Brief Statement of Research Interests
Sumanta Tewari
My research interests span a wide range of topics in theoretical condensed matter physics, including
topological superconductors (TS), topological insulators (TI), topological quantum computation (TQC),
cuprate high temperature superconductivity, and the physics of ultra-cold atoms. My work on Majorana
fermions (MFs) in topological superconducting states in spin-orbit coupled semiconductorsuperconductor heterostructures, which I began in the summer of 2009 on a short visit to the University of
Maryland, College Park, has recently led to experimental success claimed by at least six different
experimental groups worldwide (TU-Delft, Netherlands; Lund, Sweden; Purdue, USA; Weizmann, Israel;
Harvard, USA, UIUC, USA). Earlier, my proposal to realize half quantum vortices (HQVs) in p-wave
superconductors (HQV’s in such systems are supposed to carry MFs), on subsequent development by
others, led to experimental claims of its realization in strontium ruthenate.
My future research will focus on topological states in a variety of condensed matter systems including
spin-orbit coupled semiconductors (e.g. InAs, InSb), carbon nanotubes (CNTs), organic superconductors
(specifically, Bechgaard salts, (TMTSF)2 X, X=PF6 , ClO4), Lithium Molybdenum Purple Bronze
(Li0.9 Mo6 O17 ), Transition metal dichalcogenides (TMDs, e.g. MoS2 ), and cold fermion systems in optical
lattices. I will investigate possible realization and properties of TS states in class D (with invariant 𝑍2 ),
class DIII (time reversal invariant (TRI) systems, with invariant 𝑍2 ) and class BDI (chiral systems with
invariant 𝑍). The organic superconductors and Lithium Purple Bronze are good candidates for realizing
the time reversal invariant Kitaev model (with quasi-one-dimensional, equal-spin-pairing (ESP), p-wave
order parameters) which will be investigated. The edge states in TMDs are good candidates for realizing
both class D and class DIII topological superconductivity via superconducting proximity effect.
Broadly speaking, I shall focus on the superconducting states which are gapped in the bulk, break or
respect the time reversal (TR) invariance, are characterized by a Z2 or integer (Z) winding number or
Chern (TKNN) invariant, and have edge states with particular handedness or chirality (because of which
these states are called chiral). Within this class, I will be most concerned with those states which are
further classified by a Z2 topological invariant, which is given by the sign of the Pfaffian of the relevant
BCS Hamiltonian at 𝑘 = 0.The superconducting states with the value of the above Pfaffian invariant
+1 (−1) admit (do not admit) gapless, non-degenerate, anyonic Majorana modes at vortices and sample
edges which make them non-Abelian (Abelian) quantum matter. In line with my continuing research, I
shall take a broad perspective on the candidate 𝑍2 quantum systems (class D, protected only by the
particle-hole or charge-conjugation symmetry), asking questions such as, i) under what conditions such
states are experimentally realizable, and ii) how the Majorana fermions, quantum particles which can be
identified with their own anti-particles and are constituents of a true new state of matter, can be
experimentally observed. The appealing prospect of fault-tolerant quantum computation using such
systems is but one motivation of this research.
In the realm of TRI superconductivity (class DIII) my goals are, (1) to establish a relationship between
TRI superconductivity and the associated 𝑍2 invariant and chiral superconductivity (class BDI) and the
corresponding 𝑍 invariant, as is apparent in my recent work, (2) to study model and realistic TRI
topological superconducting systems, specifically in the quasi-one-dimensional limit, (3) explore the edge
states of the exciting new material transition metal dichalcogenides, the organic superconductors, and
Lithium Purple Bronze, as robust platforms for TRI superconductivity, and (4) benchmark reliable
methods to detect the Majorana-Kramers pairs in TRI topolgical systems in experiments.
In the context of both class D and DIII systems I will study the relevance of lattice point group
symmetries (e.g., reflection, crystal rotation, mirror) to the protection of MFs (the so-called “symmetryprotected topological states”), particularly, in the presence of disorder which breaks any such spatial
symmetry and yet the MFs remain un-split. This curious result, that multiple MFs persist even when their
wave-functions overlap, despite the absence of any spatial or non-spatial symmetry protecting them, was
revealed in our recent (soon-to-be-published) work. This problem will be approached in detail using the
symmetry of the numerically solved BdG wave-functions (understanding why the wave-function overlaps
are zero), and symmetry/group theory (specifically, looking for an as-yet unidentified hidden symmetry
responsible for the protection of the MFs).
My research interests also include possible realization of Weyl semi-metal and Weyl superconductor
phases in non-centrosymmetric systems with spin-orbit interaction. In principle, the Weyl phase allows a
chiral magnetic effect (electric current in response to a parallel magnetic field in the absence of an electric
field!) which may have interesting technological applications. Moreover the non-trivial Berry curvatures
near Weyl points can give rise to gyrotropic conductivity (which has its origin in the breakdown of space
inversion symmetry in the non-centrosymmetric systems) whose real and imaginary parts can give rise to
Faraday and Kerr rotations in polarization of reflected and transmitted light. These effects will be
investigated in the framework of an axionic field theory for Weyl fermions (which I recently developed
with co-author Goswami) in the continuum limit and by numerical calculations on lattices.
In the realm of high temperature cuprate superconductivity my primary interests lie in the exploration of
the pseudo-gap phase in the framework of a broken symmetry state such as the staggered flux state (or ddensity wave, DDW) and the nematic state. In my Ph. D work and thereafter I extensively worked on the
various properties of the DDW state in relation to the cuprates which will be extended. The exciting new
experimental results such as a change in Fermi surface topology (the so-called Fermi surface
reconstrution) and existence of electron pockets in the underdoped regime as revealed in quantum
oscillation experiments, and also the recently discovered finite Faraday rotation and polar Kerr effect
experiments will be investigated within the framework of the nematic state and also the recently
discovered checkerboard charge density wave (CDW) state in the underdoped cuprates. Note that, from
the experiments on polar Kerr effect (PKE) in the cuprates, it is clear that the PKE in these systems is due
to finite gyrotropic conductivity resulting from broken space and mirror symmetries, rather than from
broken time reversal symmetry which also should realize a non-zero anomalous Hall effect that is not
observed. The possible realization of finite gyrotropic effect in the cuprates will be investigated in the
context of the nematic state and other candidate states appropriate for the pseudogap regime.
Recent experimental breakthrough at NIST realizing spin-orbit coupling and Zeeman field for ultra-cold
atoms has opened exciting new possibilities for the observation of novel topological phases in cold atomic
systems. In the short term I will develop concrete schemes for realizing TS states (in all three classes, D,
DIII, and BDI) and the associated topological phase transitions using experimental techniques which have
already been realized. These include the recent realization of spin-orbit coupling in 1D systems reported
by the Spieleman group at NIST and the photoemission spectroscopy developed in the Jin group at JILA
which can be used for identification of the topological states through the excitations. With the important
experimental techniques already in place, the realization of topological physics in cold atomic systems
seems tantalizingly close to experimental reach and will be another focus of my research interests in the
future.