*ACS Nano ; 16(1): 783-791, 2022 Jan 25.*

##### RESUMO

Thinning crystalline materials to two dimensions (2D) creates a rich playground for electronic phases, including charge, spin, superconducting, and topological order. Bulk materials hosting charge density waves (CDWs), when reduced to ultrathin films, have shown CDW enhancement and tunability. However, charge order confined to only 2D remains elusive. Here we report a distinct charge ordered state emerging in the monolayer limit of 1T-VSe2. Systematic scanning tunneling microscopy experiments reveal that bilayer VSe2 largely retains the bulk electronic structure, hosting a tridirectional CDW. However, monolayer VSe2 âconsistently across distinct substratesâexhibits a dimensional crossover, hosting two CDWs with distinct wavelengths and transition temperatures. Electronic structure calculations reveal that while one CDW is bulk-like and arises from the well-known Peierls mechanism, the other is decidedly unconventional. The observed CDW-lattice decoupling and the emergence of a flat band suggest that the second CDW could arise from enhanced electron-electron interactions in the 2D limit. These findings establish monolayer-VSe2 as a host of coexisting charge orders with distinct origins, and enable the tailoring of electronic phenomena via emergent interactions in 2D materials.

*Proc Natl Acad Sci U S A ; 117(47): 29561-29568, 2020 Nov 24.*

##### RESUMO

Topological edge modes are excitations that are localized at the materials' edges and yet are characterized by a topological invariant defined in the bulk. Such bulk-edge correspondence has enabled the creation of robust electronic, electromagnetic, and mechanical transport properties across a wide range of systems, from cold atoms to metamaterials, active matter, and geophysical flows. Recently, the advent of non-Hermitian topological systems-wherein energy is not conserved-has sparked considerable theoretical advances. In particular, novel topological phases that can only exist in non-Hermitian systems have been introduced. However, whether such phases can be experimentally observed, and what their properties are, have remained open questions. Here, we identify and observe a form of bulk-edge correspondence for a particular non-Hermitian topological phase. We find that a change in the bulk non-Hermitian topological invariant leads to a change of topological edge-mode localization together with peculiar purely non-Hermitian properties. Using a quantum-to-classical analogy, we create a mechanical metamaterial with nonreciprocal interactions, in which we observe experimentally the predicted bulk-edge correspondence, demonstrating its robustness. Our results open avenues for the field of non-Hermitian topology and for manipulating waves in unprecedented fashions.

*Proc Natl Acad Sci U S A ; 115(27): 6986-6990, 2018 07 03.*

##### RESUMO

A charge density wave (CDW) is one of the fundamental instabilities of the Fermi surface occurring in a wide range of quantum materials. In dimensions higher than one, where Fermi surface nesting can play only a limited role, the selection of the particular wavevector and geometry of an emerging CDW should in principle be susceptible to controllable manipulation. In this work, we implement a simple method for straining materials compatible with low-temperature scanning tunneling microscopy/spectroscopy (STM/S), and use it to strain-engineer CDWs in 2H-NbSe2 Our STM/S measurements, combined with theory, reveal how small strain-induced changes in the electronic band structure and phonon dispersion lead to dramatic changes in the CDW ordering wavevector and geometry. Our work unveils the microscopic mechanism of a CDW formation in this system, and can serve as a general tool compatible with a range of spectroscopic techniques to engineer electronic states in any material where local strain or lattice symmetry breaking plays a role.

*Science ; 358(6368): 1314-1317, 2017 12 08.*

##### RESUMO

Bose condensation has shaped our understanding of macroscopic quantum phenomena, having been realized in superconductors, atomic gases, and liquid helium. Excitons are bosons that have been predicted to condense into either a superfluid or an insulating electronic crystal. Using the recently developed technique of momentum-resolved electron energy-loss spectroscopy (M-EELS), we studied electronic collective modes in the transition metal dichalcogenide semimetal 1T-TiSe2 Near the phase-transition temperature (190 kelvin), the energy of the electronic mode fell to zero at nonzero momentum, indicating dynamical slowing of plasma fluctuations and crystallization of the valence electrons into an exciton condensate. Our study provides compelling evidence for exciton condensation in a three-dimensional solid and establishes M-EELS as a versatile technique sensitive to valence band excitations in quantum materials.

*Phys Rev Lett ; 115(23): 236401, 2015 Dec 04.*

##### RESUMO

Artificial quasicrystals are nowadays routinely manufactured, yet only two naturally occurring examples are known. We present a class of systems with the potential to be realized both artificially and in nature, in which the lowest energy state is a one-dimensional quasicrystal. These systems are based on incommensurately charge-ordered materials, in which the quasicrystalline phase competes with the formation of a regular array of discommensurations as a way of interpolating between incommensurate charge order at high temperatures and commensurate order at low temperatures. The nonlocal correlations characteristic of the quasicrystalline state emerge from a free-energy contribution localized in reciprocal space. We present a theoretical phase diagram showing that the required material properties for the appearance of such a ground state allow for one-dimensional quasicrystals to form in real materials. The result is a potentially wide class of one-dimensional quasicrystals.

*Nat Commun ; 6: 7034, 2015 May 07.*

##### RESUMO

Niobium diselenide has long served as a prototype of two-dimensional charge ordering, believed to arise from an instability of the electronic structure analogous to the one-dimensional Peierls mechanism. Despite this, various anomalous properties have recently been identified experimentally, which cannot be explained by Peierls-like weak-coupling theories. Here, we consider instead a model with strong electron-phonon coupling, taking into account both the full momentum and orbital dependence of the coupling matrix elements. We show that both are necessary for a consistent description of the full range of experimental observations. We argue that NbSe2 is typical in this sense, and that any charge-ordered material in more than one dimension will generically be shaped by the momentum and orbital dependence of its electron-phonon coupling as well as its electronic structure. The consequences will be observable in many charge-ordered materials, including cuprate superconductors.

*Phys Rev Lett ; 110(19): 196404, 2013 May 10.*

##### RESUMO

It was recently discovered that the low-temperature, charge-ordered phase of 1T-TiSe(2) has a chiral character. This unexpected chirality in a system described by a scalar order parameter could be explained in a model where the emergence of relative phase shifts between three charge density wave components breaks the inversion symmetry of the lattice. Here, we present experimental evidence for the sequence of phase transitions predicted by that theory, going from disorder to nonchiral and finally to chiral charge order. Employing x-ray diffraction, specific heat, and electrical transport measurements, we find that a novel phase transition occurs ~7 K below the main charge ordering transition in TiSe(2), in agreement with the predicted hierarchy of charge-ordered phases.

*Proc Natl Acad Sci U S A ; 110(9): 3287-92, 2013 Feb 26.*

##### RESUMO

Materials with strong correlations are prone to spin and charge instabilities, driven by Coulomb, magnetic, and lattice interactions. In materials that have significant localized and itinerant spins, it is not obvious which will induce order. We combine electrical transport, X-ray magnetic diffraction, and photoemission studies with band structure calculations to characterize successive antiferromagnetic transitions in GdSi. GdSi has both sizable local moments and a partially nested Fermi surface, without confounding contributions from orbital effects. We identify a route to incommensurate order where neither type of moment dominates, but is rooted in cooperative feedback between them. The nested Fermi surface of the itinerant electrons induces strong interactions between local moments at the nesting vector, whereas the ordered local moments in turn provide the necessary coupling for a spin-density wave to form among the itinerant electrons. This mechanism echoes the cooperative interactions between electrons and ions in charge-density-wave materials, and should be germane across a spectrum of transition-metal and rare-earth intermetallic compounds.

*Proc Natl Acad Sci U S A ; 110(5): 1623-7, 2013 Jan 29.*

##### RESUMO

The competition between proximate electronic phases produces a complex phenomenology in strongly correlated systems. In particular, fluctuations associated with periodic charge or spin modulations, known as density waves, may lead to exotic superconductivity in several correlated materials. However, density waves have been difficult to isolate in the presence of chemical disorder, and the suspected causal link between competing density wave orders and high-temperature superconductivity is not understood. Here we used scanning tunneling microscopy to image a previously unknown unidirectional (stripe) charge-density wave (CDW) smoothly interfacing with the familiar tridirectional (triangular) CDW on the surface of the stoichiometric superconductor NbSe(2). Our low-temperature measurements rule out thermal fluctuations and point to local strain as the tuning parameter for this quantum phase transition. We use this quantum interface to resolve two longstanding debates about the anomalous spectroscopic gap and the role of Fermi surface nesting in the CDW phase of NbSe(2). Our results highlight the importance of local strain in governing phase transitions and competing phenomena, and suggest a promising direction of inquiry for resolving similarly longstanding debates in cuprate superconductors and other strongly correlated materials.

##### Assuntos

Nióbio/química , Transição de Fase , Teoria Quântica , Compostos de Selênio/química , Algoritmos , Cristalização , Condutividade Elétrica , Microscopia de Tunelamento/métodos , Modelos Químicos , Modelos Moleculares , Estrutura Molecular , Temperatura de Transição*Proc Natl Acad Sci U S A ; 109(19): 7224-9, 2012 May 08.*

##### RESUMO

Quantum criticality is a central concept in condensed matter physics, but the direct observation of quantum critical fluctuations has remained elusive. Here we present an X-ray diffraction study of the charge density wave (CDW) in 2H-NbSe(2) at high pressure and low temperature, where we observe a broad regime of order parameter fluctuations that are controlled by proximity to a quantum critical point. X-rays can track the CDW despite the fact that the quantum critical regime is shrouded inside a superconducting phase; and in contrast to transport probes, allow direct measurement of the critical fluctuations of the charge order. Concurrent measurements of the crystal lattice point to a critical transition that is continuous in nature. Our results confirm the long-standing expectations of enhanced quantum fluctuations in low-dimensional systems, and may help to constrain theories of the quantum critical Fermi surface.

##### Assuntos

Nióbio/química , Teoria Quântica , Selênio/química , Difração de Raios X/métodos , Cristalização , Modelos Químicos , Transição de Fase , Pressão , Compostos de Selênio/química , Temperatura de Transição*Phys Rev Lett ; 107(17): 176404, 2011 Oct 21.*

##### RESUMO

We investigate the dispersion of the charge carrier plasmon in the three prototypical charge-density wave bearing transition-metal dichalcogenides 2H-TaSe(2), 2H-TaS(2), and 2H-NbSe(2) employing electron energy-loss spectroscopy. For all three compounds the plasmon dispersion is found to be negative for small momentum transfers. This is in contrast with the generic behavior observed in simple metals as well as the related system 2H-NbS(2), which does not exhibit charge order. We present a semiclassical Ginzburg-Landau model which accounts for these observations, and argue that the vicinity to a charge ordered state is thus reflected in the properties of the collective excitations.

*Phys Rev Lett ; 94(23): 230401, 2005 Jun 17.*

##### RESUMO

We investigate the influence of spontaneous symmetry breaking on the decoherence of a many-particle quantum system. This decoherence process is analyzed in an exactly solvable model system that is known to be representative of symmetry broken macroscopic systems in equilibrium. It is shown that spontaneous symmetry breaking imposes a fundamental limit to the time that a system can stay quantum coherent. This universal time scale is t(spon) approximately = 2piNH/(kBT), given in terms of the number of microscopic degrees of freedom N, temperature T, and the constants of Planck (h) and Boltzmann (kB).