arXiv subjects

David F. Mross

Publications and source records attributed to David F. Mross.

48 records · Page 3Linked to original sources

arXiv2015

Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators

We show that boundaries of 3D weak topological insulators can become gapped by strong interactions while preserving all symmetries, leading to Abelian surface topological order. The anomalous nature of the weak topological insulators manifests itself in a non-trivial action of symmetries on the quasiparticles; most strikingly, translations change the anyon types in a manner impossible in strictly 2D systems with the same symmetry. As a further consequence, screw dislocations form non-Abelian defects that trap $\mathbb{Z}_4$ parafermion zero modes.

cond-mat.str-el↗

arXiv2015

Are non-Fermi-liquids stable to Cooper pairing?

States of matter with a sharp Fermi-surface but no well-defined Landau quasiparticles arise in a number of physical systems. Examples include: ${\it (i)}$ quantum critical points associated with the onset of order in metals; ${\it (ii)}$ spinon Fermi-surface (U(1) spin-liquid) state of a Mott insulator; ${\it (iii)}$ Halperin-Lee-Read composite fermion charge liquid state of a half-filled Landau level. In this work, we use renormalization group techniques to investigate possible instabilities of such non-Fermi-liquids in two spatial dimensions to Cooper pairing. We consider the Ising-nematic quantum critical point as an example of a phase transition in a metal, and demonstrate that the attractive interaction mediated by the order parameter fluctuations always leads to a superconducting instability. Moreover, in the regime where our calculation is controlled, superconductivity preempts the destruction of electronic quasiparticles. On the other hand, the spinon Fermi-surface and the Halperin-Lee-Read states are stable against Cooper pairing for a sufficiently weak attractive short-range interaction; however, once the strength of attraction exceeds a critical value, pairing sets in. We describe the ensuing quantum phase transition between ${\it (i)}$ $U(1)$ and $Z_2$ spin-liquid states; ${\it (ii)}$ Halperin-Lee-Read and Moore-Read states.

cond-mat.str-el↗

arXiv2015

Spin and pair density wave glasses

Spontaneous breaking of translational symmetry---known as `density wave' order---is common in nature. However such states are strongly sensitive to impurities or other forms of frozen disorder leading to fascinating glassy phenomena. We analyze impurity effects on a particularly ubiquitous form of broken translation symmetry in solids: a Spin Density Wave (SDW) with spatially modulated magnetic order. Related phenomena occur in Pair Density Wave (PDW) superconductors where the superconducting order is spatially modulated. For weak disorder, we find that the SDW / PDW order can generically give way to a SDW / PDW glass---new phases of matter with a number of striking properties, which we introduce and characterize here. In particular, they exhibit an interesting combination of conventional (symmetry-breaking) and spin glass (Edwards-Anderson) order. This is reflected in the dynamic response of such a system, which---as expected for a glass---is extremely slow in certain variables, but---surprisingly---is fast in others. Our results apply to all uniaxial metallic SDW systems where the ordering vector is incommensurate with the crystalline lattice. In addition, the possibility of a PDW glass has important consequences for some recent theoretical and experimental work on $La_{2-x}Ba_xCu_2O_4$.

cond-mat.dis-nn↗

arXiv2014

Composite Dirac liquids: parent states for symmetric surface topological order

We introduce exotic gapless states---`composite Dirac liquids'---that can appear at a strongly interacting surface of a three-dimensional electronic topological insulator. Composite Dirac liquids exhibit a gap to all charge excitations but nevertheless feature a single massless Dirac cone built from emergent electrically neutral fermions. These states thus comprise electrical insulators that, interestingly, retain thermal properties similar to those of the non-interacting topological insulator surface. A variety of novel fully gapped phases naturally descend from composite Dirac liquids. Most remarkably, we show that gapping the neutral fermions via Cooper pairing---which crucially does not violate charge conservation---yields symmetric non-Abelian topologically ordered surface phases captured in several recent works. Other (Abelian) topological orders emerge upon alternatively gapping the neutral Dirac cone with magnetism. We establish a hierarchical relationship between these descendant phases and expose an appealing connection to paired states of composite Fermi liquids arising in the half-filled Landau level of two-dimensional electron gases. To controllably access these states we exploit a quasi-1D deformation of the original electronic Dirac cone that enables us to analytically address the fate of the strongly interacting surface. The algorithm we develop applies quite broadly and further allows the construction of symmetric surface topological orders for recently introduced bosonic topological insulators.

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arXiv2012

Stripe melting and quantum criticality in correlated metals

We study theoretically quantum melting transitions of stripe order in a metallic environment, and the associated reconstruction of the electronic Fermi surface. We show that such quantum phase transitions can be continuous in situations where the stripe melting occurs by proliferating pairs of dislocations in the stripe order parameter without proliferating single dislocations. We develop an intuitive picture of such phases as "Stripe Loop Metals" where the fluctuating stripes form closed loops of arbitrary size at long distances. We obtain a controlled critical theory of a few different continuous quantum melting transitions of stripes in metals . At such a (deconfined) critical point the fluctuations of the stripe order parameter are strongly coupled, yet tractable. They also decouple dynamically from the Fermi-surface. We calculate many universal properties of these quantum critical points. In particular we find that the full Fermi-surface and the associated Landau quasiparticles remain sharply defined at the critical point. We discuss the phenomenon of Fermi surface reconstruction across this transition and the effect of quantum critical stripe fluctuations on the superconducting instability. We study possible relevance of our results to several phenomena in the cuprates.

cond-mat.str-el↗

arXiv2012

Theory of a continuous stripe melting transition in a two dimensional metal: Possible application to cuprates

We develop a concrete theory of continuous stripe melting quantum phase transitions in two dimensional metals and the associated Fermi surface reconstruction. Such phase transitions are strongly coupled but yet theoretically tractable in situations where the stripe ordering is destroyed by proliferating doubled dislocations of the charge stripe order. The resulting non-Landau quantum critical point (QCP) has strong stripe fluctuations which we show decouple dynamically from the Fermi surface even though static stripe ordering reconstructs the Fermi surface. We discuss connections to various stripe phenomena in the cuprates. We point out several puzzling aspects of old experimental results (Aeppli et al, Science 1997) on singular stripe fluctuations in the cuprates, and provide a possible explanation within our theory. These results may thus have been the first observation of non-Landau quantum criticality in an experiment.

cond-mat.str-el↗

arXiv2011

Two-Impurity Kondo Model: Spin-Orbit Interactions and Entanglement

Motivated by proposals to employ RKKY-coupled spins as building blocks in a solid-state quantum computer, we analyze how the RKKY interaction in a 2D electron gas is influenced by spin-orbit interactions. Using a two-impurity Kondo model with added Dresselhaus and Rashba spin-orbit interactions we find that spin-rotational invariance of the RKKY interaction - essential for having a well-controllable two-qubit gate - is restored when tuning the Rashba coupling to have the same strength as the Dresselhaus coupling. We also discuss the critical properties of the two-impurity Kondo model in the presence of spin-orbit interactions, and extract the leading correction to the block entanglement scaling due to these interactions.

cond-mat.str-el↗

arXiv2011

Decohering the Fermi liquid: A dual approach to the Mott Transition

We present a theoretical approach to describing the Mott transition of electrons on a two dimensional lattice that begins with the low energy effective theory of the Fermi liquid. The approach to the Mott transition must be characterized by the suppression of density and current fluctuations which correspond to specific shape deformations of the Fermi surface. We explore the nature of the Mott insulator and the corresponding Mott transition when these shape fluctuations of the Fermi surface are suppressed without making any a prior assumptions about other Fermi surface shape fluctuations. Building on insights from the theory of the Mott transition of bosons, we implement this suppression by identifying and condensing vortex degrees of freedom in the phase of the low energy electron operator. We show that the resulting Mott insulator is a quantum spin liquid with a spinon fermi surface coupled to a U(1) gauge field which is usually described within a slave particle formulation. Our approach thus provides a coarse-grained treatment of the Mott transition and the proximate spin liquid that is nevertheless equivalent to the standard slave particle construction. This alternate point of view provides further insight into the novel physics of the Mott transition and the spin liquid state that is potentially useful. We describe a generalization that suppresses spin anti-symmetric fluctuations of the Fermi surface that leads to a spin-gapped charge metal previously also discussed in terms of slave particle constructions.

cond-mat.str-el↗

arXiv2010

Charge Friedel oscillations in a Mott insulator

When a metal undergoes a transition to an insulator it will lose its electronic Fermi surface. Interestingly in some situations a `ghost' Fermi surface of electrically neutral spin carrying fermions may survive into the insulator. Such a novel ghost Fermi surface has been proposed to underlie the properties of a few different materials but its direct detection has proven elusive. In this paper we show that the ghost Fermi surface leads to slowly decaying spatial oscillations of the electron density near impurities or other defects. These and related oscillations stem from the sharpness of the ghost Fermi surface and are direct analogs of the familiar Friedel oscillations in metals. The oscillation period contains geometric information about the shape of the ghost Fermi surface which can be potentially exploited to detect its existence.

cond-mat.str-el↗

arXiv2010

A controlled expansion for certain non-Fermi liquid metals

The destruction of Fermi liquid behavior when a gapless Fermi surface is coupled to a fluctuating gapless boson field is studied theoretically. This problem arises in a number of different contexts in quantum many body physics. Examples include fermions coupled to a fluctuating transverse gauge field pertinent to quantum spin liquid Mott insulators, and quantum critical metals near a Pomeranchuk transition. We develop a new controlled theoretical approach to determining the low energy physics. Our approach relies on combining an expansion in the inverse number (N) of fermion species with a further expansion in the parameter ε= z_b -2 where z_b is the dynamical critical exponent of the boson field. We show how this limit allows a systematic calculation of the universal low energy physics of these problems. The method is illustrated by studying spinon fermi surface spin liquids, and a quantum critical metal at a second order electronic nematic phase transition. We calculate the low energy single particle spectra, and various interesting two particle correlation functions. In some cases deviations from the popular Random Phase Approximation results are found. Some of the same universal singularities are also calculated to leading non-vanishing order using a perturbative renormalization group calculation at small N extending previous results of Nayak and Wilczek. Implications for quantum spin liquids, and for Pomeranchuk transitions are discussed. For quantum critical metals at a nematic transition we show that the tunneling density of states has a power law suppression at low energies.

cond-mat.str-el↗

arXiv2009

The two-impurity Kondo model with spin-orbit interactions

We study the two-impurity Kondo model (TIKM) in two dimensions with spin-orbit coupled conduction electrons. In the first part of the paper we analyze how spin-orbit interactions of Rashba as well as Dresselhaus type influence the Kondo and RKKY interactions in the TIKM, generalizing results obtained by H. Imamura {\em et al.} (2004) and J. Malecki (2007). Using our findings we then explore the effect from spin-orbit interactions on the non-Fermi liquid quantum critical transition between the RKKY-singlet and Kondo-screened RKKY-triplet states. We argue that spin-orbit interactions under certain conditions produce a line of critical points exhibiting the same leading scaling behavior as that of the ordinary TIKM. In the second part of the paper we shift focus and turn to the question of how spin-orbit interactions affect the entanglement between two localized RKKY-coupled spins in the parameter regime where the competition from the direct Kondo interaction can be neglected. Using data for a device with two spinful quantum dots patterned in a gated InAs heterostructure we show that a gate-controlled spin-orbit interaction may drive a maximally entangled state to one with vanishing entanglement, or vice versa (as measured by the concurrence). This has important implications for proposals using RKKY interactions for nonlocal control of qubit entanglement in semiconductor heterostructures.

cond-mat.mes-hall↗

arXiv2008

The Two-Impurity Anderson Model at Quantum Criticality

We propose a realization of the two-impurity Anderson model in a double quantum-dot device. When charge transfer between the dots is suppressed the system exhibits a quantum phase transition, controlled by a surface of non-Fermi liquid fixed points parameterized by the charge valences of the dots. Employing conformal field theory techniques, we identify the scaling exponents that govern transport and thermodynamics close to criticality. We also determine the dynamical exponents that set the time scale for buildup of the non-Fermi liquid state after the system is suddenly shifted into the critical region, e.g. by a change of a nearby gate voltage.

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