Supervisors: Prof. Mohit Randeria, Dr. Amit Agarwal, Prof. Sudhansu S. Mandal, Prof. Jorg Schmalian, Prof. M. Lakshmanan, Dr. Anwesh Mazumdar, and Prof. Piers Coleman
We show how Oshikawa's theorem for the Fermi surface volume of the Kondo lattice can be extended ... more We show how Oshikawa's theorem for the Fermi surface volume of the Kondo lattice can be extended to the SU(N) symmetric case. By extending the theorem, we can show that the mechanism of Fermi surface expansion seen in the large N mean-field theory is directly linked to the expansion of the Fermi surface in a spin-1 2 Kondo lattice. This linkage enables us to interpret the expansion of the Fermi surface in a Kondo lattice as a fractionalization of the local moments into heavy electrons. Our method allows extension to a pure U(1) spin liquid, where we find the volume of the spinon Fermi surface by applying a spin twist, analogous to Oshikawa's, [Phys. Rev. Lett. 84, 3370 (2000)] flux insertion. Lastly, we discuss the possibility of interpreting the FL * phase characterized by a small Fermi surface in the absence of symmetry breaking, as a nontopological coexistence of such a U(1) spin liquid and an electronic Fermi liquid.
Proceedings of the National Academy of Sciences, 2021
We present exact results that give insight into how interactions lead to transport and supercondu... more We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D) Tc. We focus on on-site attraction |U| on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight D̃low≤ñ|U|Ω/2 with ñ=minn,2−n , where n is the flat-band density and Ω is the Marzari–Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for D̃low linear in |U|. We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results.
FeSe 0.45 Te 0.55 (FeSeTe) has recently emerged as a promising candidate to host topological supe... more FeSe 0.45 Te 0.55 (FeSeTe) has recently emerged as a promising candidate to host topological superconductivity, with a Dirac surface state and signatures of Majorana bound states in vortex cores. However, correlations strongly renormalize the bands compared to electronic structure calculations, and there is no evidence for the expected bulk band inversion. We present here a comprehensive angle resolved photoemission (ARPES) study of FeSeTe as a function of photon energies ranging from 15-100 eV. We find that although the top of the bulk valence band shows essentially no k z dispersion, its normalized intensity exhibits a periodic variation with k z. We show, using ARPES selection rules, that the intensity oscillation is a signature of band inversion indicating a change in the parity going from to Z. We also present a simple realistic tight-binding model which gives insight into ARPES observations. Thus we provide direct evidence for a topologically nontrivial bulk band structure that supports protected surface states.
An important open puzzle in the superconductivity of UTe2 is the emergence of time-reversal broke... more An important open puzzle in the superconductivity of UTe2 is the emergence of time-reversal broken superconductivity from a non-magnetic normal state. Breaking time-reversal symmetry in a single second-order superconducting transition requires the existence of two degenerate superconducting order parameters, which is not natural for orthorhombic UTe2. Moreover, experiments under pressure suggest that this superconductivity sets in at a single transition temperature in a finite parameter window, in contrast to splitting between the symmetry breaking temperatures expected for accidental degenerate orders. Here we demonstrate that the thermodynamic phase diagram of a triplet superconductor near a magnetic quantum phase transition can contain an extended region, where time-reversal breaking superconductivity onsets in a single, weakly first order transition. It arises due to coupling between incipient magnetic order and magnetic moments of triplet pairs, which favors a time-reversal broken superconducting state. A microscopic origin of this coupling is identified as screening of magnetic moments by chiral Cooper pairs, built out of two non-degenerate pairs-an extension of Kondo screening to unconventional pairs. We discuss the experimental signatures of such a weakly first order transition and the resulting phase diagram. Also, we demonstrate the possibility of a finite-momentum pairing due to coupling of superconductivity and antiferromagnetism, and discuss possible relations to the pair-and charge-density waves, recently observed in UTe2.
In a minimal 2-band model with attractive interactions between fermions, we calculate the gap to ... more In a minimal 2-band model with attractive interactions between fermions, we calculate the gap to single and two-particle excitations, the band-dependent spectral functions, the superfluid density and compressibility using quantum Monte Carlo (QMC) methods. We find Fermi and Bose insulating phases with signatures of incipient pairing evident in the single-particle spectral functions, and a superconducting state with three different spectral functions: (i) both bands show "BCS" behavior in which the minimum gap locus occurs on a closed contour on the underlying Fermi surface; (ii) both bands show "BEC" behavior in which the minimum gap occurs at a point; and (iii) band selective spectral characteristics, in which one band shows "BCS" while the other shows "BEC" behavior. At large interactions, we find a Mott phase of rung bosons in which the filling is one boson for every two sites, half the typical density constraint for Mott insulators.
Understanding the material parameters that control the superconducting transition temperature T c... more Understanding the material parameters that control the superconducting transition temperature T c is a problem of fundamental importance. In many novel superconductors phase fluctuations determine T c , rather than the collapse of the pairing amplitude. We derive rigorous upper bounds on the superfluid phase stiffness for multiband systems, valid in any dimension. This in turn leads to an upper bound on T c in two dimensions, which holds irrespective of pairing mechanism, interaction strength, or order-parameter symmetry. Our bound is particularly useful for the strongly correlated regime of low-density and narrowband systems, where mean-field theory fails. For a simple parabolic band in 2D with Fermi energy E F , we find that k B T c ≤ E F =8, an exact result that has direct implications for the 2D BCS-BEC crossover in ultracold Fermi gases. Applying our multiband bound to magic-angle twisted bilayer graphene, we find that band structure results constrain the maximum T c to be close to the experimentally observed value. Finally, we discuss the question of deriving rigorous upper bounds on T c in 3D.
Observing that several U and Ce based candidate triplet superconductors share a common structural... more Observing that several U and Ce based candidate triplet superconductors share a common structural motif, with pairs of magnetic atoms separated by an inversion center, we hypothesize a triplet pairing mechanism based on an interplay of Hund's and Kondo interactions that is unique to this structure. In the presence of Hund's interactions, valence fluctuations generate a triplet superexchange between electrons and local moments. The offset from the center of symmetry allows spintriplet pairs formed by the resulting Kondo effect to delocalize onto the Fermi surface, precipitating superconductivity. We demonstrate this mechanism within a minimal two-channel Kondo lattice model and present support for this pairing mechanism from existing experiments.
FeSe 0.45 Te 0.55 (FeSeTe) has recently emerged as a promising candidate to host topological supe... more FeSe 0.45 Te 0.55 (FeSeTe) has recently emerged as a promising candidate to host topological superconductivity, with a Dirac surface state and signatures of Majorana bound states in vortex cores. However, correlations strongly renormalize the bands compared to electronic structure calculations, and there is no evidence for the expected bulk band inversion. We present here a comprehensive angle resolved photoemission (ARPES) study of FeSeTe as function of photon energies ranging from 15-100 eV. We find that although the top of bulk valence band shows essentially no k z dispersion, its normalized intensity exhibits a periodic variation with k z. We show, using ARPES selection rules, that the intensity oscillation is a signature of band inversion indicating a change in the parity going from Γ to Z. Thus we provide the first direct evidence for a topologically non-trivial bulk band structure that supports protected surface states. PACS numbers: 74.25.Jb, 74.70.Dd, 71.20.Be Iron-based superconductors (FeSCs) have been intensely investigated since their discovery in 2008 [1] as strongly correlated materials that harbor high temperature superconduc-tivity. Recently, interest in this field has increased greatly due to new experiments that suggest that some of these systems may be topological superconductors [2] that harbor Majorana bound states (MBS) in their vortex cores, which could be potentially important for quantum information processing [3]. Wang et al. [9] first suggested that FeSe 0.5 Te 0.5 (FeSeTe) can host topologically protected Dirac surface states, which were recently observed directly using angle resolved photoe-mission spectroscopy (ARPES) [10]. Soon after, such states were found in other FeSCs [11] and in thin films [7]. In addition , clear zero bias conductance peaks (ZBCP) were observed [8, 9] in the superconducting vortex cores in FeSeTe using scanning tunneling spectroscopy (STS), and identified as the MBS expected in topological superconductors. In fact, the strong correlations in these materials, which leads to surprisingly large ∆/E F ratios [10, 11], helps in separating the ZBCP from (topologically) trivial vortex core bound states. Despite these exciting developments, direct evidence for the topological nature of the bulk band structure-responsible for the topologically protected surface states and MBS-is lacking. Density functional theory (DFT) calculations [9] for FeSeTe find a p z band that is highly dispersive along k z , which mixes with an appropriate linear combination of the d xz,yz bands. As a result, the orbital character and the parity of the band changes as one goes from Γ(0,0,0) to Z(0,0,π/c). However, no such highly dispersive band is observed in the data, as we shall show below, and-at first sight-there seems to be no evidence for the band inversion expected in a topo-logically nontrivial bulk band structure. FeSeTe is known to be the most strongly correlated member of the FeSC family [12, 13], making it difficult to directly compare ARPES measurements with DFT. It offers an exciting opportunity to study the interplay between the topological nature of the band structure and the effect of the strong electronic correlations. In this letter, we present a systematic ARPES study of FeSeTe for a broad range of incident photon energies (15 to 100 eV) to investigate the k z-dispersion of the bulk electronic structure. Using symmetry analysis and dipole selection rules, we present clear evidence for the change in the parity eigenvalue going from Γ to Z, in spite of the absence of any highly dispersive band. We also present a tight-binding model, with reasonable values of renormalization parameters relative to DFT and of spin-orbit coupling, which gives insight into ARPES observations. We thus provide compelling evidence for bulk "band inversion", the hallmark of a topo-logical band structure via the Fu-Kane invariant [14], which leads to a protected Dirac surface state in the energy gap near the Γ point. We used high quality Fe 1.02 Se 0.45 Te 0.55 single crystals for ARPES measurements. Fig. 1(a,b) shows the geometry of our ARPES experiments. We will focus on near-normal emission with (k x , k y) near (0, 0), and light incident in the YZ plane in either LV (linear vertical) or LH (linear horizontal) po-larizations, as shown. This geometry will be crucial in the analysis of the selection rules later in the paper. Our laboratory axes (X,Y, Z) conform with the literature [10, 11], however , we label orbitals with reference to the crystallographic axes (x, y, z), irrespective of sample rotations, consistent with Refs. [5, 6, 15]. We show ARPES data along the Γ-M direction using 22 eV LV photons in Fig. 1 (c), and its second derivative [18] sharpened image in panel (d). This allows us to see in addition to a dispersive bulk band, which we label as α 1 , an intense state at a binding energy (BE) of around 10 meV, that lies between the top of the α 1 band (BE 18 meV) and the chemical potential (BE = 0 meV). This state is similar to the linearly dispersive Dirac surface state (SS), recently been reported by Zhang et. al. [10]. In Fig. 1 (e) we show LH polarization data where in addition to the states seen in LV data of panel (c), we also see another dispersive α 2 band. The ARPES intensity allows a direct mapping of the electronic dispersion for momenta parallel to the sample surface.
Understanding the material parameters that control the superconducting transition temperature T c... more Understanding the material parameters that control the superconducting transition temperature T c is a problem of fundamental importance. In many novel superconductors phase fluctuations determine T c , rather than the collapse of the pairing amplitude. We derive rigorous upper bounds on the superfluid phase stiffness for multiband systems, valid in any dimension. This in turn leads to an upper bound on T c in two dimensions, which holds irrespective of pairing mechanism, interaction strength, or order-parameter symmetry. Our bound is particularly useful for the strongly correlated regime of low-density and narrow-band systems, where mean-field theory fails. For a simple parabolic band in 2D with Fermi energy E F , we find that k B T c ≤ E F =8, an exact result that has direct implications for the 2D BCS-BEC crossover in ultracold Fermi gases. Applying our multiband bound to magic-angle twisted bilayer graphene, we find that band structure results constrain the maximum T c to be close to the experimentally observed value. Finally, we discuss the question of deriving rigorous upper bounds on T c in 3D.
We predict two topological superconducting phases in microscopic models arising from the Berry ph... more We predict two topological superconducting phases in microscopic models arising from the Berry phase associated with the valley degree of freedom in gapped Dirac honeycomb systems. The first one is a topological helical spin-triplet superconductor with a nonzero center-of-mass momentum that does not break time-reversal symmetry. We also find a topological chiral-triplet superconductor with Chern number ±1 with equal-spin pairing in one valley and opposite-spin-triplet pairing in the other valley. Our results are obtained for the Kane-Mele model in which we have explored the effect of three different interactions, onsite attraction U , nearest-neighbor density-density attraction V , and nearest-neighbor antiferromagnetic exchange J, within self-consistent Bogoliubov-de Gennes theory. Transition metal dichalcogenides and cold atom experiments are promising platforms to explore these phases.
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Papers by Tamaghna Hazra