compatible with a non-centrosymmetric space group. For such insulators, it is impossible to continuously tune the $\boldsymbol{k}$-dependent shift vector to zero throughout the Brillouin zone. Suitably averaged, the shift vector is quantized to a rational multiple of a Bravais lattice vector. Even with wide band gaps, the frequency-integrated shift conductivity greatly exceeds $e^3/h^2$, and is at least three orders of magnitude larger than the conductivity of the prototypical ferroelectric BaTiO$_3$. The large conductivity is attributed to an interplay between quantized intra- and inter-band Berry phases. In particular, topological defects of the inter-band Berry phase can enhance the shift current, even for unpolarized insulators with negligible intra-band Berry phase.

cond-mat.mes-hall↗

arXiv2023

$\mathbb{Z}_{2}$ Spin Hopf Insulator: Helical Hinge States and Returning Thouless Pump

We introduce a time-reversal-symmetric analog of the Hopf insulator that we call a spin Hopf insulator. The spin Hopf insulator harbors nontrivial Kane-Mele $\Z_2$ invariants on its surfaces, and is the first example of a nonmagnetic delicate topological insulator with spin-orbit coupling. We show that the Kane-Mele $\Z_2$ topology on the surface is generically unstable, but can be stabilized by the addition of a composition of the particle hole and spatial inversion symmetry. Such a symmetry not only protects the surface $\Z_2$ invariant, but also protects gapless helical hinge states on the spin Hopf insulator. Furthermore, we show that in the presence of four-fold rotational symmetry, the spin Hopf insulator exhibits a returning Thouless pump, as well as surface states on sharp boundary terminations.

cond-mat.mes-hall↗

arXiv2023

Reply to: Low-frequency quantum oscillations in LaRhIn$_5$: Dirac point or nodal line?

We thank G.P. Mikitik and Yu.V. Sharlai for contributing this note and the cordial exchange about it. First and foremost, we note that the aim of our paper is to report a methodology to diagnose topological (semi)metals using magnetic quantum oscillations. Thus far, such diagnosis has been based on the phase offset of quantum oscillations, which is extracted from a "Landau fan plot". A thorough analysis of the Onsager-Lifshitz-Roth quantization rules has shown that the famous $π$-phase shift can equally well arise from orbital- or spin magnetic moments in topologically trivial systems with strong spin-orbit coupling or small effective masses. Therefore, the "Landau fan plot" does not by itself constitute a proof of a topologically nontrivial Fermi surface. In the paper at hand, we report an improved analysis method that exploits the strong energy-dependence of the effective mass in linearly dispersing bands. This leads to a characteristic temperature dependence of the oscillation frequency which is a strong indicator of nontrivial topology, even for multi-band metals with complex Fermi surfaces. Three materials, Cd$_3$As$_2$, Bi$_2$O$_2$Se and LaRhIn$_5$ served as test cases for this method. Linear band dispersions were detected for Cd$_3$As$_2$, as well as the $F$ $\approx$ 7 T pocket in LaRhIn$_5$.

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arXiv2022

Temperature dependence of quantum oscillations from non-parabolic dispersions

The phase offset of quantum oscillations is commonly used to experimentally diagnose topologically non-trivial Fermi surfaces. This methodology, however, is inconclusive for spin-orbit-coupled metals where $π$-phase-shifts can also arise from non-topological origins. Here, we show that the linear dispersion in topological metals leads to a $T^2$-temperature correction to the oscillation frequency that is absent for parabolic dispersions. We confirm this effect experimentally in the Dirac semi-metal Cd$_3$As$_2$ and the multiband Dirac metal LaRhIn$_5$. Both materials match a tuning-parameter-free theoretical prediction, emphasizing their unified origin. For topologically trivial Bi$_2$O$_2$Se, no frequency shift associated to linear bands is observed as expected. However, the $π$-phase shift in Bi$_2$O$_2$Se would lead to a false positive in a Landau-fan plot analysis. Our frequency-focused methodology does not require any input from ab-initio calculations, and hence is promising for identifying correlated topological materials.

cond-mat.str-el↗

arXiv2022

Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond

Pontrjagin's seminal topological classification of two-band Hamiltonians in three momentum dimensions is hereby enriched with the inclusion of a crystallographic rotational symmetry. The enrichment is attributed to a new topological invariant which quantifies a $2π$-quantized change in the Berry-Zak phase between a pair of rotation-invariant lines in the bulk, three-dimensional Brillouin zone; because this change is reversed on the complementary section of the Brillouin zone, we refer to this new invariant as a returning Thouless pump (RTP). We find that the RTP is associated to anomalous values for the angular momentum of surface states, which guarantees metallic in-gap states for open boundary condition with sharply terminated hoppings; more generally for arbitrarily terminated hoppings, surface states are characterized by Berry-Zak phases that are quantized to a rational multiple of $2π$. The RTP adds to the family of topological invariants (the Hopf and Chern numbers) that are known to classify two-band Hamiltonians in Wigner-Dyson symmetry class A. Of these, the RTP and Hopf invariants are delicate, meaning that they can be trivialized by adding a particular trivial band to either the valence or the conduction subspace. Not all trivial band additions will nullify the RTP invariant, which allows its generalization beyond two-band Hamiltonians to arbitrarily many bands; such generalization is a hallmark of symmetry-protected delicate topology.

cond-mat.mes-hall↗

arXiv2021

Multicellularity of delicate topological insulators

Being Wannierizable is not the end of the story for topological insulators. We introduce a family of topological insulators that would be considered trivial in the paradigm set by the tenfold way, topological quantum chemistry, and the method of symmetry-based indicators. Despite having a symmetric, exponentially-localized Wannier representation, each Wannier function cannot be completely localized to a single primitive unit cell in the bulk. Such multicellular topology is shown to be neither stable, nor fragile, but delicate, i.e., the topology can be nullified by adding trivial bands to either valence or conduction band.

cond-mat.mes-hall↗

arXiv2021

Quantized surface magnetism and higher-order topology: Application to the Hopf insulator

We identify topological aspects of the subextensive magnetic moment contributed by the surfaces of a three-dimensional crystallite -- assumed to be insulating in the bulk as well as on all surface facets, with trivial Chern invariants in the bulk. The geometric component of this subextensive moment is given by its derivative with respect to the chemical potential, at zero temperature and zero field, per unit surface area, and hence corresponds to the surface magnetic compressibility. The sum of the surface compressibilities contributed by two opposite facets of a cube-shaped crystallite is quantized to an integer multiple of the fundamental constant $e/h c$; this integer is in one-to-one correspondence with the net chirality of hinge modes on the surface of the crystallite, manifesting a link with higher-order topology. The contribution by a single facet to the magnetic compressibility need not be quantized to integers; however, symmetry and/or Hilbert-space constraints can fix the single-facet compressibility to half-integer multiples of $e/hc$, as will be exemplified by the Hopf insulator.

cond-mat.mes-hall↗

arXiv2020

Diabolical touching point in the magnetic energy levels of topological nodal-line metals

For three-dimensional metals, Landau levels disperse as a function of the magnetic field and the momentum wavenumber parallel to the field. In this two-dimensional parameter space, it is shown that two conically-dispersing Landau levels can touch at a diabolical point -- a Landau-Dirac point. The conditions giving rise to Landau-Dirac points are shown to be magnetic breakdown (field-induced quantum tunneling) and certain crystallographic spacetime symmetry. Both conditions are realizable in topological nodal-line metals, as we exemplify with CaP$_3$. A Landau-Dirac point reveals itself in anomalous batman-like peaks in the magnetoresistance, as well as in the onset of optical absorption linearly evolving to zero frequency as a function of the field magnitude/orientation.

cond-mat.mes-hall↗

arXiv2020

Teleportation of Berry curvature on the surface of a Hopf insulator

The existing paradigm for topological insulators asserts that an energy gap separates conduction and valence bands with opposite topological invariants. Here, we propose that \textit{equal}-energy bands with opposite Chern invariants can be \textit{spatially} separated -- onto opposite facets of a finite crystalline Hopf insulator. On a single facet, the number of curvature quanta is in one-to-one correspondence with the bulk homotopy invariant of the Hopf insulator -- this originates from a novel bulk-to-boundary flow of Berry curvature which is \textit{not} a type of Callan-Harvey anomaly inflow. In the continuum perspective, such nontrivial surface states arise as \textit{non}-chiral, Schrödinger-type modes on the domain wall of a generalized Weyl equation -- describing a pair of opposite-chirality Weyl fermions acting as a \textit{dipolar} source of Berry curvature. A rotation-invariant lattice regularization of the generalized Weyl equation manifests a generalized Thouless pump -- which translates charge by one lattice period over \textit{half} an adiabatic cycle, but reverses the charge flow over the next half.

cond-mat.str-el↗

arXiv2019

Crystallographic splitting theorem for band representations and fragile topological photonic crystals

The fundamental building blocks in band theory are band representations (BRs): bands whose infinitely-numbered Wannier functions are generated (by action of a space group) from a finite number of symmetric Wannier functions centered on a point in space. This work aims to simplify questions on a multi-rank BR by splitting it into unit-rank bands, via the following crystallographic splitting theorem: being a rank-$N$ BR is equivalent to being splittable into a finite sum of bands indexed by $\{1,2,\ldots,N\}$, such that each band is spanned by a single, analytic Bloch function of $k$, and any symmetry in the space group acts by permuting $\{1,2,\ldots,N\}$. Applying this theorem, we develop computationally efficient methods to determine whether a given energy band (of a tight-binding or Schrödinger Hamiltonian) is a BR, and, if so, how to numerically construct the corresponding symmetric Wannier functions. Thus we prove that rotation-symmetric topological insulators in class AI are fragile, meaning that the obstruction to symmetric Wannier functions is removable by addition of BRs. An implication of fragility is that its boundary states, while robustly covering the bulk energy gap in finite-rank tight-binding models, are unstable if the Hilbert space is expanded to include all symmetry-allowed representations. These fragile insulators have photonic analogs that we identify; in particular, we prove that an existing photonic crystal built by Yang et al. [Nature 565, 622 (2019)] is fragile topological with removable surface states, which disproves a widespread perception of 'topologically-protected' surface states in time-reversal-invariant, gapped photonic/phononic crystals. Our theorem is finally applied to derive various symmetry obstructions on the Wannier functions of topological insulators, and to prove their equivalence with the nontrivial holonomy of Bloch functions.

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arXiv2019

Glide-resolved photoemission spectroscopy: Measuring topological invariants in nonsymmorphic space groups

The two classes of 3D, time-reversal-invariant insulators are known to subdivide into four classes in the presence of glide symmetry. Here, we extend this classification of insulators to include glide-symmetric Weyl metals, and find a finer $Z_4\oplus Z$ classification. We further elucidate the smoking-gun experimental signature of each class in the photoemission spectroscopy of surface states. Measuring the $Z_4$ topological invariant by photoemission relies on identifying the glide representation of the initial Bloch state before photo-excitation - we show how this is accomplished with relativistic selection rules, combined with standard spectroscopic techniques to resolve both momentum and spin. Our method relies on a novel spin-momentum locking that is characteristic of all glide-symmetric solids (inclusive of insulators and metals in trivial and topological categories). As an orthogonal application, given a glide-symmetric solid with an ideally symmetric surface, we may utilize this spin-momentum locking to generate a source of FULLY spin-polarized photoelectrons, which have diverse applications in solid-state spectroscopy. Our ab-initio calculations predict Ba$_2$Pb, stressed Na$_3$Bi, and KHgSb to realize all three, nontrivial insulating phases in the $Z_4$ classification.

cond-mat.mtrl-sci↗

arXiv2019

Landau quantization of nearly degenerate bands, and full symmetry classification of avoided Landau-level crossings

Semiclassical quantization rules compactly describe the energy dispersion of Landau levels, and are predictive of quantum oscillations in transport and thermodynamic quantities. Such rules -- as formulated by Onsager, Lifshitz and Roth -- apply when the spin-orbit interaction dominates over the Zeeman interaction (or vice versa), but does not generally apply when the two interactions are comparable in strength. In this work, we present a generalized quantization rule which treats the spin-orbit and Zeeman interactions on equal footing, and therefore has wider applicability to spin-orbit-coupled materials lacking a spatial inversion center, or having magnetic order. More generally, our rule describes the Landau quantization of any number of nearly degenerate energy bands -- in any symmetry class. The resultant Landau-level spectrum is generically non-equidistant but may contain spin (or pseudospin) degeneracies. To tune to such degeneracies in the absence of crystalline point-group symmetries, three real parameters are needed. We have exhaustively identified all symmetry classes of cyclotron orbits for which this number is reduced from three, thus establishing symmetry-enforced 'non-crossing rules' for Landau levels. In particular, only one parameter is needed in the presence of spatial rotation or inversion; this single parameter may be the magnitude or orientation of the field. Signatures of single-parameter tunability include (i) a smooth crossover between period-doubled and -undoubled quantum oscillations in the low-temperature Shubnikov-de Haas effect, as well as (ii) 'magic-angle' magnetoresistance oscillations. We demonstrate the utility of our quantization rule, as well as the tunability of Landau-level degeneracies, for the Rashba-Dresselhaus two-dimensional electron gas -- subject to an arbitrarily oriented magnetic field.

cond-mat.mes-hall↗

arXiv2019

Quantized frequency-domain polarization of driven phases of matter

Periodically driven quantum systems can realize novel phases of matter that do not exist in static settings. We study signatures of these drive-induced phases on the $(d+1)$-dimensional Floquet lattice, comprised of $d$ spatial dimensions plus the frequency domain. The average position of Floquet eigenstates along the frequency axis can be written in terms of a non-adiabatic Berry phase, which we interpret as frequency-domain polarization. We argue that whenever this polarization is quantized to a nontrivial value, the phase of matter cannot be continuously connected to a time-independent state and, as a consequence, it captures robust properties of its dynamics. We illustrate this in driven topological phases, such as superconducting wires and the anomalous Floquet Anderson insulator; as well as in driven symmetry-broken phases, such as time crystals. We further introduce a new dynamical phase of matter that we construct by imposing quantization conditions on its frequency-domain polarization. This illustrates the potential for using this kind of polarization as a tool to search for new driven phases of matter.

cond-mat.mes-hall↗

arXiv2018

Topological Bloch oscillations

Bloch oscillations originate from the translational symmetry of crystals. These oscillations occur with a fundamental period that a semiclassical wavepacket takes to traverse a Brillouin-zone loop. We introduce a new type of Bloch oscillations whose periodicity is an integer ($μ{>}1$) multiple of the fundamental period. The period multiplier $μ$ is a topological invariant protected by the space groups of crystals, which include more than just translational symmetries. For example, $μ$ divides $n$ for crystals with an $n$-fold rotational or screw symmetry; with a reflection, inversion or glide symmetry, $μ$ equals two. We identify the commonality underlying all period-multiplied oscillations: the multi-band Berry-Zak phases, which encode the holonomy of adiabatic transport of Bloch functions in quasimomentum space, differ pairwise by integer multiples of $2π/μ$. For a class of multi-band subspaces whose projected-position operators commute, period multiplication has a complementary explanation through the real space distribution of Wannier functions. This complementarity follows from a one-to-one correspondence between Berry-Zak phases and the centers of Wannier functions. A Wannier description of period multiplication does not always exist, as we exemplify with band subspaces with either a nonzero Chern number or $\mathbb{Z}_2$ Kane-Mele topological order. To help identify band subspaces with $μ{>}1$, a general theorem is presented that outputs Zak phases that are symmetry-protected to integer multiples of $2π/n$, given the point-group symmetry representation of any gapped band subspace. A cold-atomic experiment that has observed period-multiplied Bloch oscillations is discussed, and directions are provided for future experiments.

cond-mat.other↗

arXiv2018

Modern semiclassical theory of magnetic transport and breakdown

The Bohr-Sommerfeld quantization rule lies at the heart of the modern semiclassical theory of a Bloch electron in a magnetic field. This rule is predictive of Landau levels and quantum oscillations for conventional metals, as well as for a host of topological metals which have emerged in the recent intercourse between band theory, crystalline symmetries and topology. The essential ingredients in any quantization rule are connection formulae that match the semiclassical (WKB) wavefunction across regions of strong quantum fluctuations. Here, we propose (a) a multi-component WKB wavefunction that describes transport within degenerate-band subspaces, and (b) the requisite connection formulae for saddlepoints and type-II Dirac points, where tunneling respectively occurs within the same band, and between distinct bands. (a-b) extend previous works by incorporating phase corrections that are subleading in powers of the field; these corrections include the geometric Berry phase, and account for the orbital magnetic moment and the Zeeman coupling. A comprehensive symmetry analysis is performed for such phase corrections occurring in closed orbits, which is applicable to solids in any (magnetic) space group. We have further formulated a graph-theoretic description of semiclassical orbits. This allows us to systematize the construction of quantization rules for a large class of closed orbits (with or without tunneling), as well as to formulate the notion of a topological invariant in semiclassical magnetotransport -- as a quantity that is invariant under continuous deformations of the graph. Landau levels in the presence of tunneling are generically quasirandom, i.e., disordered on the scale of nearest-neighbor level spacings but having longer-ranged correlations; we develop a perturbative theory to determine Landau levels in such quasirandom spectra.

cond-mat.other↗